Methods for Measuring Cancer Disparities:Using Data Relevant to Healthy People 2010

Cancer-Related Objectives

Sam HarperJohn Lynch

Center for Social Epidemiology and Population HealthUniversity of Michigan

Current contact information:Department of Epidemiology, Biostatistics and Occupational HealthMcGill University, Purvis HallMontreal QC H3A 1A2Email: sam.harper@mcgill.ca / john.lynch@mcgill.caPhone: (514) 398–6261Fax: (514) 398–4266

This report was written under contract from the Surveillance Research Program (SRP) and the AppliedResearch Program (ARP) of the Division of Cancer Control and Population Sciences of the NationalCancer Institute, NIH. Additional support was provided by the Office of Disease Prevention in the Officeof the Director at the National Institutes of Health. It represents the interests of these organizations inhealth disparities related to cancer, quantitative assessment and monitoring of these disparities, andinterventions to remove them. NCI Project Officers for this contract are Marsha E. Reichman, Ph.D. (SRP),Bryce Reeve, Ph.D. (ARP), and Nancy Breen, Ph.D. (ARP).

Table of Contents

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EExxeeccuuttiivvee SSuummmmaarryy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

IInnttrroodduuccttiioonn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Initiatives to Eliminate Health Disparities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Brief History of Measuring Disparities in the United States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Health Inequality and Health Inequity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

DDeeffiinniinngg HHeeaalltthh DDiissppaarriittiieess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

IIssssuueess iinn EEvvaalluuaattiinngg MMeeaassuurreess ooff HHeeaalltthh DDiissppaarriittyy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Total Disparity vs. Social-Group Disparity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Relative and Absolute Disparities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Reference Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Social Groups and “Natural” Ordering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

The Number of Social Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Population Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Socioeconomic Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Monitoring Over Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Transfers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Subgroup Consistency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Decomposability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Scale Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Transparency/Interpretability for Policy Makers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

iv

MMeeaassuurreess ooff HHeeaalltthh DDiissppaarriittyy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Measures of Total Disparity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Measures of Social-Group Disparity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Measures of Average Disproportionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

CChhoooossiinngg aa SSuuiittee ooff HHeeaalltthh DDiissppaarriittyy IInnddiiccaattoorrss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Summary Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

AAppppeennddiixx:: EExxaammppllee AAnnaallyysseess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

RReeffeerreenncceess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

FFiigguurreess

Figure S1. Absolute and Relative Gender Disparity in Stomach Cancer Mortality, 1930–2000 . . . . . . . . . . 1

Figure S2. Proportion of Women Age 40 and Over Who Did Not Receive a Mammogram in thePast 2 Years by Level of Educational Achievement, 1990–2002, Trends in Absolute andRelative Disparity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Figure 1. Lung Cancer Mortality, Females, U.S., 1995–1999 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Figure 2. Lung Cancer Incidence by Gender and Race/Ethnicity, 1992–1999 . . . . . . . . . . . . . . . . . . . . . . . . 8

Figure 3. Mean and 10th–90th Percentiles of Body Mass Index by Education, NHIS, 1997 . . . . . . . . . . . . 20

Figure 4. Hypothetical Distributions of Life Expectancy in Two Populations . . . . . . . . . . . . . . . . . . . . . . . 21

Figure 5. Absolute and Relative Gender Disparity in Stomach Cancer Mortality, 1930–2000 . . . . . . . . . . 22

Figure 6. Relative Risk (RR) of Incident Cervical Cancer Among Hispanics According to VaryingReference Groups, 1996–2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Figure 7. Age-Adjusted Incidence of Kidney/Renal Pelvis Cancer and Myeloma by Race and Ethnicity,1996–2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Figure 8. Proportion of Men Reporting Recent Use of Screening Fecal Occult Blood Tests (FOBT),by Race and Ethnicity, 1987–1998 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Figure 9. Percent Change in Population Size by Race and Hispanic Origin, 1980–2000 . . . . . . . . . . . . . . 28

Figure 10. Absolute and Relative Black-White Disparities in Prostate and Stomach Cancer Incidence,1992–1999 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Figure 11. Example of a Simple Regression-Based Disparity Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Figure 12. Income-Based Slope Index of Inequality for Current Smoking, NHIS, 2002 . . . . . . . . . . . . . . . 40

Figure 13. Example of the Population-Attributable Risk Percent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Figure 14. Disparity in Mammography Screening Among Racial/Ethnic Groups, NHIS, 2000 . . . . . . . . . 45

Figure 15. Age-Adjusted Lung Cancer Mortality by U.S. Census Division, 1968–1998 . . . . . . . . . . . . . . . . 46

Figure 16. Example of the “Disproportionality” of Deaths and Population, by Gender and Education,2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Figure 17. Representation of the Gini Coefficient of Disparity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Figure 18. Representation of the Health Concentration Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Figure 19. Relative Concentration Curves for Educational Disparity in Obesity in New York State,BRFSS, 1990 and 2002 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Figure 20. Absolute Concentration Curves for Educational Disparity in Obesity in New York State,BRFSS, 1990 and 2002 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Figure A1. Proportion of Women Age 40 and Over Who Did Not Receive a Mammogram in thePast 2 Years by Educational Attainment, 1990–2002 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Figure A2. Trends in Education-Related Disparity and Prevalence for the Proportion of WomenAge 40 and Over Who Did Not Receive a Mammogram in the Past 2 Years, 1990–2002 . . . . . . . . . . . . . . 69

Figure A3. Trends in Mortality from Colorectal Cancer by Race, Ages 45–64, 1990–2001 . . . . . . . . . . . . . 71

Figure A4. Racial Disparity Trends in Working-Age (45–64) Mortality from Colorectal Cancerby Race, 1990–2001 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

TTaabblleess

Table 1. Incidence of Esophageal Cancer, Ages 25–64 by Race, 12 SEER Registries, 1992–2000 . . . . . . . . . 44

Table 2. Commonly Used Disproportionality Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Table 3. Educational Disparity in Lung Cancer Mortality, 1999 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Table 4. Example of Extended Relative and Absolute Concentration Index Applied to the Changein Educational Disparity in Current Smoking, Michigan, 1990 and 2002 . . . . . . . . . . . . . . . . . . . . . . . . . 56

Table 5. Summary Table of Advantages and Disadvantages of Potential Health Disparity Measures . . . . . 64

Table A1. Example of Relative and Absolute Concentration Index Applied to the Change inEducational Disparity in Mammography, 1990 and 2002 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

Table A2. Example of Theil Index and the Between-Group Variance Applied to the Change in RacialDisparity in Colorectal Cancer Mortality, 1990 and 2001 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

v

Executive Summary

1

Healthy People 2010 has two overarching goals: toincrease the span of healthy life and to eliminatehealth disparities across the categories of gender,race or ethnicity, education or income, disability,geographic location, and sexual orientation (1).This report raises some conceptual issues andreviews different methodological approachesgermane to measuring progress toward the goal ofeliminating cancer-related health disparities (2).Despite the increased attention to socialdisparities in health, no clear framework exists todefine and measure health disparities. This maycreate confusion in communicating the extent ofcancer-related health disparities and hinder theability of public health organizations to monitorprogress toward the Healthy People 2010 cancerobjectives. The recommendations in this reportare based on the following considerations:

• Choosing a particular measure of healthdisparity reflects, implicitly or explicitly, differentperspectives about what quantities orcharacteristics of health disparity are thought tobe important to capture. For instance, mostresearch in health disparities is based on relativecomparisons (e.g., a ratio of rates), but it is equallyappropriate to make absolute comparisons (e.g.,the arithmetic difference between rates). Figure S1shows male/female disparities in stomach cancermortality during the 20th century. If we use anabsolute comparison (arithmetic difference inrates), disparities have declined since about 1950;if we use a relative comparison (ratio of rates),they have increased almost continuously. This isan example of how the same underlying datapotentially could generate two divergentinterpretations of trends in cancer-related health

Figure S1. Absolute and Relative Gender Disparity in Stomach Cancer Mortality, 1930–2000

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Figure S1. Absolute and Relative Gender Disparity in Stomach Cancer Mortality, 1930-2000

outcomes—dependent on which measure ofdisparity is used.

• In this report, we adopt a “population health”perspective on health disparities. A populationhealth perspective reflects a primary concern forthe total population health burden of disparitiesby considering the number of cases of the cancer-related health outcome (e.g., mortality, incidence,screening, etc.) that would be reduced oreliminated by an intervention. This perspectiveemphasizes absolute differences between groupsand the size of the population subgroupsinvolved. We believe that such an approach offersa justifiable basis on which to assess the totalpopulation burden of disparity and thus providesuseful epidemiological input into decision makingabout policy to reduce cancer-related healthdisparities. This in no way precludes that theremay be other valid inputs into the policy-makingprocess that are based on different perspectives,such as a purely relative assessment of cancer-related health disparities.

• To better monitor the population healthburden of disparities over time, disparityindicators should be sensitive to two sources ofchange: change in the size of the populationsubgroups involved and change in the level ofhealth within each subgroup. For instance, socialpolicy can change both the number of peoplewho are poor and the behavior and health statusof the poor.

Recommendations

We recommend using a sequence of steps,described below, to assess health disparity. The

first step is to inform any assessment of healthdisparity with a simple tabular and graphicalexamination of the underlying “raw” data (rate,proportion, etc., and subgroup population size).This may provide valuable insights into the basicquestion of whether the particular disparity hasincreased or decreased over time. The graphicalpresentation of the underlying data is depicted inFigure S2 (page 3), which shows educationaldisparity trends in the proportion of women nothaving had a mammogram for the past 2 years.

If, as for Healthy People 2010, the goal is toquantitatively monitor progress toward theelimination of health disparities across all socialgroups, then summary measures of healthdisparity are warranted. Figure S2 also containstwo summary measures of health disparity—anabsolute measure, the Absolute ConcentrationIndex (ACI), and a relative measure, the RelativeConcentration Index (RCI). The choice of specificsummary measures also will be guided by whetherthe groups have an inherent ranking (such aseducation) or are unordered (such as gender).

Choosing measures of health disparityinvolves consideration of conceptual, ethical, andmethodological issues. This report discusses someof these issues and provides recommendations fora suite of measures that can be used to monitorhealth disparities in cancer-related healthoutcomes.

Our recommendations for measuringdisparity are:

1. To visually inspect tables and graphs of theunderlying “raw” data.

2

2. When the question involves only comparisonsof specific groups, then pairwise absolute andrelative comparisons may be sufficient. When theobjective is to provide a summary across allgroups, then the use of summary measures ofhealth disparity is warranted.

3. If the social group has a natural ordering, aswith education and income, then we recommendusing either the Slope Index of Inequality (SII) orthe Absolute Concentration Index (ACI) as ameasure of absolute health disparity, and either

the Relative Index of Inequality (RII) or theRelative Concentration Index (RCI) as a measureof relative disparity.

4. When comparisons across multiple groups thathave no natural ordering (e.g., race/ethnicity) areneeded, we recommend the Between-GroupVariance (BGV) as a summary of absolutedisparity, and the general entropy class ofmeasures, more specifically the Theil index andthe Mean Log Deviation, as measures of relativedisparity.

3

Figure S2. Proportion of Women Age 40 and Over Who Did Not Receive a Mammogram in the Past2 Years by Level of Educational Achievement, 1990–2002, Trends in Absolute and Relative Disparity

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001* 2002

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Figure S2. Proportion of Women Age 40 and Over Who Did Not Receive a Mammogram in the Past 2 Years by Level of Educational Achievement, 1990-2002, Trends in Relative Disparity

Source: CDC, Behavioral Risk Factor Surveillance Surveys 1990–2002. *Note: Question not asked in 2001.

Source: CDC, Behavioral Risk Factor Surveillance Surveys 1990–2002.*Note: Question not asked in 2001.

5

Introduction

The goals of this report are to:

1. Highlight major issues that may affect thechoice of disparity measure.

2. Systematically review measures of healthdisparity.

3. Provide a basis for selecting a “suite ofindicators” to measure disparities in screening,risk factors, and other cancer-related healthobjectives.

Initiatives to Eliminate HealthDisparities

In 1979, U.S. Surgeon General Julius B. Richmondfirst conceptualized the idea for national publichealth goals (3) and established specific publichealth objectives for reducing mortality andchronic illness in five age groups, which later wereto be implemented in 15 strategic areas during the1980s (4). Building on this foundation, HealthyPeople 2000 subsequently replaced the age-specificgoals of 1990 with three overarching goals for theyear 2000: increase the span of healthy life,reduce health disparities, and provide access topreventive health services (5). The explicit focuson reducing health disparities in Healthy People2000 represented an important step towardestablishing health disparities as a part of routinepublic health surveillance. Establishing differenthealth targets for different social groups, however,

could be construed as implying that a group’shealth potential was somehow constrained by itssocial-group membership, a factor over whichgroup members may have little or no control. Forexample, the year 2000 target rate (per 100,000)for cancer mortality was 130 for the totalpopulation, but it was 175 for blacks.

The implication of setting different targetsfor different social groups was not lost on publichealth policy makers or politicians. In a 1998radio address that celebrated Black HistoryMonth, President Clinton put forth a somewhatmore radical national public health goal: “By theyear 2010, we must eliminate racial and ethnicdisparities in infant mortality, diabetes, cancerscreening and management, heart disease, AIDS,and immunization.” Racial and ethnic disparitiesin these and other areas are extensive and welldocumented, and given the context of theirorigins in the United States, there is ample reasonto focus attention on their elimination. Similarhealth disparities, however, are evident not justbetween racial/ethnic groups but also betweenother social and demographic groups, a fact thatnow is reflected in the goals of Healthy People2010 that specify eliminating health disparities bygender, income and education, disability,geographic location, and sexual orientation inaddition to race and ethnicity (1). Similar healthdisparity targets also have been adopted by anumber of state and local health agencies (see6,7,8). The Healthy People 2010 policy goals thus

represent an important shift toward “elimina-tion,” and not just “reduction,” of existing healthdisparities.

The goal of eliminating health disparities alsoimplies that a systematic scientific frameworkexists to measure health disparities and tomonitor them over time across multiple socialgroups and measures of health status. We arguethat no such clear-cut consensus frameworkcurrently exists in the United States, within eitherthe research or the policy communities as to howhealth disparity should be measured. Animportant first step toward the elimination ofhealth disparities is to carefully consider theconceptualization of health disparity to betterunderstand what we mean by the term “healthdisparity,” how we operationalize the concept of“eliminating health disparity,” and how then toapply appropriate health disparity monitoringstrategies.

Cancer-Related Goals of Healthy People 2010

The specific issues that motivate this project arerelated to the Healthy People 2010 framework forcancer-related goals, of which the overarchinggoal is to “reduce the number of new cancercases as well as the illness, disability, and deathcaused by cancer” (9, page 3-3). The objectivesfor specific cancers are to reduce the rates ofmelanoma, lung, breast, cervical, colorectal,oropharyngeal, and prostate cancers, and, inkeeping with the goals of Healthy People 2010,disparities in the above cancers and their majorrisk factors also should be eliminated. Thus, thisreport focuses on social-group and geographicaldisparity in cancer-related outcomes such as risk

behaviors, screening, incidence, survival, andmortality.

Figure 1 (page 7) is typical of the sort ofcancer-related data that motivate this project.These data show socioeconomic and racial/ethnicdisparities in lung cancer mortality among U.S.females for 1995–1999. Although these data helpto characterize disparity, they do not explicitlyquantify the extent or variability in disparity.Several questions may be asked about this data.For instance, is the socioeconomic disparity inlung cancer mortality larger among Asian/PacificIslanders or blacks? Or is the racial/ethnicdisparity between non-Hispanic whites and blackslarger than the socioeconomic differences withineach group? Additionally, variation exists in thedirection of the socioeconomic disparity indifferent racial/ethnic groups. Among Hispanics,the age-adjusted death rate increases as areapoverty decreases; among American Indian/AlaskaNatives, however, rates increase as area povertyincreases. Casual visual inspection of such graphsreveals that there are differences between andamong groups. The challenge is whether we canmove beyond the simple recognition of suchdifferences (disparities) toward a strategy toquantify their magnitude in a scientificallyreliable and transparent way that can beunderstood by all stakeholders. This will be evenmore important when monitoring changes indisparity over time.

Figure 2 (page 8) shows the annual rate oflung cancer incidence by race and gender for theperiod 1992–1999. How should we summarize thedisparity in trends in lung cancer incidence? Wemight focus on comparing pairs of rates over

6

7

Figure 1. Lung Cancer Mortality, Females, U.S., 1995–1999A

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Percent of County Population Below Poverty Level in 1990<10% 10% to 19.9% 20% or higher

Figure 1. Lung Cancer Mortality, Females, U.S., 1995-1999

Source: Gopal Singh et al. Area Socioeconomic Variations in U.S. Cancer Incidence, Mortality, Stage, Treatment, and Survival, 1975–1999, 2003.Source: Gopal Singh et al. Area Socioeconomic Variations in U.S. Cancer Incidence, Mortality, Stage, Treatment, and Survival, 1975–1999, 2003.

time—e.g., the gap between white andAsian/Pacific Islander females or between blackmales and black females. As the number of groupsand years of data increase, however, there arediminishing returns to such a strategy because ofthe large number of possible pairwise comparisonsand the inherent difficulty in summarizing them.For example, from Figure 2 in 1992, one couldcalculate the following incidence ratios: black towhite males, 1.55; Asian/Pacific Islander toAmerican Indian/Alaska Native males, 2.11; blackto white females, 1.03; and Asian/Pacific Islanderto American Indian/Alaska Native females, 1.71.The same comparisons in 1999 provide respective

ratios of 1.48, 2.29, 1.12, and 3.33. What can weconclude about the racial disparity in lung cancerincidence, given that incidence ratios aredecreasing for some comparisons (e.g., black vs.white males) but increasing for others (e.g.,Asian/Pacific Islander to American Indian/AlaskaNative males)? There is no clear way to summarizethe changes in these relative pairwisecomparisons. Therefore, in addition to seeing howa particular social group’s cancer-related healthoutcomes change with respect to another group,we also may be interested in whether we aremaking progress toward eliminating disparitiesacross all racial/ethnic or socioeconomic groups,

which is consistent with the overarching goals ofHealthy People 2010. That is, we may want toknow whether the disparity in lung cancerincidence across all racial groups is decreasing.How should we answer that question when thereare a multitude of pairwise and time-relatedcomparisons that can be made? Pairwisecomparisons have been the mainstay ofepidemiological effect measures and clearly arecentral to disparity measurement, but there also isa place for summary measures of overall disparity.

Brief History of Measuring Disparitiesin the United States

Measuring Disparities in Public Health

This section briefly reviews selected historicalstudies of social-group disparities in healthoutcomes. Generally, the strong reliance in thepast on pairwise relative and, less frequently,absolute disparity, and the difficulties such a

8

Figure 2. Lung Cancer Incidence by Gender and Race/Ethnicity, 1992–1999

1992 1993 1994 1995 1996 1997 1998 1999

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Figure 2. Lung Cancer Incidence by Gender and Race/Ethnicity, 1992-1999

* API = Asian/Pacific Islander** AI/AN = American Indian/Alaska NativeSource: Surveillance, Epidemiology, and End Results (SEER) Program SEER*Stat Database: 11Registries, National Cancer Institute, DCCPS, Surveillance Research Program, Cancer Statistics Branch.

*API = Asian/Pacific Islander**AI/AN = American Indian/Alaska NativeSource: Surveillance, Epidemiology, and End Results (SEER) Program (www.seer.cancer.gov) SEER*Stat Database: Incidence—Seer 11 RegsPublic-Use, Nov. 2001 Sub for Expanded Races (1992–1999), National Cancer Institute, DCCPS, Surveillance Research Program, CancerStatistics Branch.

strategy may raise for a broader, more population-focused understanding of health disparities andtheir assessment over time, are emphasized. Thetask of measuring disparity in public healthoutcomes usually has been taken on byepidemiologists, who tend to rely on relative riskmeasures to characterize effect estimates (10). It isinteresting that few references can be found tomeasuring health disparity per se in standardepidemiological texts. In some ways this is notsurprising, but it helps to explain why standardepidemiologic metrics, such as relative andabsolute risk differences, have been the generalmethod of choice applied to measuring healthdisparity. A brief guide to health disparitymeasurement can be found in a recent textbookon epidemiologic methods in health policy (11),but this topic is not addressed in more recentfoundational texts in either general epidemiology(12,13) or social epidemiology (14). This is not tosuggest that more traditional epidemiologicmeasures are not applicable to the measurementand monitoring of health disparities, but that,before choosing the methods to best capturesocial concerns over the extent of health disparityand before attempting to devise policies toreduce/eliminate such disparities, one should beaware that such measures have certain limitations.These issues will be discussed in more detail laterin this monograph.

Trends in Social Group Health Disparities

Are health disparities increasing in the UnitedStates? Despite consistent interest in social-groupdisparities in public health, limited data provideinformation on both social-group characteristicsand health at the national and local levels(15–17). This in turn has resulted in a relatively

small number of studies of health disparity trendsfor the United States as a whole. The landmarkstudy in the social epidemiology of mortality byKitagawa and Hauser (18), which involved aspecial matching of 1960 death-certificate recordsto the 1960 U.S. decennial census, serves as thebenchmark against which most socioeconomicdisparity trends are referenced. In that study,Kitagawa and Hauser measured disparity in termsof the standardized mortality ratio (SMR). The SMRis calculated as the ratio of the number ofobserved deaths to the number expected based onthe mortality rates of the United States as a whole.If, for example, there is no educational disparityamong white males ages 25–64, then the numberof observed deaths in each educational groupshould equal the number expected based on themortality rate for all white males ages 25–64,corresponding to an SMR of 1.0. Kitagawa andHauser found, however, that the SMR for whitemales ages 25–64 with less than 5 years ofeducation was 1.15 (i.e., 15% more deaths wereobserved than were expected) and was 0.70among those with a college degree (i.e., 30% fewerdeaths were observed than were expected).Generally, Kitagawa and Hauser found that highersocioeconomic position—whether measured byincome or education—was associated with lowermortality and that mortality was higher amongnonwhite and nonmarried individuals.Interestingly, they also reported that educationand income had independent effects—incomedisparities existed within education groups andeducational disparities existed within incomegroups. It is important to note that, in terms ofmeasuring disparity, this important study reliedon pairwise comparisons of specific groups to thepopulation average and did not use any summarymeasure of disparity.

9

Health Disparities According to Income

Pappas and colleagues (19) used the NationalMortality Followback Survey (NMFS) from 1986 toevaluate trends in education and incomedisparities since Kitagawa and Hauser’s 1960study. To use the information from allsocioeconomic groups, Pappas and colleaguescreated a summary disparity measure. Similarly toKitagawa and Hauser, they calculated an SMR foreach socioeconomic group within gender andracial categories based on the sex-race-specificmortality rates for the entire United States. Theythen took the absolute value of the differencebetween each socioeconomic subgroup’s (e.g.,those with <12 years of education) SMR and 1.0and weighted it by the respective proportion ofthe population in that socioeconomic subgroup.Their index was the sum of these weightedabsolute differences across all subgroups; thus, avalue of 0.5 would be interpreted as the weightedaverage deviation of the socioeconomic groups’SMRs from 1.0. Pappas and colleagues found thatmortality disparities had increased since 1960 forboth whites and blacks, with steeper increases forincome as compared with education as themeasure of socioeconomic position. Thus, becausethe sum of population-weighted SMR differencesfor income increased more than for education,they concluded that income-related disparitiesincreased more than educational disparities. Notethat because each group’s SMR was weighted by itspopulation share, an increase in disparity whenusing this index could be observed even in theabsence of changes in subgroup-specific mortalityrates if the subgroups with the largest SMRdifferentials increased their share of thepopulation.

Duleep (20) used data linking the 1973Current Population Survey (CPS) to Social Securitylongitudinal mortality data up to 1978 and alsomeasured disparity by SMRs. Unlike Kitagawa andHauser, however, she used her entire CPSsample—rather than the total U.S. population—togenerate the expected number of deaths in eachincome group. She also concluded thatsocioeconomic disparities had not narrowedbecause the ratio of observed-to-expected deathsfor most but not all income groups was furtherfrom 1.0 in 1973–1978 than it was in 1960. Forexample, the SMR for individuals earning $10,000or more (the richest group) decreased from 0.84 in1960 to 0.71 in 1973–1978. Schalick andcolleagues (21), using the 1967 and 1986 NMFS,investigated disparity trends in mortality byincome with different measures of disparity, theslope index and relative index of inequality. Thesedisparity measures are similar to the index usedby Pappas and colleagues (19) in that they weighteach socioeconomic group by its populationshare, but the index is not based on SMRs. Rather,income groups are ordered from lowest to highest,and a line is fitted to the data using weightedlinear regression. The slope of this line is theresulting “slope” index and is interpreted as theabsolute difference in mortality across the entirerange of income. Dividing this slope index by theactual mortality rate in the population gives the“relative” index and is the percent difference inmortality across the entire range of income.Similarly to Pappas and colleagues (19), Schalickand colleagues found that relative mortalitydisparities increased when measured by therelative index of inequality, particularly for males;they also found that absolute disparities decreasedduring the same period when measured by the

10

slope index of inequality, primarily because theabsolute declines in mortality were greater for theleast well-off groups.

Finally, using a different measure of disparity,the Population Attributable Risk percent (PAR%),Hahn and colleagues reported that the share ofmortality in the United States due to poverty hadincreased from 1973 to 1991 (22). The PAR%essentially is a summary index designed toestimate the population health impact ofeliminating health-damaging exposures and is afunction of the prevalence of the exposure and itsassociated relative risk. In this case the exposure ispoverty, and the interpretation of the index is thepercent by which the population death rate woulddecrease if poverty were eliminated. Thus, thePAR% is a population-focused disparity index inthat it measures the impact on the totalpopulation of eliminating the health disparitybetween the poor and the nonpoor. If the poorrepresent a small fraction of the population, or ifthe health effects of being poor are small, thenthe PAR% will show that the elimination of theexposure—poverty—will have a marginal effect onpopulation health. Hahn et al. report that, from1973 to 1991, the PAR% increased from 16.1% to17.7%, indicating that the population healthbenefit of eliminating mortality disparities bypoverty status increased. The increase, however,was due entirely to an increased PAR% amongmen, as the PAR% decreased for both black andwhite women.

Health Disparities According to Education

Feldman and colleagues (23) investigated trendsin educational disparities in mortality amongwhites between 1960 and 1971–1984 using the

matched data of Kitagawa and Hauser and thefirst National Health and Nutrition ExaminationSurvey Epidemiologic Followup Study (NHEFS).They measured disparity using a standardepidemiological “rate ratio”—the mortality rate inthe least-educated group divided by the mortalityrate in the most-educated group (i.e., a pairwisecomparison of extreme socioeconomic groups).The researchers concluded that educationaldisparities increased, but this effect was primarilyseen among white men. Interestingly, in theirdiscussion, Feldman and colleagues noted that thedistribution of education changed enormouslyover the period of study but concluded that themagnitude of the increase was “probably not largeenough to have a major impact on trends indifferentials” (23, page 929). The researchers,however, did not empirically examine thisassumption, which perhaps is why Elo andPreston revisited this question using the samedata (24) and conducted a similar analysis oftrends in educational disparity in mortality usingmultiple measures of disparity (slope index ofinequality, relative index of inequality) thataccount specifically for the changing distributionof education over time. Similar to previousanalyses (19,23), Elo and Preston found that theeducational disparity had increased among whitemen. Whereas Feldman and colleagues found nochange or a small disparity increase for whitewomen, however, Elo and Preston found thatboth absolute and relative disparities haddecreased for white women of all ages. Thesestudies highlight the important issue of whethermeasures of health disparity should be sensitive tochanges in the size of the “exposed group”—inthis case, the most disadvantaged in terms ofincome or education. The issue of the effect onhealth disparities of the movement of individuals

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into and out of different social groups over timealso is important and has been neglectedsomewhat in the United States, despite havingreceived consistent emphasis in the healthdisparities literature (25–27).

The above studies indicate that relativemortality disparities generally appear to haveincreased since 1960, but the extent of disparitydiffers with different measures of disparity andsocioeconomic position. Because all of the aboveanalyses use different data sources and differentmeasures of health disparity, it is difficult to reacha firm conclusion as to how much thesocioeconomic disparity in overall mortality hasincreased or decreased over time. This perhaps isnot surprising given that, even for simpledisparity measures such as the relative comparisonof the lowest and highest social groups, differentnational data sources can provide differentestimates of the size of the same health disparity(28).

Health Disparities According to Race/Ethnicity

Despite the longstanding interest in healthdisparities between racial/ethnic groups in theUnited States, surprisingly few studies haveanalyzed racial/ethnic disparity trends.Additionally, the major racial/ethnic focus in theUnited States has been on disparities betweenblacks and whites (or nonwhites and whites),which makes understanding trends somewhat lessdifficult because the inequality between twogroups may be summarized easily with either asimple difference or ratio measure. Thecontinuing increase in U.S. racial/ethnic diversityand the growing need to compare multipleracial/ethnic groups and to examine individual

populations that usually are grouped together(i.e., Chinese with Japanese or Mexican Americanswith Puerto Ricans), however, make the use ofpairwise comparisons for summarizing inequalitytrends more difficult to understand andcommunicate. The inherent difficulty of talkingabout trends in health inequality by reference toseveral relative risks is one reason for attemptingto summarize inequality with a single index. Onepotential summary measure, the Index ofDisparity (IDisp), was introduced formally byPearcy and Keppel (30) and was applied to 17health status indicators during the period1990–1998 for five racial/ethnic groups: non-Hispanic whites, non-Hispanic blacks, Hispanics,American Indian/Alaska Natives, and Asian/PacificIslanders (31). The IDisp measures variations inhealth across dimensions of a social group (e.g.,race/ethnicity) relative to some reference point—in this case, the total population rate. Thus, adecline in the IDisp indicates that the variation inhealth across racial/ethnic groups declined relativeto the total population rate. From 1990 to 1998,the researchers found that the IDisp decreased formost mortality measures and infant healthoutcomes (i.e., racial/ethnic disparity decreased),but increased for teenage pregnancy, motorvehicle deaths, suicide, work-related injury deaths,and tuberculosis case rates. It is important to notethat, unlike some disparity measures mentionedpreviously, the IDisp does not weight social groupsby their population share. That is, the IDisp takes aperspective on disparity that what matters is thedifference in subgroup rates of health, regardlessof the number of individuals that may be affected.Thus, it is more focused on strict equality ofhealth status measures, regardless of social-groupsize and the extent to which social-group healthdifferences may impact population health.

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Socioeconomic Disparity Trends in Cancer

In general, there have been fewer studies ofsocioeconomic disparity trends in cancerincidence and mortality. One of the difficulties inmonitoring disparity trends in cancer with respectto socioeconomic groups is that the major sourceof data on cancer incidence and survival, theNational Cancer Institute’s Surveillance,Epidemiology, and End Results (SEER) Program,does not collect socioeconomic data onindividuals (17). A number of studies, such asthose by Singh and colleagues (32) and Kriegerand colleagues (33), however, have usedinformation on residential location collected onincident cancer cases to create a measure ofsocioeconomic position. This is accomplished bylinking the neighborhood or county in which anindividual cancer case resides to the U.S. census toget a measure of the socioeconomic status of thatarea—for example, the poverty rate. Such “area-based” measures of socioeconomic positioncertainly are an improvement over having nomeasure at all, but they also require additionalassumptions that may hinder their utility formonitoring cancer-related disparities. Forexample, the use of area-based measures assumesthat the average socioeconomic status of the areais representative of the status of the individual,and that, because the census is conducted onlyevery 10 years, the socioeconomic status of anarea in, say, 1990 is an accurate representation ofthe same area for a cancer case diagnosed in 1997.

Using area-based measures of socioeconomicposition (e.g., census tract poverty rates), Singhreported a reversal in the socioeconomic gradientamong men in overall cancer mortality from 1950

to 1998 (34). Singh used relative pairwisecomparisons of the highest and lowestsocioeconomic groups and showed that, in 1950,mortality rates were 49% higher in highersocioeconomic areas; this disparity decreased overthe next 30 years and, by the late 1980s, cancermortality rates were 19% higher in lowersocioeconomic areas. Thus, over the past 50 years,the pattern of higher cancer mortality amongindividuals in higher socioeconomic areasdisappeared and was replaced by a pattern ofhigher cancer mortality among individuals oflower socioeconomic position. A similar pattern ofreversing gradients also was evident for lungcancer and colorectal cancers (35). With regard tocancer incidence, from 1975 to 1999, the trend insocioeconomic disparity for all cancers amongboth men and women was inconsistent (32) asmeasured by the incidence rate among thoseliving in areas with >20% of the population inpoverty relative to the rate in areas with <10% inpoverty (i.e., relative pairwise comparison ofextreme groups). This likely is due to differingdisparity trends for specific cancer sites.Compared to the highest socioeconomic group,cancer mortality rates were higher among thelowest socioeconomic group for lung and prostatecancers among males, and the ratio of the lowestto the highest socioeconomic area widened from1975 to 1999. Incidence of melanoma was higheramong males in higher socioeconomic areas in1975, and this relative difference increased by1999. Colorectal cancer was more frequent amongmales in higher socioeconomic areas in 1975; therelative difference decreased by 1999. Amongfemales, women in poorer socioeconomic areashad higher incidences of lung and cervical cancersin 1975; the disparity in lung cancer incidence

13

remained relatively constant, whereas thedisparity for cervical cancer declined. Womenliving in higher socioeconomic areas had a higherincidence of melanoma, colorectal, and breastcancers in 1975; by 1999, this disparity narrowedfor colorectal cancer and widened for breastcancer and melanoma. This analysis highlightsthe importance of examining site-specific ratherthan overall cancer trends, as the overall cancerrate is a diverse amalgam of specific types ofcancer that differ in their etiology and, therefore,their social distribution.

Few studies have assessed trends ineducational disparities in cancer. Steenland andcolleagues (36) analyzed trends in educationaldisparities in cancer mortality using data from theAmerican Cancer Society’s Cancer PreventionStudy cohorts (CPS-I and CPS-II). They usedordinary least squares regression to calculate aregression-based relative effect of education.Instead of simply comparing the most- and least-educated groups, this disparity measure uses themortality rates for all educational groups and isinterpreted as the increase in cancer mortality foreach 1-year decrease in the number of years ofeducation. The study found that educationaldisparities increased from 1959–1972 to1982–1996 for lung and colorectal cancers anddecreased for breast cancer. The researchers didnot, however, account for changes in the socialdistribution of education during this period andwere forced to conclude that “the educationalcategories were not comparable between the twopopulations.” (36, page 20). Thus, theirconclusions were less than clear. If the educationcategories are not comparable, and this fact is notaccounted for in the disparity measure, then it is

difficult to know how to interpret the reporteddisparity trend among these cohorts.

Racial/Ethnic Disparity Trends in Cancer

Although racial/ethnic disparities in cancer havereceived significant attention, especially withregard to treatment (2,37), relatively few studieshave assessed long-term trends in these disparities.Again, the general lack of detailed historicalracial/ethnic information in cancer-related datasources often limits analyses of long-termdisparity trends to a pairwise comparison ofwhites and blacks or whites and nonwhites.Within the last decade, focus on and efforts topromote population health data for major ethnicgroups have increased. Ten-year trends now areavailable for some groups. For subgroups withinmajor racial/ethnic groups, this is complicatedfurther by the lack of inter-censal estimates ofpopulation size as well as issues of comparabilityof reporting for numerator (incidence) anddenominator (population size) data. Other issuesthat arise in comparing groups by race/ethnicityinclude differences between subpopulationscommonly grouped together, such as differencesin cancer incidence rates between AmericanIndians and Alaska Natives and between variousAmerican Indian tribes.

With regard to mortality from all cancers,whites had higher mortality rates than nonwhitesuntil the middle of the 20th century, after whichnonwhites have had higher mortality rates. Thegap between whites and nonwhites increasedfrom the mid-20th century until the early 1990s,after which it declined (38,39). The primaryreasons for the widening gap between white and

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nonwhite cancer mortality since mid-centurywere relatively larger increases in nonwhitemortality from lung, prostate, colorectal, breast,and ovarian cancers (39).

Still fewer studies have attempted to use anysummary measure of health disparity acrossseveral racial/ethnic groups. Keppel and colleaguesused the Index of Disparity to compare lung andfemale breast cancer mortality rates in 1990 and1998 across five racial/ethnic groups: non-Hispanic whites, non-Hispanic blacks, Hispanics,American Indian/Alaska Natives, and Asian/PacificIslanders (31). Racial/ethnic disparity declined forboth cancers—significantly so for lung cancer.

Health Inequality and Health Inequity

The language of “eliminating health disparities”seems simple and straightforward—somethingthat everyone understands in the same way andcan agree on. When we say we want to eliminatehealth disparity, do we really mean we wanteveryone to have the same level of health? Is thegoal that all individuals/social groups should havethe same health, regardless of how healthy or sickthey might be? Or do we mean that it isimproving the health of the most disadvantagedindividuals/social groups so that they approachthe health of the more advantaged (i.e., priority tothe worst-off/least healthy)? In regard to reducingincome disparities, we are comfortable as a societyin considering the need to reduce the incomes ofthe advantaged via taxation in order to increasethe incomes of the impoverished. In other words,we are willing to engage in policy discussionsfocused on income redistribution from the rich tothe poor. It is not clear that this idea applies to

health disparity. That is to say, in public health wegenerally are not willing to accept health declinesin a healthier or more socially advantaged groupto foster improved health in those who are lesshealthy or socially disadvantaged. Yet, it isplausible that, for example, the health of the richand the poor both improve, but the rich improveat a better rate, therefore increasing the relativedisparity between the two groups. This situationhighlights the possible tension that may arise indesigning policies to simultaneously achieve thetwo overarching goals of Healthy People 2010—improving average health and eliminating healthdisparities. Such questions only scratch the surfacebut underscore the potential implications of aliteral interpretation of the language of theHealthy People 2010 initiative to “eliminate”health disparities (1).

The health disparity concept involves bothdescriptive and normative elements. The task is tounderstand what the elements are and to developsensible measures of disparity that capture both ofthese dimensions (40,41). In the United States theuse of the term “disparity” implies two coreconcepts. First, it suggests that there are health“differences” between individuals or social groups;second, it suggests that such differences in someway are unfair and an affront to our moralconcepts about social justice. Thus, the term“disparity” often mixes ideas of “inequality” and“inequity.” The term “inequality” literally meansdifference—that two quantities are not the same—but the term “inequity” implies an ethicaljudgment about those differences. Inequality is ameasurable, observable quantity that can bereasonably and unambiguously judged; inequityrelies on a moral, ethical judgment about justice

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and thus is not unambiguously measurable orobservable. The classification of health differencesas unequal is a relatively easy task compared tothe classification of health differences asinequitable. Judgements concerning inequity relyon social, political, and ethical discourse aboutwhat a society believes is unfair (42).

Another crucial dimension to ideas ofinequity and concepts of justice comes fromdiscussions about disparities in health that areavoidable and those that are unavoidable (43,44).Both types contribute to health disparities, butonly potentially avoidable determinantscontribute to inequity (45). Thus, “avoidability”implies a capacity to intervene (via social policy,medical care, etc.) with respect to the

determinants of disparity. It often is difficult toidentify the determinants of disparities or todistinguish between avoidable and unavoidabledeterminants. Determinants of disparity may beunavoidable in the short run and avoidable in thelong run. It is easier to measure disparity betweengroups than it is to identify the determinants ofthe disparity or to decide which determinants areavoidable and which are unavoidable. Toeliminate disparities in health between groups,however, the determinants of disparities in healthmust be identified and avoidable determinantsmodified. The first task, though, is to arrive atmethods to identify and quantify healthdisparities over time as the basis for evaluationand action.

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Defining Health Disparities

This section introduces concepts of healthdisparity and discusses important issues involvedin their measurement. It also highlights the factthat “disparity” is a fundamentally ambiguousconcept with multiple dimensions that differentmeasures of disparity emphasize to a greater orlesser extent. On its face, the concept of a healthdisparity seems rather simple. In fact, when oneattempts to formally define what constitutes ahealth disparity, difficulties emerge. For example,consider the following definitions of whatconstitutes a health disparity for the purposes ofmeasurement:

“Health disparities occur when one group ofpeople has a higher incidence or mortalityrate than another, or when survival rates areless for one group than another.”—NCICenter to Reduce Cancer Health Disparities,2003 (46)

“A population is a health disparity popula-tion if . . . there is a significant disparity in theoverall rate of disease incidence, prevalence,morbidity, mortality, or survival rates in thepopulation as compared to the health statusof the general population.”—Minority Healthand Health Disparities Research andEducation Act of 2000 (47, page 2498)

“For all the medical breakthroughs we haveseen in the past century, there remainsignificant disparities in the medical

conditions of racial groups in this country. . . .[W]hat we have done through this initiativeis to make a commitment—really, for the firsttime in the history of our government—toeliminate, not just reduce, some of the healthdisparities between majority and minoritypopulations.”—Dr. David Satcher, FormerU.S. Surgeon General, 1999 (48, page 18–19)

“Health disparities are differences in theincidence, prevalence, mortality, and burdenof diseases and other adverse healthconditions that exist among specificpopulation groups in the United States.”—NIH Strategic Research Plan and Budget toReduce and Ultimately Eliminate HealthDisparities, Vol. 1, Fiscal Years 2002–2006

Although these definitions share the samebasic sentiment, there are some potentiallyimportant differences that reflect underlyingassumptions (explicit or implicit) about whatconstitutes a health disparity. For instance, underthe first definition above, a disparity is adifference in health between any two populations,whereas in the second definition (from the lawthat established the NIH initiative), a disparity is adifference in health between some specificpopulation and the general population. Thisdefinition also introduces the idea that a disparitymust be “significant” in magnitude. Thesedifferences may seem to be inconsequentialsemantics, but for the purposes of monitoring

progress toward eliminating health disparities, thedifferent definitions imply different metrics forassessing progress. One could imagine a scenarioin which two minority groups have identicalmortality rates, both of which differ substantiallyfrom that of the general population. A moreextreme (but unlikely) scenario might be a case inwhich one minority group’s health is better butnot “significantly” different from that of thegeneral population, whereas another minoritygroup’s health is worse but also not “significantly”different from that of the general population. It ispossible, however, that the difference in healthbetween the two minority groups is “significant.”Thus, for the same observed data we mightconclude either that a disparity exists (under thefirst definition above) or that a significantdisparity does not exist (under the seconddefinition above). Also note that the definition

offered by former Surgeon General Satcher statesthat disparity exists between the minority andmajority population, which suggests a thirdpossible reference point—the majoritypopulation—though it is not clear how thatmajority is to be defined.

Our purpose is not to focus on semantics butrather to illustrate the lack of clarity in healthdisparity definitions and how this is important inchoosing measures to monitor disparity. It isunlikely we will agree on a single definition ofdisparity. It is more likely that there are severallegitimate, competing perspectives on healthdisparity that can be adopted. We want toemphasize the importance of understanding thelink between ethical perspectives and the choiceof quantitative health disparity measures.

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Issues in Evaluating Measures of Health Disparity

This section discusses several issues—conceptual,pragmatic, and technical—that potentially areimportant in choosing health disparity measures.Many of these issues receive expanded discussionsin the more technical descriptions of the measuresthat follow in later sections. The intention here isto highlight the set of main issues that might beconsidered.

Total Disparity vs. Social-GroupDisparity

There is an important conceptual issue regardingthe specific quantity to be determined whenevaluating health disparities. The fundamentaldistinction to be made is between measuring totaldisparity, or total variation, and measuringdisparities between social groups. The formerinvolves evaluating the univariate distribution ofhealth among all individuals in a population,without regard to their group membership; thelatter involves assessing health differencesbetween individuals from certain a priori chosensocial groups. The World Health Organization(WHO) initiative to measure health inequality, ledby Chris Murray and colleagues, has advocatedstrongly for an approach to the measurement ofhealth disparity as total health disparity amongindividuals that is blind to social groups (49,50).Initially, this seems at odds with our notions ofwhy we are evaluating disparity in the first place(51). That is, the initiative to eliminate healthdisparities arose within the United States because

of the persistent presence of social-group healthdisparities, not out of concern for a wideningoverall distribution of health. Yet, a deeperunderstanding of the overall task of determiningvariation in population health requires that weappreciate the concept of total health disparity. Itis likely that the between-group disparity we seekto measure in regard to initiatives such as those inthe United States may be relatively smallcompared to the total disparity that existsbetween individuals in a population.

Figure 3 (page 20) shows the average bodymass index (BMI) for five education groups in the1997 National Health Interview Survey (NHIS). Itis clear that there is a gradient of decreasing BMIwith increasing education when comparingaverage BMI among education groups. The plotsof the 10th through the 90th percentiles of BMI,however, show that there is much greatervariation in BMI within education groups thanbetween education groups. Thus, basing themeasure of health disparity on between-groupaverage differences may not capture much of thetotal health variation among individuals. This isnot a problematic statement itself but should beunderstood—and is why indicators of total healthinequality can be informative. Thus, based on thegroup averages and a desire to reduce obesity inthe population, focusing a health intervention onthe “high-risk” social group (those with less thanan 8th-grade education) will in practice target onlya limited proportion of those at high risk, because

high-risk individuals exist in every educationgroup.

Measures of total health disparity may masksubstantial social-group disparities, however.Figure 4 (page 21), adapted from Asada andHedemann (52), shows the populationdistributions of life expectancy in twohypothetical societies, A and B. Both populationshave the same average life expectancy, but SocietyA has a much narrower overall distribution of lifeexpectancy; were we to use a measure of totaldisparity, we would judge Society A to have thesmaller disparity. Within Society A, however, thereis a substantial gap in life expectancy betweensocial groups 1 and 2, whereas in Society B,groups 1 and 2 have nearly identical life

expectancy distributions. If we use a measure ofsocial-group disparity, we likely would judgeSociety A as having the greater disparity becausethe distribution of life expectancy between thegroups is unequal. The point of this example is toshow that measures of total disparity andmeasures of group disparity may or may not leadto similar judgments about the extent of disparityin two populations or at two time periods. Thusfar, the evidence seems to indicate that totaldisparity and social-group disparity measuredifferent aspects of population health. Two cross-national studies found little correspondencebetween measures of total disparity and measuresof socioeconomic disparity for either child (53) oradult (54) mortality. That is, countries with thelargest amount of overall mortality variation did

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Figure 3. Mean and 10th–90th Percentiles of Body Mass Index by Education, NHIS, 1997

<8th

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not necessarily have larger socioeconomicmortality variation, and countries with the largestsocioeconomic mortality disparities did not havethe largest overall mortality disparities.

Relative and Absolute Disparities

The most frequent method of communicatinginformation about social disparities in publichealth and epidemiology is in relative terms—through measures of association such as therelative risk. In epidemiology, relative risks are themost common measures of “effect size,” partlybecause they have advantageous properties not

shared by absolute risk differences (12,55).Relative and absolute health differences betweensocial groups are the primary language of healthdisparities, but they provide fundamentallydifferent types of information. Figure 5 (page 22)demonstrates this essential point by showingtrends in absolute and relative disparity betweenmales and females in stomach cancer mortalityover the past 70 years. Clearly, there wasenormous progress in reducing stomach cancermortality rates among both males and femalesduring the 20th century. As the rates for bothgroups declined, however, the ratio of male-to-female mortality (i.e., the relative disparity)

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Figure 4. Hypothetical Distributions of Life Expectancy in Two Populations

Distribution ofLife Expectancy

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Figure 4. Hypothetical Distributions of Life Expectancy in Two Populations

Average Life Expectancy: Society A = Society B

Total Disparity in Life Expectancy: Society A < Society BGroup Disparity in Life Expectancy: Society A > Society B

steadily increased. If the difference between maleand female mortality (i.e., the absolute disparity)is used as the measure of disparity, however, weobserve a different trend. The male-female gapincreased from 1930 to about 1950, as femalerates declined faster than male rates, and hasdeclined steadily since 1950. Thus, Figure 5illustrates the possibility that one might arrive atopposite conclusions about what happened to thishealth disparity, depending on which measurewas chosen—the absolute or relative disparity. Thereason is that the relative disparity cannot reflectchanges in absolute rates—the disparity is relativeto the rate in the comparison group.

Reference Groups

The language of disparity—defined literally as“difference”—implies a comparison group. Amajor question in choosing disparity measures isthe choice of comparison group. As noted above,the different definitions of disparity implydifferent comparison groups, and thus the answerone would get about the extent and patterning ofdisparity may differ according to which groups arecompared. Figure 6 (page 23) shows the situationfor cervical cancer mortality rates among severalracial/ethnic groups. Hispanic women clearly havethe highest incidence of cervical cancer, but how

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Figure 5. Absolute and Relative Gender Disparity in Stomach Cancer Mortality, 1930–2000

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0

Relative D

isparityM

ale/Fem

ale Ratio

Relative Disparity(Male ÷ Female)

Absolute Disparity(Male – Female)

Males

Figure 5. Absolute and Relative Gender Disparity in Stomach Cancer Mortality, 1930-2000

Source: Wingo et al. Cancer 2003;97(11 Suppl):3133–275, and SEER Cancer Statistics Review, 1975–2000.

Females

Source: Wingo et al. Cancer 2003;97(11 Suppl):3133–275, and SEER Cancer Statistics Review, 1975–2000.

large is the disparity in cervical cancer incidence?The answer depends on the choice of thereference group. If the Hispanic disparity ismeasured relative to the general population (i.e.,the total rate), then the relative disparity is 1.75.If, however, we follow Dr. Satcher’s recom-mendation (48) and focus on the disparity fromthe majority population—non-Hispanic whites—the relative disparity is 2.21. Or, if the “best-off”group—American Indian/Alaska Natives—ischosen as the reference group, we obtain a relativedisparity of 2.43.

Average Population Member

One logical reference group might be thepopulation average, where the disparity measurereflects the gap between the health of differentsocial groups and the mean health of the entirepopulation. The population average is appealingintuitively as a reference point and, as notedabove, often is also used explicitly in definingwhat constitutes a health disparity.

23

Figure 6. Relative Risk (RR) of Incident Cervical Cancer Among Hispanics According to Varying ReferenceGroups, 1996–2000

Total

20

18

16

14

12

10

8

6

4

2

0

Rat

e pe

r 10

0,00

0

Non-HispanicWhite

Black Hispanic AI/AN* API**

12.4

7.6

9.6

16.8

6.9

10.2

Figure 6. Relative Risk (RR) of Incident Cervical Cancer Among Hispanics According to Varying Reference Groups, 1996-2000

* AI/AN = American Indian/Alaska Native** API = Asian/Pacific IslanderSource: SEER Cancer Statistics Review, 1975-2000

RRHispanic vs. Total

RRHispanic vs. NH White

RRHispanic vs. Am Ind/AN

= 1.75= 2.21= 2.43

*AI/AN = American Indian/Alaska Native**API = Asian/Pacific IslanderSource: SEER Cancer Statistics Review, 1975–2000.

Best-Off Group/Person/Rate

This perspective suggests that one might measuredisparity as a difference between each social groupcompared to the healthiest group (or even thehealthiest person). This is similar to Sen’s conceptof shortfalls (56), in which it is assumed implicitlythat every social group in the society has thepotential to achieve the health of the best-offgroup. It should be noted, however, that the best-off social group may be relatively small in size,which may lead to substantial variation andinstability and could make assessing trends indisparities more difficult.

All Those Better Off

It also is possible to measure disparities bycomparison to all those individuals or groups thatare better off than a particular group or person.This may seem similar to the “best-off group”reference point, but it differs in a subtle way thatmay best be illustrated with an example usingactual cancer data. Figure 7 (page 25) showscancer incidence from 1996–2000 by race andethnicity for two different cancers, kidney/renalpelvis and myeloma. In both cases, there is asubstantial difference between the group with thehighest incidence rate, blacks, and the group withthe lowest or “best” rate, Asian/Pacific Islanders.When we look at the incidence rates of othergroups, however, we see two different situations.In the case of kidney cancer, Hispanics and whiteshave rates more similar to blacks, whereas, in thecase of myeloma, they have rates more similar toAsian/Pacific Islanders. Relative to all those betteroff than blacks, most people might judge thedisparity to be worse in the case of myeloma

compared to kidney cancer; yet, if measuredrelative to the “best-off” group perspective, wewould be unable to capture this nuance.

Fixed/Target Rate

The prior three reference groups are inherentlyrelative as they change over time, which maymake assessments of trends in disparitiesinconclusive if using pairwise comparisons. Oneadvantage of a fixed or target rate is that thereference level does not change over time unless anew target is adopted.

Social Groups and “Natural”Ordering

The Healthy People 2010 initiative mandateseliminating health disparities within a number ofdifferent types of social groupings: gender, incomeand education, disability, geographic location,sexual orientation, and race and ethnicity. Suchgroupings were chosen because they representimportant normative dimensions of U.S. society,and it has been shown repeatedly that healthdifferences exist between these social groups. Theabove groups, however, also differ in ways thatmay have implications for monitoring healthdisparities. The social groups that measuredimensions of socioeconomic position—educationand income—have an inherent ordering regardlessof the health status of their members. Individualswith less than a high-school educationunambiguously have less formal education thando individuals with a college degree. The samecannot be said for the other groups targeted bythe Healthy People 2010 initiative. There simply is

24

no inherent way to rank individuals by their race,ethnicity, disability status, or sexual orientation.Certain measures of disparity cannot be used tomeasure or monitor disparities between groupsthat have no implicit ranking. For example, theslope index of inequality and the concentrationand achievement indices cannot be used except inthe case of education and income, because thereis no inherent way to rank some social groupssuch as racial/ethnic groups or genders (except bytheir health level). In the Healthy People 2010parlance, groups with a “natural” ordering includeeducation and income but do not include gender,race/ethnicity, sexual orientation, disability status,and geography.

The Number of Social Groups

Should the measure of disparity includeinformation from all social groups (i.e., the entirepopulation), or is it sufficient to reflect only theexperiences of the best- and worst-off (extreme)groups? Many empirical studies of healthdisparities measure disparity by comparing theextreme groups (e.g., the lowest income groupcompared with the highest income group). This,however, ignores the health status of other groupsand additionally may only reflect the disparitybetween two very small population groups. Forexample, in 2000 there was a three-fold relativedifference in death rates from melanoma of the

25

Figure 7. Age-Adjusted Incidence of Kidney/Renal Pelvis Cancer and Myeloma by Race and Ethnicity,1996–2000

Kidney and Renal Pelvis

20

15

10

5

0

Inci

denc

e R

ate

per

100,

000

Myeloma

All Races Black Hispanic White Asian/Pacific Islander

Figure 7. Age-Adjusted Incidence of Kidney/Renal Pelvis Cancer and Myeloma by Race and Ethnicity, 1996-2000

Source: SEER Cancer Statistics Review, 1975–2000.Source: SEER Cancer Statistics Review, 1975–2000.

skin across U.S. states. The states with the lowest(North Dakota, 1.3 per 100,000) and the highest(Wyoming, 3.7 per 100,000) rates, however,collectively accounted for only 0.4% of the U.S.population in that year. Eliminating this disparitywould have little impact on reducing thepopulation burden of melanoma mortalitybecause only a fraction of melanoma cases residein these two states. Additionally, although thereare good reasons for focusing attention on specificcomparisons, such as the disparity between blacksand whites in the receipt of treatment for cancersof similar stage (57), such pairwise comparisonsdo not quantify the disparity across allracial/ethnic groups, which is precisely the goal of

initiatives to eliminate health disparities by theyear 2010. For example, the gap between whiteand black men in the recent use of fecal occultblood test (FOBT) screening for colorectal cancernarrowed between 1987 and 1998 (58); however,this pairwise comparison conceals the fact thatthe gap between Hispanics and whites andbetween Hispanics and blacks increased (seeFigure 8). Despite the utility of measuringdisparities between two groups, pairwisecomparisons may conceal importantheterogeneity and thus provide a limited view inmonitoring progress toward eliminating healthdisparities across the entire range of social groups.

26

Figure 8. Proportion of Men Reporting Use of Screening Fecal Occult Blood Tests (FOBT), by Race andEthnicity, 1987–1998

1987

40

30

20

10

0

Per

cent

Rep

ortin

g S

cree

ning

1998

Black HispanicWhite

1992

19.5

11.5

6.8

25.0

19.3

10.2

29.9

24.3

15.9

Figure 8. Proportion of Men Reporting Use of Screening Fecal Occult Blood Tests (FOBT), by Race and Ethnicity, 1987-1998

Source: Breen et al. J Natl Cancer Inst 2001;93:1704–13.

Source: Breen et al. J Natl Cancer Inst 2001;93:1704–13.

Population Size

Should the disparity measure incorporate the sizeof the groups being compared? If we use apairwise comparison of extreme groups, would itmatter that one or both of those groups comprisesa very small proportion of the population? Forexample, Pearcy and Keppel’s Index of Disparity(30) gives equal weight to each group, eventhough the groups may represent differentproportions of the population. This has importantimplications for monitoring disparities and isanother case in which a statistical choice reflectsan ethical choice. That is, the decision of whetheror not to weight social groups by their populationsize also is a decision regarding how much weightto give individuals within each social group. Forexample, if we measure the disparity in prostatecancer mortality among U.S. states in 2000without weighting states by their population size,California and Wyoming receive equal weightdespite the fact that California has nearly 70times as many males as Wyoming. Thus, in anunweighted analysis of U.S. states, individualmales in California receive approximately 1/70th

the weight of males in Wyoming.

Another important issue in using unweightedmeasures of health disparity is their inability toincorporate the demographic changes thatinevitably occur over time. For example, Figure 9(page 28) shows the percentage increase inpopulation subgroups between the 1980 and 2000Census (59). These demographic shifts can haveenormous impact on the population’s health andshould be factored into the assessment of healthdisparity. In their analysis of the effects ofeducation on all-cause and cause-specificmortality in the American Cancer Society’s Cancer

Prevention Study cohorts (CPS-I and CPS-II),Steenland and colleagues (who used ordinary leastsquares regression) noted that changes in thedistribution of education made it difficult tocompare the extent of disparity between the twopopulations studied (36). The proportion of thepopulation with less than a high-school educationwas 20% in CPS-I and 6% in CPS-II, while thosewith a college degree were 16% and 30% of thepopulation in the two respective cohorts. Inepidemiological language, the proportion of thepopulation “exposed” changed dramatically withlarge population shifts out of the mostdisadvantaged groups. For a measure of healthdisparity to allow for an unambiguouscomparison across time, it should be sensitive tochanges in the distribution of social groups overtime. This sensitivity to changes in the proportionof people exposed to disadvantageous socialpositions especially is important whenconsidering the so-called “upstream”determinants of health disparities. It iscommonplace in health disparity research todiscuss how distal social policy affects health andhealth disparity. The policies and programs thatdefine the nature of stratification in a societycreate educational opportunity, allocate income,and affect the types of jobs that are available.When these “upstream” social policy factors affectthe nature of social stratification by reducing thenumber of minimally educated individuals, forinstance, thus reducing the number of individualsexposed to that form of social disadvantage, thenmeasures of health disparity should account forthat change. The same situation exists when theproportion of a particular population subgroupchanges over time, as in the case of the migrationof Hispanics and Asian/Pacific Islanders as shownin Figure 9.

27

Socioeconomic Dimension

Another potential criterion for a measure ofhealth disparity, first articulated by Wagstaff andcolleagues (60), is whether the measure is able tocapture health gradients associated withsocioeconomic position. By health gradients, wemean a situation where a measure of health statuseither increases or decreases with increasingsocioeconomic position. A good example is theincreasing rate of cancer incidence amongindividuals living in U.S. counties withsuccessively higher poverty rates (32). That is, isthe measure sensitive to the direction of the

association between social group and health? Forinstance, if at one time health status increaseswith social-group ordering and at another timehealth decreases with the same social-groupordering, the disparity measure will reflect thischange if it is sensitive to the direction of thegradient. Of necessity, this criterion is applicableonly for measuring inequality between socialgroups that have an inherent ranking. The lack ofinherent ordering among racial/ethnic groups, forexample, means that the “socioeconomicdimension” criterion cannot be applied todisparity measures used to monitor racial/ethnichealth disparities.

Figure 9. Percent Change in Population Size by Race and Hispanic Origin, 1980–2000

Total

250

200

150

100

50

0

Per

cent

Cha

nge

in P

opul

atio

n

Black API* Hispanic Non-Hispanic

MinorityWhite AI/AN** Other Non-Hispanic

White

30.8

12.3

24.2

204.0

74.3

127.3

141.7

16.17.9

87.7

Figure 9. Percent Change in Population Size by Race and Hispanic Origin, 1980-2000

* Asian/Pacific Islander** American Indian/Alaska NativeSource: Hobbs F. Stoops N. Demographic Trends of the 20th Century, 2002.

*Asian/Pacific Islander**American Indian/Alaska NativeSource: Hobbs F, Stoops N. Demographic Trends of the 20th Century, 2002.

28

Monitoring Over Time

Inherent in the goals of Healthy People 2010 is theidea that we monitor progress toward theelimination of health disparities. That means it isdesirable that measures of disparity areinterpretable over time. This represents importantchallenges for the use of simple pairwise relativedisparity indicators and indicators that are notpopulation-weighted. Because both the healthstatus within different social groups and thepopulation distribution of social groups changeover time, which together reflects the overallpublic health burden of health disparities,measures that are sensitive to both dimensions ofchange may be more suitable for monitoringdisparities over time.

Transfers

The issue of how measures of disparity respond tohypothetical transfers between individuals hasbeen an important part of evaluating theperformance of income disparity measures ineconomics. The major test in economics is theprinciple of transfers—sometimes called thePigou-Dalton condition (61,62)—which maintainsthat a transfer of income from a richer to a poorerperson should result in a decrease in the measureof disparity (assuming that everyone else’s incomeremains unchanged and the transfer is not largeenough to reverse anyone’s relative positions).This is an intuitively powerful and desirablenotion that corresponds well with what webelieve disparity measures should be able tocapture. Yet, theoretically, this is a somewhatdifficult concept to employ for judgments abouthealth disparity. Is “health” a fungible good like

income that can be redistributed in differentways? It is hard to imagine social mechanisms(perhaps apart from organ donation) throughwhich a “healthy” person can directly transfersome of her health to someone who is lesshealthy, though it is possible to conceive ofredistributing health resources. The task, however,is to measure disparities in health, not healthresources.

We have noted that measuring disparity inhealth versus income differs in at least oneimportant respect, namely that goods such asincome or wealth are, in fact, transferable fromone individual to another. One potential way toavoid this difficulty is to think of comparingdisparity in two different populations (e.g., in tworepeated observations of a cohort). One mightthen think of a transfer-like principle according towhich we evaluate a measure of health disparity.If the health of every individual remains thesame, but a single “healthier” person becomes lesshealthy and a previously “less healthy” person’shealth improves, the measure of health disparityshould decrease (25). This seems a plausible-enough principle to warrant evaluating a measureof health disparity, but health disparities andincome distributions are dissimilar in anotherway. Even if we are willing to put aside the issueof the literal inability to “transfer” health, it is notat all clear in the previous example that we wouldbe willing to accept the decreased health of oneperson for the sake of increasing the health ofanother. For income, this is not a problembecause it is the distribution of the good itself thatis under question. Most people generally believethat it is unfair that some have enormousincomes while others live in extreme poverty. Do

29

we truly believe, however, that some individualspossess more than their fair share of health? Aswas emphasized earlier, one of the major reasonsfor the increasing focus on health inequalities isnot simply that some are healthy while others aresick. It is that some kinds of individuals or themembers of some social groups are healthy whileother kinds are sick. It is the normativedistinction between the kinds of healthy orunhealthy individuals that drives our concernthat health differs so markedly by social group.The concern over health disparities then, at leastin the current historical period, is not that thereare health differences in society but that thesehealth differences systematically covary withmembership in particular social groups.

Subgroup Consistency

Generally, this criterion says that if the measure ofoverall disparity includes, for example, threegroups, and disparity within two groups remainsunchanged while increasing within the third, themeasure of disparity should increase. This is ofmost relevance when we are interested inmeasuring the overall disparity (i.e., across theentire population). For instance, suppose we wereexamining alcohol consumption at two points intime in a population composed of two socialgroups (rich and poor). At each time, both thesize of these groups and their average alcoholconsumption remain constant, but the disparityin consumption increases within the poor andremains constant within the rich. Subgroupconsistency requires that any measure of overalldisparity also should register an increase in this

scenario. This is not likely to be an importantcriterion for health disparity measures in thecontext of Healthy People 2010 because it does notfocus on health disparities within subgroups of asocial group (e.g., within the poor).

Decomposability

Decomposition as a property of statisticalmeasures is common in both economics andepidemiology. In economics, it typically refers tothe ability to decompose a measure of disparity bysources of income or into between-group andwithin-group partitions (40). Decomposabledisparity measures are seen as advantageous asthey can offer information about the sources ofincreasing or decreasing disparity as indicated in asummary statistic. In public health,decomposition often is used to capture differencesin summary rates. For example, a difference inage-adjusted mortality rates between twopopulations can be “decomposed” into differencesbetween mortality rates and differences in agestructure.

Scale Independence

Scale independence (or invariance) often is seenas a desirable property of disparity measures. Itoften is argued that, all else being equal, ifeveryone’s health “doubles,” the disparitymeasure should remain unchanged. It is arguable,however, whether for public health, where we alsoare concerned about the absolute level of illhealth, this is a desirable property.

30

Transparency/Interpretability forPolicy Makers

Finally, it seems salient that an interpretabilitycriterion be included as a factor in decisions aboutmeasures of disparity. For instance, despite otherdesirable properties, the actual value of moresophisticated summary measures such as theConcentration Index have no obviousinterpretation and thus may makecommunicating health disparity indices to thecommunity and policy makers potentially more

difficult. Thus, the extent to which differentmeasures of disparity can be captured graphicallyto aid communication might be important indeciding which measures are most appropriate formonitoring cancer-related health disparities.Perhaps the use of real-time graphical displays ofchanges in outcomes of interest may aid theunderstanding of health disparity. This dimensionof health disparity monitoring should not beunderestimated, as evidenced by the lack ofgeneral application of more sophisticated disparitymeasures in health disparity research.

31

33

Measures of Health Disparity

This section reviews most of the statistics that areavailable to measure health disparities. The goal isto provide a brief overview of each measure,followed by the method of calculation andstatistical interpretation and, often, an example ofits actual or potential use for measuring disparitiesin cancer-related health objectives.

Note that there are methods to calculateindicators of precision (e.g., 95% confidenceinterval) for all of the measures reviewed here.These can be found in the source publicationsdetailed in the references. Although issues ofvariability and precision are important, they arenot germane to the choice of disparity measurebecause they ultimately derive from the precisionof the underlying rates, prevalence, andproportions that are used to generate a particulardisparity measure.

Measures of Total Disparity

A measure of “total disparity” in health is asummary index of health differences across apopulation of individuals. Generally, measures oftotal disparity do not account for social groupingand have been used chiefly by health economists(see, for example, 25,49). They are an importantfirst step in understanding the scope of healthvariation in a population and have advantageousproperties for monitoring trends, particularly forcross-country comparisons. They do not, however,inform about systematic variation in health

among population subgroups, which is inherentin the Healthy People 2010 health disparityinitiatives. The measurement of health disparityas total disparity is associated most closely withand endorsed by the WHO as a component of itsgeneral framework for routinely assessing theperformance of health systems in differentcountries. The WHO, however, is not the onlyadvocate of measuring total disparity. Somehealth economists also advocate for themeasurement of total health disparity (25,63,64)as the primary form of assessing healthinequalities.

A number of criticisms have been levied atthis kind of measure, primarily because it does notdistinguish among individuals from differentsocial groups (51,53,54,65). In addition, empiricalinvestigations using measures of total disparityappear difficult to interpret (54,66,67). Those whoendorse this measure often cite as their primaryjustification the weighty normative choices thatmust be made to measure health differencesbetween social groups and note that the absenceof such a priori choices makes disparity betweenindividuals a more “objective” measure of healthdisparity. We recognize that Healthy People 2010specifically calls for social-group monitoring andnot total variation, but we include measures oftotal group disparity because they are prominentin the overall framework of efforts to monitorglobal health disparity and because they providean essential context for understanding the

“decomposition” of health disparity measures, asdescribed below.

Individual-Mean Differences

Individual-mean difference (IMD) measures ofhealth disparity calculate the difference betweenthe health of every individual in the populationand the population average. The general formulafor the class of individual/mean differencemeasures is given by Gakidou and colleagues (49)as:

[1]

where an individual i’s health is yi, µ is the meanhealth of the population, and n is the number ofindividuals in the population. The parameters α

and β specify, respectively, the significanceattached to health differences at the ends of thedistribution relative to the mean and whether theindividual-mean difference is absolute or relativeto the mean health of the population. Forinstance, large values of α emphasize greaterdeviations from the mean, and larger values of β

emphasize relative disparity because of heavierweighting of the mean. Those familiar with basicstatistics will note that, when α = 2 and β = 0, theIMD simply is the variance; and when α = 2 andβ = 1, the IMD is the coefficient of variation (49).Similar to many other disparity measures, the IMDis a “dimensionless” index that is not measured inunits because it always is relative to the mean inthe population.

Inter-Individual Differences (IID)

The IID measures health differences between allindividuals in the population and is consistentwith the Gini coefficient but may be weighted inaccordance with differential aversion to disparity(i.e., the value chosen for α). These measures aredifferent from the IMD class because theycompare every individual in the population withevery other individual in the population, whereasthe IMD measures disparity relative to thepopulation average. It should be clear thatdifferent measures of disparity implicitly expressdifferent perspectives on which aspects ofdisparity should be emphasized in the measure.The class of inter-individual difference measures is(49):

[2]

where yi is individual i’s health, yj is individual j’shealth, µ is the mean health of the population,and n is the number of individuals in thepopulation. The parameters α and β are defined asfor the IMD above, and it is worth noting that,when α = 2 and β = 1, the IID is equal to the morewell-known Gini coefficient. Gakidou and Kinghave used this disparity measure (with α = 3 andβ = 1) to compare total disparity in child survivalamong 50 countries (68). Weighting α = 3 impliesthat the measure should be more sensitive tolarger than smaller pairwise deviations betweenindividuals and thus reflects additional concernabout larger health differences betweenindividuals. To our knowledge, there is only onestudy of total disparity that uses data from theUnited States (69).

IID( ) = | yi – yj |

2n2 µα,β

αΣj = 1

n

Σi = 1

n

β

IMD( ) = | yi – µ |

nµα,β

αΣi = 1

n

β

34

Measures of Social-Group Disparity

The measures of total variation described abovehave a number of merits, including their ability tomake unambiguous health disparity comparisonsbetween populations and over time. In defininghealth disparity as disparity between individualsinstead of between social groups, such measuresavoid the difficulty of comparability of groupsbetween populations or over time (50). Thismakes them particularly attractive for cross-country comparisons, in which definingcomparable social groups is challenging becauseof differences in how social groups are classifiedin different countries (70).

The disparity goals of Healthy People 2010,however, explicitly are goals that relate to social-group differences in health. It is an open questionas to whether measures of total disparity andsocial-group disparity are “better” or “worse”disparity measures, but the concern among healthpolicy makers in the United States specifically isexpressed in terms of social-group differences inhealth. Measures of total disparity therefore areinsufficient for monitoring progress towardeliminating cancer-related health differencesamong social groups in the United States.

Pairwise Comparisons

Simple comparisons of some health indicatorbetween two groups in a population (so-calledpairwise comparisons) clearly are one of the moststraightforward ways to measure progress towardeliminating disparities between groups. Forexample, age-adjusted incidence rates of lungcancer for black and white females in 1973 were,

respectively, 23.6 and 20.4 per 100,000. By 1999,rates for both groups had increased, to 57.0 forblacks and 52.3 for whites (71). It would seemeasy enough to answer the question: Did black-white disparity grow from 1973 to 1999?Unfortunately, however, the answer depends onthe measure of disparity. If the disparity measureis the absolute difference between the black andwhite rates, then we would conclude that theblack-white disparity increased from 3.2 to 4.7.If the disparity measure is the relative differencebetween the black and white rates (i.e., blackrate ÷ white rate), however, we would concludethe opposite because the relative disparitydecreased from 1.16 to 1.09. Both answers arecorrect. This has been a source of continuingconfusion and sometimes unresolved debate inthe health disparities literature (72,73) and,although most of the empirical work in healthdisparities has been in terms of “relativedisparity,” it should always be kept in mind thatlarge relative differences can mask very smalldifferences in absolute terms, which can bemisleading with respect to the disparity’spopulation-health impact. Conversely, there maybe situations where large relative disparities maybe viewed as grossly unjust, despite the fact thatthey reflect small absolute differences.

Absolute Disparity

The absolute disparity between two health-statusindicators is the simple arithmetic difference. It iscalculated as:

[3]

where r1 and r2 are indicators of health status intwo social groups. In this case, r2 serves as thereference population, and the AD is expressed in

AD = r1 – r2

35

the same units as r1 and r2. A typical disparitymeasure that uses the absolute difference betweentwo rates for an entire population is the range,where case r1 above corresponds to the least-healthy group and r2 to the most-healthy group.

Relative Disparity

For the same pairwise group comparison inequation [3], we also can divide r1 into r2 tocalculate the relative disparity as:

[4]

where, again, r2 is the reference population. Thisrate ratio can be transformed easily into apercentage difference by multiplying the ratio by100. Figure 10 shows the absolute and relative

black-white disparity for prostate and stomachcancer incidence from 1992–1999. Clearly, there isa much larger absolute disparity in prostate cancerincidence because the rates for both groups arerelatively high compared to the stomach cancerrates; however, the relative disparity is larger forstomach cancer.

Regression-Based Measures

One drawback of the pairwise comparisonmeasures of disparity is that, when a social grouphas more than two subgroups (as most do),information on the other groups is ignored.Normally it is desirable to use as much of theinformation present in the data as possible. If we

RD = r1/r2

36

Figure 10. Absolute and Relative Black-White Disparities in Prostate and Stomach Cancer Incidence,1992–1999

Prostate

300

250

200

150

100

50

0

Rat

e pe

r 10

0,00

0

Stomach

Black

White

Figure 10. Absolute and Relative Black-White Disparities in Prostate and Stomach Cancer Incidence, 1992-1999

Absolute DisparityRelative Disparity

Prostate Stomach

102.41.6

6.01.8

compare the “best” group to the “worst” group,we effectively ignore the information on thehealth status of all the groups in between, asidefrom knowing that they fall somewhere betweenthe best and worst groups. One possible solutionwould be to calculate a series of (j–1) pairwisecomparisons for j groups using one group as thereference point, or j pairwise comparisons usingan external reference point. Although feasible, asthe number of groups, time periods, or bothincreases, attempting to evaluate the disparitytrend may become complicated in terms ofsummarizing the many pairwise comparisons. Toovercome this limitation and make use of theinformation for all groups, one might considercalculating a summary measure of disparity. Thischoice, however, undoubtedly involves additionalcomplexity and assumptions that must be tradedoff against the insights about disparity gleanedfrom the use of a summary measure (74).

Simple Linear Regression

If one is willing to assume that the relationshipbetween social group and health status is linear(i.e., that each step up the social-group scaleresults in an equivalent health gain/loss), then apotential way to include information on all of thegroups is to calculate a summary measure ofdisparity using regression. One way of writing thisis:

[5]

where yi is a measure of health status forindividual i, β0 is the value of the health variablewhen Xi is 0 (e.g., if Xi is a continuous measure ofincome, then β0 is the health status of anindividual with zero income), Xi indexes socialgroup, and β1 is the summary measure ofdisparity. In general terms, β1 is equal to the

covariation of Xi and yi expressed in terms of thevariance of Xi. The specific interpretation of β1

depends on the particular health status measureused and the specification of the model. If yi is anuntransformed health status measure—forexample, BMI—then β1 is the absolute increase inBMI associated with a one-unit change in socialgroup and is referred to as a Regression-BasedAbsolute Effect or RAE (70). It is an absolutemeasure because it is expressed in the same unitsas the quantity of health measured in yi.Continuous types of health outcomes, however,are relatively less common in the area of cancer-related data. More likely are noncontinuous typesof health data (e.g., the presence or absence ofcancer, receipt or nonreceipt of screening), wherethe linear relationship in equation [5] applies tosome transformation of the dependent variable yi.For transformations of the dependent variable yi

(e.g., the logarithmic or logit transformation),β1 then becomes a relative-risk (logarithmictransformation) or odds-ratio (logittransformation) and is interpreted as theproportional increase in health status for a one-unitchange in social group and referred to as aRegression-Based Relative Effect or RRE (70).Figure 11 (page 38) graphically shows a simpleregression-based disparity measure, applied in thiscase by Steenland et al. to the risk of lung canceramong men of different education groups(grammar, some high school, high-schoolgraduate, some college, college graduate) in the1982–1996 Cancer Prevention Study II (36). They-axis is the risk of mortality relative to thosecompleting graduate school (whose relative risk isby definition equal to 1.0), the x-axis is theapproximate number of years of education foreach education group (Xi in equation [5]), and thefitted line indicates the linear decrease in relative

yi = 0 + β 1X i β

37

risk—which Steenland and colleagues reported asabout 10%—for each 1-year increase in thenumber of years of education. (It is important tonote that, for ease of presentation, the plottedpoints in Figure 11 show only the average relativerisk for each education group. The actualregression equation is performed on all 500,000 orso individuals in the CPS-II.) Relative-effectmeasures also may be transformed into absoluteeffect measures by applying them to the rates ofhealth in the referent social group. An additionaldrawback to the RAE and RRE is that theassumption of linearity between health and socialgroup may be problematic. For example, whileKunst and colleagues find linear associations

between education and self-rated health (75),Manor et al. report nonlinearity betweeneducation and a number of chronic conditions(76), and Backlund and colleagues report anonlinear association between income andmortality (77).

Slope Index of Inequality

The regression-based methods outlined above,subject to the assumptions of the model, workwell for calculating a summary measure of healthdisparity at a single point in time. As noted above,however, over time the distribution of thepopulation in various social groups may change

38

Figure 11. Example of a Simple Regression-Based Disparity Measure

0

3.0

2.8

2.6

2.4

2.2

2.0

1.8

1.6

1.4

1.2

1.0

Rel

ativ

e R

isk

of M

orta

lity

182 4 6 8 10 12 14 16Years of Education

Systematic Association Between Education and Lung Cancer Mortality Risk

Figure 11. Example of a Simple Regression-Based Disparity Measure

Source: Adapted from Steenland et al. Am J Epidemiol 2002;156:11-21.Source: Adapted from Steenland et al. Am J Epidemiol 2002;156:11–21.

drastically, and it would be advantageous for ameasure of health disparity to be sensitive to suchchanges. One measure that does so is the SlopeIndex of Inequality (SII). To calculate the SII, thesocial groups first are ordered from lowest tohighest. The population of each social-groupcategory covers a range in the cumulativedistribution of the population and is given a scorebased on the midpoint of its range in thecumulative distribution in the population. Forexample, in the 2001 NHIS those with an income-to-poverty ratio of less than 0.5 (approximately<$9,000 for a family of four) were 3.45% of thepopulation, and those in the next highest incomegroup—with an income-to-poverty ratio of 0.5 to0.74—comprised 3.02%, in which case the lowestgroup is assigned a score of [0 + (.0345 – 0)/2] =.0173, and the next lowest group is assigned ascore of [.0345 + (.0647 – .0345)/2] = .0496.

Health status then is plotted against thismidpoint socioeconomic category variable, and aregression line is fitted to the data. The SII thus issimilar to the regression-based methods above,but differs because it uses the midpoint of thecumulative social group distribution and becauseit (usually) is based on grouped data and is aweighted index, where the weights are based onthe size of the social groups. By weighting socialgroups by their population share, the SII is able toincorporate changes in the distribution of socialgroups over time that affect the population healthburden of health disparities. Figure 12 (page 40)shows the predicted slope for the income disparity(based on income-to-poverty ratio) in currentsmoking for the United States in 2001. Note that,in Figure 11, the location of the data points onthe x-axis is based on the estimated number of

years of education, whereas in Figure 12, thelocation is based on the group’s share of thepopulation. This reflects the fact that theeducation groups actually comprise differentproportions of the population distribution.Formally, the SII, which was introduced byPreston, Haines, and Pamuk (78), may be ob-tained via regression of the mean health variableon the mean relative rank variable:

[6]

where j indexes social group, is the averagehealth status, is the average relative ranking ofsocial group j, β0 is the estimated health status of ahypothetical person at the bottom of the socialgroup hierarchy (i.e., a person whose relative rankRj in the social group distribution is zero), and β1

is the difference in average health status betweenthe hypothetical person at the bottom of thesocial group distribution and the hypotheticalperson at the top (i.e., Rj = 0 vs. Rj = 1). Becausethe relative rank variable is based on thecumulative proportions of the population (from0 to 1), a “one-unit” change in relative rank isequivalent to moving from the bottom to the topof the social group distribution. Because thisregression is run on grouped data (as opposed toindividual data as in equation [5]), it is estimatedvia weighted least squares, with the weights equalto the population size nj of group j (60). Thecoefficient β1 in equation [6] is the SII, which isinterpreted as the absolute difference in healthstatus between the bottom and top of the social-group distribution. Thus, the regression equationin Figure 12 shows that the absolute difference inthe prevalence of smoking across the entire

Rj yj

yj = 0 + β 1R j β

39

distribution of income is –18.1 percentage points.The same regression also may be run onindividual data (as in equation [5]), but replacingXi with Ri, with Ri being an individual’s relativerank in the social-group distribution. In this case,the data would be self-weighting and could beestimated by ordinary least squares.

Relative Index of Inequality

The SII discussed above is a measure of absolutedisparity. Dividing this estimated slope by themean population health, however, provides a

relative disparity measure, the Relative Index ofInequality or RII (79):

[7]

where µ is mean population health and the SII isthe estimate of β1 from equation [6]. Itsinterpretation is similar to the SII, but it nowmeasures the proportionate (in regard to theaverage population level) rather than the absoluteincrease or decrease in health between the highestand lowest socioeconomic groups. In the incomeand smoking example seen in Figure 12, the RII iscalculated as –18.1/24.6 = –0.74, indicating that a

RII = SII / 1 /βµ = µ

40

Figure 12. Income-Based Slope Index of Inequality for Current Smoking, NHIS, 2002

0.0

40

35

30

25

20

15

10

5

0

Per

cent

of C

urre

nt S

mok

ers

1.00.2 0.4 0.6 0.8

Cumulative Percent of Population, Ranked by Income-to-Poverty Ratio (X)

ObservedPredicted

Figure 12. Income-Based Slope Index of Inequality for Current Smoking, NHIS, 2002

Average Smoking Rate = 24.6SII = –18.1RII = –0.74

y = 33.7 - 18.1x

move from the bottom to the top of the incomedistribution is associated with a 74% decline inthe prevalence of smoking. Kunst andMackenbach (70) modified this definition of theRII slightly by dividing the estimated health of thehypothetical person at the bottom of the social-group distribution by the estimated health of thehypothetical person at the top of the social-groupdistribution:

[8]

where β0 and β1 are defined as in equation [6].From Figure 12, this is calculated as 33.7/(33.7 –18.1) = 2.16, indicating that the rate of smoking is2.16 times higher at the bottom of the incomedistribution than at the top. Thus, the Kunst-Mackenbach RII is more like a traditional relativerisk measure in that it compares the health of theextremes of the social distribution, but it isestimated using the data on all social groups andis weighted to account for social-group sizes. Asnoted above, the use of the SII and RII indices (aswell as the Health Concentration Index discussedbelow) depends on having a social-groupclassification scheme that is hierarchical. Thisseems straightforward with respect to educationand income, but social-group classifications basedon occupation may be somewhat morechallenging because there inherently is moreambiguity in the ranking of occupations (80). Intheir international study of occupationalmortality differences, Kunst and Mackenbach (81)note this difficulty as a possible explanation forthe lack of consistency of their results with thoseof Wagstaff for the size of disparity in Finlandversus England and Wales (60).

Population Impact Measures

Population Attributable Risk

The Population Attributable Risk (PAR) and itsrelative analogue, the PAR%, are longstandingepidemiologic measures of the population burdenthat is associated with differential health betweengroups. Although typically applied to groupsdefined by their exposure status (e.g., comparingsmokers with nonsmokers), it also may be appliedin the context of health differences between socialgroups (poor vs. nonpoor). It is a summary ofdifferences between each social group’s health andthe health of the “best” group. For example, itindicates the absolute (or relative, in the case ofthe PAR%) aggregate health improvement thatwould be obtained if all education groups had thehealth of the healthiest education group. Thebasic formulas for PAR and PAR% as healthdisparity indicators (70) are:

[9]

[10]

where rpop is the rate in the total population andrref is the rate of health or disease in the referencegroup, typically the best-off social group. Whilenot immediately clear from the above formula,the PAR% in fact is a population-weighted (bysocial-group size) sum of the relative risks (RRs) foreach group (13) and also may be written as:

[11]

where pj is the group’s population share and RRj isthe relative rate of group j compared to thereference group. To see this, note that we could

PAR% = pj (RRj – 1)Σ

pj (RRj – 1) + 1Σ

PAR% = rpop – rref

rpop

PAR = rpop – rref

RIIKM = = 0 + SIIβ1β

0β

0 + β0β

41

substitute rj/rref for RRj and rref /rref for 1 in equation[11] and multiply through by rref to get:

[12]

Because and , equation[12] reduces to equation [10]. The PAR% variesfrom 0 to 100 and is interpreted as the percentimprovement in the health of the totalpopulation that would be achieved if all socialgroups had the rates of health in the best-offsocial group, a commonly used metric for

describing the impact of health disparities. Forexample, Navarro argues that “the interventionthat would add the most years of life to thepopulations of Spain or the USA (or, for thatmatter, any other country) would be one thatwould lead to all social classes having the samemortality rates as those at the top” (65, page1701). In the example in Figure 13, thepopulation average rate of cervical cancer wouldbe improved by 28% if all social groups had therate experienced by American Indians and AlaskaNatives.

Σ pj rref = rrefΣ pj rj = rpop

PAR% = pj (rj – rref )Σ

pj (rj – rref ) + rrefΣ

42

Figure 13. Example of the Population-Attributable Risk Percent

Total

18

16

14

12

10

8

6

4

2

0

Inci

denc

e R

ate

per

100,

000

API**Non-HispanicWhite

Black Hispanic AI/AN*

9.6

6.9

Figure 13. Example of the Population-Attributable Risk Percent

Cervical Cancer Incidence by Race and Hispanic Origin, 1996–2000

PAR% = (9.6 – 6.9) / 9.6 = 28.1%

Observed RatesIf All Groups Had Best Rate

* American Indian/Alaska Native** Asian/Pacific IslanderSource: SEER Cancer Statistics Review, 1975–2000.

*American Indian/Alaska Native**Asian/Pacific IslanderSource: SEER Cancer Statistics Review, 1975–2000.

Index of Dissimilarity

The Index of Dissimilarity (ID) originally wasdeveloped as a measure of residential segregationof population groups (82). For example, in thecontext of black-white segregation amongneighborhoods within a city, the ID measures theproportion (using the relative version) or number(using the absolute version) of blacks (or whites)that would have to move to a differentneighborhood to achieve a racial distribution ineach neighborhood that was similar to that of thecity as a whole. As such, the ID is a summarymeasure of the disparity between eachneighborhood’s racial composition and the racialcomposition of the city as a whole. Similarly, inthe context of health disparity measurement, wecan think of the ID as a summary measure of thedisparity between, for example, each racial group’scancer rate and the cancer rate of the wholepopulation. In this case, the ID would beinterpreted as the number or proportion of cancercases that would have to be redistributed acrossracial groups for each group’s cancer rate to be thesame as the rate in the whole population. Theformula for the relative ID with respect to healthis given in Wagstaff and colleagues (60) as:

[13]

where j indexes social groups, sjh is the jth group’sshare of health (e.g., share of all cancer cases), andsjp is the jth group’s share of the total population.According to Kunst and Mackenbach (70),equation [13] is the relative version of the ID. Therelative ID compares how each social group’sshare of the population’s health compares with itsshare of the total population and represents theproportion of all cases (e.g., the proportion of all

cancer cases) that would have to be redistributedacross social groups so that each group has thesame rate as the total population. The absoluteversion of the ID is calculated as:

[14]

where dj and pj are, respectively, the observednumber of cancer cases and the population of thejth social group, rpop is the cancer rate in the totalpopulation, so that pjrpop is the expected numberof cancer cases that would be observed if group jhad the same cancer rate as the total population.One could also derive the absolute version of theID by multiplying the relative ID by the totalnumber of cases to determine the absolutenumber of cases that need to be redistributedacross groups.

Table 1 on page 44 shows how one mightcalculate the absolute and relative ID foresophageal cancer incidence among working-age(ages 25–64) racial groups during 1992–2000. Acomparison of columns (3) and (5) shows that theshare of cancer cases is lower than the share ofthe SEER population for all groups except blacks,who represent 13.5% of all esophageal cancercases but only 10.5% of the population. Similarlyfor the absolute ID, a comparison of columns (2)and (6) shows that if all groups experienced thepopulation rate of esophageal cancer, more caseswould be observed for all groups except for blacks.The relative ID in this case is 3.4, which meansthat 3.4% of the 17,186 cases of esophagealcancer need to be redistributed across racialgroups to eliminate the racial disparity. Inabsolute terms, this means redistributing 592cases of esophageal cancer.

Absolute ID = | dj – pj rpop |21 Σ j = 1

J

Relative ID = | sjh – sjp |21 Σ

j = 1

J

43

Index of Disparity

The Index of Disparity, which we will abbreviateas IDisp to distinguish it from the Index ofDissimilarity (ID), summarizes the differencebetween several group rates and a reference rateand expresses the summed differences as aproportion of the reference rate. This measure wasformally introduced by Pearcy and Keppel (30)and is calculated as:

[15]

where rj indicates the measure of health status inthe jth group, rref is the health status indicator inthe reference population, and J is the number ofgroups compared. Although in principle anyreference group may be chosen, the authorsrecommend using the best group rate as thecomparison because that represents the ratedesirable for all groups to achieve. In this case, itis not necessary to take the absolute value of therate differences because they all will be positive.Other potential reference rates include the totalpopulation rate, the average of group rates, orsome external target rate. A similar disparitymeasure was developed by Gaswirth (83), but itweights each group’s deviation from the best rate

by its population size, so that the disparity index(U) becomes:

[16]

where pj is each group’s population size. In thiscase, U is calculated as the weighted sum of thehealth difference between each group and thereference group. Similar to the Index of Disparity,above, this value also can be expressed relative tothe health status of the total population, whichGaswirth defines as G = U ÷ rpop. For example,Gaswirth applied this disparity measure to rates ofmammography screening among non-Hispanicwhite, non-Hispanic black, Hispanic, and Otherwomen ages 50–65 in the 2000 NHIS (83). Theoverall screening rate was 78.6%, and Figure 14(page 45) shows that white women had thehighest rates of screening (81%). The fraction ofthe entire population that is “underserved” (U,the shaded area in Figure 14) in this case is 2.04%,and if the population screening rate wereincreased by G = 2.6% and targeted to minoritywomen, the screening disparity would have beeneliminated. This measure has the additionaldesirable feature of intuitive graphicalrepresentation. Although not immediately clearfrom equation [16], however, it should be noted

U = pj (rj – rref )Σj = 1

J – 1

IDisp = | rj – rref | / J /rref x 100Σj = 1

J – 1( (

44

Table 1. Incidence of Esophageal Cancer, Ages 25–64 by Race, 12 SEER Registries, 1992–2000

% of % of Cases if

T otal T otal No ID IDRace Rate Cases Cases Population Population Disparity Relative Absolute

(1) (2) (3) (4) (5) (6) | (3) – (5) | | (2) – (6) |

American Indian/Alaska Native 5.7 133 0.8 2,316,609 1.3 226 0.5 93Asian/Pacific Islander 8.7 1,648 9.6 18,850,492 10.7 1,835 1.1 187Black 12.9 2,395 13.9 18,518,113 10.5 1,803 3.5 592White 9.5 13,010 75.5 136,864,686 77.5 13,323 1.8 313

T otal 9.7 17,186 100.0 176,549,900 100.0 17,186 3.4% 592

that, in practice, when the reference group is thegroup with the best rate, Gaswirth’s measure U isequivalent to the PAR described above, and G isequivalent to the PAR% because their calculationsare identical to the PAR and PAR%.

The Between-Group Variance

The variance is a commonly used statistic thatsummarizes all squared deviations from apopulation average. In the case of grouped data,this is the Between-Group Variance (BGV), and itis calculated according to the following formula

that squares the differences in group rates fromthe population average and weights by theirpopulation sizes:

[17]

where pj is group j’s population size, yj is group j’saverage health status, and µ is the average healthstatus of the population. The Between-GroupVariance may be a useful indicator of absolutedisparity for unordered group data because itweights by population group size and is sensitiveto the magnitude of larger deviations from the

BGV = pj ( yj – µ)2Σj = 1

J

45

Figure 14. Disparity in Mammography Screening Among Racial/Ethnic Groups, NHIS, 2000

0.0

1.0

0.8

0.6

0.4

0.2

0.0

Pro

port

ion

Hav

ing

a M

amm

ogra

min

the

Pre

viou

s 2

Year

s

1.00.2 0.4 0.6 0.8

O H B W

U = Fraction of the Entire Population“Under-treated” Relative to the Best Group

Subpopulations in Order of TheirMammogram Screening Rates

Figure 14. Disparity in Mammography Screening Among Racial/Ethnic Groups, NHIS, 2000

Source: Gastwirth JL. Prev Med (forthcoming).

U

Source: Gastwirth JL. Prev Med (forthcoming).

population average. As an example, Figure 15shows trends in age-adjusted lung cancermortality among U.S. Census divisions.

The between-region variance in lung cancermortality in 1968 was 7.1 deaths per 100,000, butin 1998 the BGV was 22.8 deaths per 100,000.This larger absolute disparity in regional mortalityindicates divergent regional trends in lung cancerover time (see Figure 15). The use of the varianceas a measure of disparity in economics sometimesis discouraged because it is not “scale invariant.”In other words, it is sensitive to absolute changes,such as when everyone’s income doubles overtime. In this case, economists sometimes feel that

it is not desirable for the disparity measure also todouble, because relative inequality is maintained.Although this may be an undesirable propertywhen dealing with income disparity, however, webelieve it is not necessarily a limitation fordiscussing health disparity, in which we areinterested in absolute disparity burdens (84). Froma population health perspective, in which we maybe concerned with the health care implications ofincreasing absolute disparity, we may care aboutsituations in which the absolute disparityincreases, and it is appropriate that the disparityindicator reflect this increased concern. In thiscase, then, using the variance (which squares theabsolute deviations from the population average)

46

Figure 15. Age-Adjusted Lung Cancer Mortality by U.S. Census Division, 1968–1998

1968

80

70

60

50

40

30

20

10

0

Rat

e pe

r 10

0,00

0

20001972 1976 1980 1984 1988 1992 1996

Figure 15. Age-Adjusted Lung Cancer Mortality by U.S. Census Division, 1968-1998

Source: NCHS. Compressed Mortality Files 1968-1998

East North CentralEast South CentralMiddle AtlanticMountainNew EnglandPacificSouth AtlanticWest North CentralWest South Central

Source: NCHS. Compressed Mortality Files 1968–1998.

is consistent with a population health perspective.In the example above of changes in regional lungcancer disparity, the overall rates increase by 70%,the coefficient of variation (the variance dividedby the mean) increases by 89% (indicating thatrelative disparity increases as well), but thevariance increases by 320%. Thus, choosing thisas the measure of disparity reflects our concernswith widening absolute differences among theregions.

Measures of AverageDisproportionality

When describing health inequalities, publichealth researchers and policy makers often usewhat might be called the “language ofdisproportionality.” For example, in the context ofarguing for the importance of measuring healthinequalities between socially meaningfulpopulation groups, Braveman and colleaguesstated that “a disproportionate share of ill-healthand premature mortality is borne by the sociallydisadvantaged” (51, page 233). Similarly, indiscussing health disparity trends, the Secretary ofHealth and Human Services recently noted thatvarious racial/ethnic groups in the United States“suffer an unequal burden of death and disease,despite improvements in the overall health of thegeneral population over the past decade” (85).The terms “disproportionate share” and “unequalburden” are important descriptors because theycommunicate the ethical notions inherent in thecollective concerns over health disparities. That is,they capture the notion that it is unfair that somegroups experience more ill health than others; ajust distribution of health implies that ill health

should be experienced proportionately bydifferent social groups. A more explicit examplecan be found in the Guidance for the U.S. NationalHealthcare Disparities Report in which, in discussingthe disparity in cardiac catheterization ratesbetween blacks and whites, LaVeist states that the“degree to which the predicted percentage ofcatheterization deviates from the observedpercentage indicates the degree of disparity,” andconcludes that “African Americans received 67%of the catheterizations that they should havereceived, and whites received 14% more thantheir share” (86, page 90).

The quotations above make clear that healthdisparity often is equated with the concept ofdisproportionality. What is perhaps less clear isthat, in the context of the commonly used“language of disproportionality,” there usually isan implied reference group, which is the generalpopulation. In fact, in the catheterizationexample, LaVeist was arguing explicitly againstmeasuring health disparity using a relativemeasure such as a risk ratio or odds ratio, becausedoing so means using a particular social group (inthis case, whites) as the reference group, whichnecessarily assumes that the rate in the referencegroup is “most desirable.” Thus, he argued thatdisparity measures that use whites as the referencegroup would not be able to identify their “over-utilization” of cardiac catheterization. Theintuitive ethical notion expressed in thequotations above is that the amount of ill healthin social group j is far greater than would beexpected if ill health were evenly distributed withrespect to all J social groups. An even distributionof ill health across J social groups implies that the

47

number of individuals of social group j withcondition y is proportionate to group j’s share ofthe total population, so that the rate of ill health,Yj, in each of the j groups is exactly the same,which would necessarily equal the rate in thetotal population. Thus, the proportionaldistribution of y among J groups implies that

(the mean of y) for all groups.

This is an important point because manycommonly used measures of income disparity(e.g., the Gini coefficient) and residentialsegregation (e.g., the Index of Dissimilarity), someof which currently are employed to measurehealth disparities, may be expressed convenientlyas measures of average disproportionality (87–89).For each social group j, we can define a health (orill health) ratio as the ratio of measure y in the jthgroup to that of the mean of y for the wholepopulation, so that for each group. Notethat this makes such measures relative rather thanabsolute disparity indicators. In this framework,measures of disparity take the general form

[18]

where pj is group j’s proportion of the totalpopulation and f(rj) is some disproportionalityfunction of the ratio . It should be clearthat equation [18] is a weighted disparity measurebecause each group’s disproportionality functionf(rj) is multiplied by its population share pj.Measures of this type of disparity indicator differbecause they implement different disproportion-ality functions. Perhaps one of the appealingfeatures of such measures is that they provide arather direct correspondence between the

commonly used languages of health disparity interms of “disproportionality” with theoperationalization of the measurement.

Figure 16 (page 49) depicts the concept of“disproportionality” using data on all deaths inthe United States, by gender and education, forthe year 2000. Among males, those with less than12 years of education bear a disproportionateburden of all deaths, as they account for 24% ofall male deaths but account for only 12% of themale population. Conversely, males with greaterthan 12 years of education account for 55% of thetotal population but only 32% of all deaths. Thelevel of disproportionality for females with lessthan 12 years of education is slightly smaller.

Table 2 (page 49) shows some commonlyused statistical measures and theirdisproportionality functions. Readers should notethat the measures differ only in how they expressthe difference between shares of health and sharesof population.

Entropy Indices

One class of disproportionality measures thatoften is favored by economists are measures ofgeneral entropy, developed by Henri Theil (90).The example described below is for measuring thedisparity in BMI, which is a risk factor for anumber of cancer sites (91,92). Theil’s index givesrelatively more weight to the concentration in theupper end of the health distribution and iscalculated (with grouped data) by summing theproduct of each group’s BMI share of thepopulation’s total BMI and the natural log of each

rj = Y j / Y

I = pj f ( rj )Σ j

rj = Y j / Y

Yj = Y

48

49

Figure 16. Example of the “Disproportionality” of Deaths and Population, by Gender and Education,2000

Deaths Population Deaths Population

Figure 16. Example of the “Disproportionality” of Deaths and Population, by Gender and Education, 2000

Source: NCHS. Deaths: Final Data for 2000, Natl Vit Stat Rep 2002;50(15).

Shares of All Deaths and Population, by Gender and Education, 2000

Males Females

>12 yrs >12 yrs

12 yrs 12 yrs

<12 yrs <12 yrs

32%

45%

24%

55%

32%

13%

33%

46%

21%

55%

32%

12%

Source: NCHS. Deaths: Final Data for 2000, Natl Vit Stat Rep 2002;50(15).

Table 2. Commonly Used Disproportionality Functions

Index Name Disproportionality Function

Squared coefficient of variation (CV 2) (rj – 1)2

Gini index (G) Individual-level data: | ri – rj | / 2Grouped data: rj(qj – Qj ), where qj is the proportion of the total population in groups less healthy than group j, andQj is the proportion of the total population in groups healthier than group j (i.e., pj + qj + Qj = 1)

Relative concentration index (RCI ) Same as for G, but groups are ranked by social group position instead of by health, so that qj is the proportion ofthe total population in groups less advantaged than group j, and Qj is the proportion of the total population ingroups more advantaged than group j (i.e., pj + qj + Qj = 1)

Theil index (T ) rj ln(rj )Mean logarithmic deviation (MLD) ln(1/rj ) = –ln(rj )Variance of log-health (VarLog) [ln rj – ∑(ln rj )]2

Note: Adapted from Firebaugh, 2003 (88).

group’s BMI share. For individual-level data, totaldisparity in BMI measured by Theil’s index can bewritten as

[19]

where pi is an individual’s population share(which in the case of individual data will be 1/n,so that pi = 1) and ri is the ratio of theindividual’s BMI to the population average BMI(i.e., ). When the population ofindividuals is arranged into J groups, Theilshowed that equation [19] is the exact sum of twoparts: between-group disparity and a weightedaverage of within-group disparity:

[20]

where Tj is the disparity in BMI within group j.The within-group component (the second termon the right side of equation [20] is weighted by,in this case, group j’s share of the total BMI,because (where sj is the share of totalBMI) when the denominator for rj is the meanBMI for the total population. More importantly,the above decomposition also makes it clear thatit is possible to calculate between-group disparityin BMI—the primary quantity of interest withrespect to social disparities in health—in theabsence of data on each individual. The only dataneeded are the group proportions and the ratio ofthe group’s BMI to the population average BMI.Between-group disparity, however, may increasebecause total disparity is increasing (i.e., bothbetween-group and within-group disparity areincreasing simultaneously). The primaryadvantage of using additively decomposableinequality measures is that they allow us todetermine not just whether between-group

disparity is increasing, but whether the share oftotal disparity that is due to disparity betweengroups is increasing or decreasing. Although thismeasure has attractive qualities, the between-group/within-group decomposition requirescontinuous outcome data measurable inindividuals, so it is not clear whether this can beapplied to many relevant cancer outcomes thatare based on events (e.g., incidence, mortality, orscreening). Even for noncontinuous outcomes,however, entropy indices easily can be used tocalculate between-group disparities in the absenceof individual-level data. For example, suppose thatinstead of BMI we wanted to measure thebetween-group disparity in obesity rates. We coulddo this by calculating the first term on the rightside of equation [20] using only the data on eachgroup’s proportion in the population (pj) and thegroup’s rate of obesity relative to the overallpopulation rate (rj)—data that are more likely tobe readily available.

Measuring between-group inequality in BMIin the above manner makes clear that changes inthe value of disparity over time are a function oftwo quantities: changing group proportions andchanging social group BMI ratios. This isimportant— in the case of obesity, for example—because differentiating between these twocomponents of change has different implicationsfor obesity as a public health problem and may bethe result of very different social policies. If wefind that disparity is increasing but that the mainreason for the observed change is that the share ofthe population among social groups at the tails ofthe BMI distribution has increased, it simplydemonstrates that the inequality increase is dueprimarily to the movement into and out of

pj x r j = s j

T = pj rj ln (rj ) + pj rjTjΣ j = 1

J Σ j = 1

J

ri = yi / Y

1n pj

sjsj ( (Σ

T = pi ri ln (ri )Σ i = 1

N

50

different social groups—not to differentiallyincreasing rates of BMI within subgroups of asocial group. However, if we find that populationshares have remained relatively constant overtime but BMI disparity has increased because BMIratios are increasing, this implicates differentialsources of BMI change among particular groups—which may then become the target of publichealth intervention.

Atkinson’s Measure

Atkinson’s index actually is not a single index ofdisparity but depends on specifying the relativesensitivity of the index to different parts of thedistribution. One way of writing Atkinson’s indexis:

[21]

where pj and rj are again, respectively, the share ofpopulation and the health ratio (relative to thetotal population rate), as defined above. Clearlywith this index, the extent of disparity hinges onspecifying the parameter ε, which indicates thedegree of “aversion to disparity.” Larger values of ε

indicate stronger aversion to disparity, which alsomay be interpreted as placing increased weight onthe least healthy groups. For example, if we areparticularly concerned about improving thehealth of least-healthy individuals, we could makethe measure of disparity more sensitive to changesin the bottom of the health distribution.

Gini Coefficient

The Gini coefficient summarizes social groupdifferences in, for example, BMI for the entirepopulation and can be thought of as a measure ofassociation between each social group’s share ofpopulation, ranked by the group’s health and its

share of health. Its formula for individual data isgiven above for the IID in equation [2], whenα = 2 and β = 1. Formally, the Gini coefficient isthe ratio of the area between the line of equalityin Figure 17 (page 52) and the Lorenz curve to thetotal area of the triangle beneath the line ofequality (40). Because the Gini coefficient is afunction of the disproportionality between sharesof population and shares of health, one can seefrom Figure 17 that health disparity increases asthe Lorenz curve moves further away from theline of equality (i.e., as the disproportionalitybetween shares of population and shares of healthincreases).

Concentration Index

The Concentration Index (CI) is calculatedsimilarly to the Gini index, but it results from abivariate distribution of health and social-groupranking. In the same way that the Gini coefficientis derived from the Lorenz curve, the CI is derivedfrom a concentration curve, where the populationis ordered first by social-group status (rather thanby health status, as for the Gini), and thecumulative percent of the population then isplotted against the group’s share of total illhealth. When the y-axis is the share of ill health,this results in the Relative Concentration Index(RCI); however, an Absolute Concentration Index(ACI) also may be derived by plotting thecumulative share of the population against thecumulative amount of ill health (i.e., thecumulative contribution of each subgroup to themean level of health in the population). Figure 18(page 53) gives a graphical representation of arelative concentration curve. Note the similaritywith the Lorenz curve drawn in Figure 17 toillustrate the Gini coefficient. The two curves and

A = 1 – [ pj rj

1 – ] , > 01 / [1 – ]Σ j = 1

J εε

ε

51

thus the Gini coefficient and the RCI arecalculated similarly, the only difference being theway in which social groups are ordered. In thecase of the Gini coefficient, social groups areordered by their health status (lowest to highest),regardless of their socioeconomic group ranking;for the RCI, social groups are ordered by theirranking in terms of, for example, years ofeducation, regardless of their health status. It isimportant to note that, because theConcentration Index incorporates informationon both health and social-group status, theconcentration curve may lie either above or below the line of equality. The general formula forthe Relative Concentration Index (RCI) for

grouped data is given by Kakwani and colleagues(93) as:

[22]

where pj is the group’s population share, µj is thegroup’s mean health, and Rj is the relative rank ofthe jth socioeconomic group, which is defined as:

[23]

where pγis the cumulative share of the population

up to and including group j, and pj is the share ofthe population in group j. Rj essentially indicatesthe cumulative share of the population up to themidpoint of each group interval, similar to thecategorization of the Slope and Relative Index of

Rj = pγ – p jΣ j = 1

J

21

RCI = [ pj j Rj]– 1Σ j = 1

J

µ µ2

52

Figure 17. Representation of the Gini Coefficient of Disparity

0 100

100

0

Cum

ulat

ive

Per

cent

of H

ealth

Cumulative Percent of Population, Ranked by Health

Figure 17. Representation of the Gini Coefficient of Disparity

Line of Equality

Lorenz Curve

Inequality above. In fact, the RCI has a specificmathematical relationship with the RII (60):

[24]

where R is the relative rank variable identified inequation [23]. Thus, the SII/RII and the ACI/RCIwill produce the same rank ordering of healthinequality over time but will differ in scale. Theabsolute version of the Concentration Index (ACI)is calculated by multiplying the RCI by the meanrate of the health variable:

[25]

where µ is the mean level of health in thepopulation. It also is worth pointing out that,when using continuous health outcomes, the RCI

is unbounded and takes minimum and maximumvalues of –1 and +1, but when using binary healthoutcomes, the possible values of the RCI arelimited by the mean (e.g., the prevalence) of thedistribution (94). Adam Wagstaff shows that, for agiven nonzero mean of a binary variable (µ), theminimum of the RCI is [ ] and themaximum is [ ], with n being thesample size. This of course has implications foranalyses that compare the extent ofsocioeconomic inequality in health between areasor outcomes with very different levels of averagehealth, and one potential strategy for facilitatingcomparisons is to normalize the ConcentrationIndex by dividing it by its bound (95).

1 – µ + (1/n)µ – 1 + (1/n)

ACI = µRCI

RCI = 2var(R)RII

53

Figure 18. Representation of the Health Concentration Curve

0 100

100

0

Cum

ulat

ive

Per

cent

of I

ll H

ealth

Cumulative Percent of Population, Ranked by Socioeconomic Position

Figure 18. Representation of the Health Concentration Curve

Disparities Favorthe “Worse-off”

No Social Disparity

Disparities Favorthe “Better-off”

Table 3 shows a simple example of how theRCI and ACI are calculated using equations [22]and [25] with grouped data using lung cancermortality rates by educational attainment. Onecan see that lung cancer mortality rates decreasewith increasing education, and the negative valueof both indices shows that the disparity in lungcancer mortality favors the better educated.

One of the reasons the ACI and RCI (and, byextension, the SII/RII indices) are favored by someis that they “reflect the socioeconomic dimensionto inequalities in health” (60, page 548). That is, adownward health gradient (such that healthworsens with increasing social-group rank) resultsin a positive index, whereas an upward healthgradient results in a negative index. For example,if the data in Table 3 were reversed so that lungcancer mortality rates for those with <12 years ofeducation were 16.9 and the rates were 49.8 forthose with >12 years of education, the RCI thenwould be calculated as 0.114 and the ACI as4.873, indicating that lung cancer mortalityactually favors the less educated. This sensitivityto the direction of the health gradient is not aproperty of other disproportionality measures,such as the Gini coefficient and the Index of

Dissimilarity, because they do not depend on thestrict ordering of social groups.

This undoubtedly is an advantage of the RCI,but, as with all disparity measures, it also may beseen as a disadvantage. Because of its sensitivity tosocioeconomic gradients in health, the RCI maynot register any disparity when health is notranked directly by social group. Thus, when asocial group ranked in the middle of a hierarchybears a disproportionate burden of ill health, theRCI well may register this as zero disparity. This isnot just a theoretical limitation of the RCI. Forinstance, age-adjusted rates of breast cancer deaths(per 100,000) in the United States in 1998 were20.0 among those with less than a high-schooleducation, 28.4 among those with a high-schooleducation, and 22.0 among those with at leastsome college education (9). If the respective sharesof the population in each of the education groupswere approximately 38.8%, 20%, and 41.2%, theRCI would be virtually zero, indicating noeducational mortality disparity; yet those with ahigh-school education will contribute roughly40.3% of breast cancer deaths. A reasonable casecould be made that a disproportionate burden ofbreast cancer falls on the high-school-educated

54

Table 3. Educational Disparity in Lung Cancer Mortality, 1999Education Rate per 100,000 Population Share Midpoint (%) CI

<12 years 49.8 0.128 0.064 0.40812 years 41.0 0.327 0.292 3.913

>12 years 16.9 0.545 0.728 6.699

T otal 29.0 1.0 1 1.020

Relative Concentration Index →→ –0.240

Absolute Concentration Index →→ –6.959

Note: Rates are for persons aged 25–64 years and exclude the following states: Georgia, Kentucky, Rhode Island, and South Dakota. Rate data are fromDATA2010…the Healthy People 2010 Database, April 2004 edition, and SEER*Stat. Population data are from NCHS, Deaths: Final Data for 1999: Table VII.

(using this categorization of education), but theRCI would not reveal this pattern. This pattern ofthe worst health among those in the middle socialgroup is not simply an artifact of breast cancer asan unusual cause of death. This pattern also isseen for colorectal and prostate cancers andmelanoma as well where rates across orderedsocial groups are not simple gradients.

We use the breast cancer example notnecessarily to suggest that the RCI is a poor indexfor measuring social-group disparities in health,but rather to emphasize that all disparitymeasures have advantages and disadvantages thatshould be considered when selecting andinterpreting a disparity index; no summarydisparity measure should be used as a substitutefor detailed inspection of the health statusindicators for each social group via tables andgraphs.

Wagstaff also derived a method forincorporating a society’s degree of aversion todisparity into the RCI, which he calls the“extended” Concentration Index (96). Theaversion parameter changes the weight attachedto the health of different socioeconomic groups ina manner similar to the Atkinson Index describedabove. The formula for this extended version ofthe RCI for grouped data is:

[26]

where ν is the “aversion parameter,” and the otherquantities are defined as in the RCI in equation[22] above. Setting ν = 1 weights every group’s

health equally (i.e., complete indifference toinequality), and setting ν = 2 gives the standardRCI defined above. As ν increases, the weightattached to the health of lower socioeconomicgroups increases, and the weight attached to thehealth of higher socioeconomic groups decreases.Table 4 (page 56) shows the effect of varying theweight placed on the health of the less-educatedgroups for the disparity in current smoking in thestate of Michigan in 1990 and 2002. The tworightmost columns are the calculated RCIs, withdiffering aversions to disparity. Setting ν = 2 givesthe standard RCI of –0.129, indicating that thedisparity in current smoking favors the bettereducated. Increasing the weight placed on thehealth of the less-educated groups in 1990 resultsin only a marginal increase in the measure ofdisparity to –0.178, most likely because the rate ofsmoking among those with <8 years of educationactually is quite low. The major effect of thedifferential weighting of the RCI can be seen inthe disparity change from 1990 to 2002; in 2002,the standard RCI(2) was –0.19, a disparity increaseof 48.5%, and the more bottom-sensitive RCI(4)was –0.32, indicating a much larger 81% increasein the relative education disparity in smoking.The reason the increase in disparity is so muchlarger for RCI(4) is that, although rates of smokingdecreased overall and in every other educationcategory, the estimated rate of current smokingactually increased among the least-educatedgroup. This example shows how we canincorporate an ethical judgment (particularconcern about the health status of the leasteducated) into a measure of health disparity.

RCI(v) = pj µj (1 – R j )v – 1Σ

j = 1

J

µvpj (1 – R j )

v – 1Σj = 1

J

v –

55

Combining Health Disparity and AverageHealth

As we emphasized in the above discussion ofrelative and absolute health disparities, the goalsof Healthy People 2010 are couched specifically interms of both health disparities and average levelsof population health. Thus, we also may beinterested in investigating potential ways toincorporate both average health and healthdisparity into a single summary measure. Onepotential measure, created by Adam Wagstaff, iscalled the Health Achievement Index or HAI (96).

The Health Achievement Index

The HAI in some respects is similar to the ACIdescribed above, but combines disparity andaverage health by essentially subtracting theAbsolute Concentration Index from the

population’s average health, creating a “disparity-discounted” level of average health. The formulafor the HAI is (96):

[27]

where µ is the population’s average health andRCI(ν) is the extended Relative ConcentrationIndex defined above. Thus, applying equation[27] to the data on the average rate andeducational disparity (using RCI[2]) in smokingin Michigan, the HAI(2) for Michigan in 1990is 0.29 x (1 – [–0.129]) = 0.33, and is 0.24 x(1 – [–0.191]) = 0.29 in 2002. Clearly, if RCI = 0,then the HAI is equal to the population averagerate of health, and the larger the RCI, the furtheraway the HAI is from the population average—akind of “disparity penalty” applied to thepopulation average rate. In this sense, the HAI is

HAI(v) = µ 1 – RCI(v)= µ – ACI(v)

56

Table 4. Example of Extended Relative and Absolute Concentration Index Applied to the Change inEducational Disparity in Current Smoking, Michigan, 1990 and 2002Education Population (%) % Smokers Midpoint (%) RCI ( νν = 2) RCI ( νν = 4)

1990

<8 years 4.5 27.2 2.3 0.006 0.0119–11 years 12.4 39.9 10.7 –0.082 –0.131

12 years 36.9 33.3 35.4 –0.068 –0.05713–15 years 27.3 29.6 67.5 –0.003 –0.00116+ years 18.9 13.6 90.6 0.019 0.000

T otal 100.0 29.1 –0.129 –0.178

ACI = –3.75 ACI = –5.162002

<8 years 2.0 36.6 1.0 –0.021 –0.0419–11 years 7.8 36.3 5.9 –0.073 –0.130

12 years 31.4 31.3 25.5 –0.137 –0.15213–15 years 29.6 24.5 56.0 –0.003 –0.00116+ years 29.2 12.2 85.4 0.042 0.002

T otal 100.0 24.2 –0.191 –0.321

ACI = –4.63 ACI = –7.77

Note: Data is for current smoking and is drawn from the 1990 and 2002 Behavioral Risk Factor Surveillance System (BRFSS).

not exactly a measure of health disparity but apotentially useful way of capturing bothaggregative (Healthy People 2010 Goal 1) anddisparity (Healthy People 2010 Goal 2) concerns ina single summary measure, at least with respect toordered social groups. For example, while bothrelative and absolute education disparity insmoking increased in Michigan over the 12-yearperiod (i.e., education disparity unambiguouslyincreased, see Table 4), health achievementactually improved because almost all educationgroups experienced a decrease in the rate ofsmoking (in this case, health “achievement”increases as the population rate of smokingdecreases).

Two populations (or time periods) thereforemight have the same value on the AchievementIndex but differ greatly on both average healthand the extent of health disparity. For example, inFigure 19 (page 58) the relative concentrationcurves for education disparity in obesity in NewYork State are plotted for 1990 and 2002. Becausethe 2002 curve is beneath the 1990 curve for everyeducation group, we can unambiguously declare

that relative education inequality in obesity inNew York decreased from 1990 to 2002. Thestandard RCIs summarizing the two curves alsoreflect the decrease in disparity, going from –0.284in 1990 to –0.125 in 2002. As was mentioned atthe outset, however, we do not believe thatdisparity is all that matters. We also are concernedwith the average health of the population, andthe estimated obesity rate in New York more thandoubled over this period, from 9.8% in 1990 to20.6% in 2002. Figure 20 (page 59) shows theabsolute concentration curves, which clearlyreflect the increase in obesity among all groups.Inspection of the education-group-specific obesityrates reveals that, in general, the educationdisparity in obesity declined because of increasingobesity rates, particularly among the middle- andbetter-educated groups. When we incorporate theadverse changes in overall population rates ofobesity with the changes in disparity, the changein the Health Achievement Index (for whichlarger values are worse because the healthoutcome, obesity, is negative) indicates thatthings became worse, having increased from 0.13in 1990 to 0.23 in 2002.

57

58

100

Cumulative Percent of Population, Ranked by Education

Figure 19. Relative Concentration Curves for Educational Disparity in Obesity in New York State, BRFSS, 1990 and 2002

806040200

100

80

60

40

20

0

Cum

ulative Percent of O

bese Persons (B

MI >

=30)

Equality19902002

Figure 19. Relative Concentration Curves for Educational Disparity in Obesity in New York State, BRFSS,1990 and 2002

59

100

Cumulative Percent of Population, Ranked by Education

Figure 20. Absolute Concentration Curves for Educational Disparity in Obesity in New York State, BRFSS, 1990 and 2002

806040200

25

20

15

10

5

0

Cum

ulative Percent of Total O

besity Rate

Equality19902002

Figure 20. Absolute Concentration Curves for Educational Disparity in Obesity in New York State, BRFSS,1990 and 2002

61

Choosing a Suite of Health Disparity Indicators

Monitoring progress toward the elimination ofdisparities in cancer-related health objectivesinvolves a number of ethical, conceptual, andmethodological issues that must be given carefulconsideration to answer the question of whichmeasure or measures should be employed tomonitor progress toward the elimination of healthdisparities between social groups.

One possibly useful way to approach themeasurement of health disparity is to consider asequence of methodological approaches.

• First, we cannot emphasize enough the closeinspection of the underlying subgroup-specifichealth outcomes (rate or prevalence, etc), eithervia tabular or graphical inspection. This is likelyto reveal important population health patterns,highlight the situation of specific subgroups ofinterest, and lend an understanding of anyunderlying heterogeneity that a summarymeasure of health disparity may not emphasize.

• Next, consider the relevant question that is tobe answered. If one is interested in the healthdisparity between two particular groups—forexample, the trend in the disparity between blackand white males in lung cancer mortality—thenthe use of a pairwise comparison of trends issufficient.

• Even for assessing health-disparity trendsbetween two groups using a pairwise comparison,

we recommend using both an absolute and arelative disparity measure. This is especiallywarranted when making long-term comparisonsthat may involve steep declines or increases for allsocial groups. Although the relative disparitymeasure gives some indication of the progress (orlack thereof) one group is making, regardless ofthe actual level of health, absolute disparitymeasures provide a context in which to judge thepublic health impact of relative health disparities.Thus, we would argue for the primacy of theabsolute indicator of disparity. Efforts to improvepublic health often rely on the absolute burden ofdisease; thus, the absolute disproportionality inhealth disparity also should have priority. This isthe case especially when comparing the size ofsocial-group disparity across different canceroutcomes and risk factors. We also understand,however, that this in no way excludes particularcases in which the relative inequality may bejudged—for other equally good reasons—to be ofhigh priority despite low levels of dispropor-tionate absolute burden. For instance, the two-fold relative disparity in cervical cancer betweenblack and white women may be judged to beespecially important because it is a healthdisparity that is almost entirely avoidable throughthe routine use of screening, even though theabsolute disparity involves only about 5 deathsper 100,000.

• If one is interested in monitoring the healthdisparity trend across the entire range of

62

subgroups within a social-group category—forexample, across all racial/ethnic groups ratherthan comparing, say, blacks and whites—or if thesocial-group category has many subgroups—suchas the disparity across the 50 U.S. states—thensummary measures of health disparity arewarranted. The first decision involved in choosinga summary measure is dictated by whether or notthe social groups in question have a naturalordering.

Summary Indicators

Ordered Social Groups

If the social group does have a natural ordering, aswith education and income groups, then werecommend using either the AbsoluteConcentration Index (ACI) or Slope Index ofInequality (SII) as a measure of absolute healthdisparity, and the Relative Concentration Index(RCI) or the Relative Index of Inequality (RII) as ameasure of relative disparity. The major reasonsfor choosing these particular measures are that

• they account for changes in the underlyingpopulation distributions in the social groups overtime and use information across the entire rangeof social groups;

• they are flexible enough to allow differentlevels of aversion to disparity to be incorporated;and

• they are sensitive to the direction of the socialgradient in health.

Although this last criterion mainly is whatdistinguishes these measures from other summarymeasures of inequality, such as the Ginicoefficient or the Index of Dissimilarity, we wouldalso reemphasize that, if the social groups in themiddle of the distribution (e.g., those with a high-school education as opposed to those with less ormore education) experience a disproportionateburden of ill health, our selected measures mayindicate that no disparity exists when it in factcould be argued otherwise. Of course, if thesequence laid out above is adhered to, then Step1—a simple and careful inspection of the basicsubgroup data—should reveal this.

This is part of the “cost” of using summarymeasures of disparity, but in this case acomparison of the RCI or RII with anothermeasure of disproportionality that is not strictlysensitive to health gradients, such as the Ginicoefficient or Theil index, may reveal importantinformation about the social distribution ofhealth. Lastly, because the RCI has a mathematicalrelationship to the RII, and the ACI has such arelationship to the SII, they always will result inthe same rank ordering of health distributions.That being said, one additional desirable featureof the ACI and RCI is the ability to graph theirassociated health concentration curves. Althoughthe ability of any summary measure of healthdisparity to communicate important informationabout disparity trends to health policy makersmay be limited, the ACI and RCI may serve thispurpose better than the RII and SII.

63

Unordered Social Groups

Our recommendations for health disparitymeasures for ordered groups restate therecommendations of earlier reviews of healthdisparity measures (60,70). In the context of theHealthy People 2010 goals, however, groups with anatural ordering represent only a small number ofthe social groups across which we want toeliminate disparities in cancer-related healthoutcomes. Therefore, we also need to think aboutdisparity measures that can be applied tounordered social groups. Again, we wouldemphasize choosing a summary measure of healthdisparity only when one is interested inmonitoring the extent of disparity across morethan two or three social groups. For comparisonsof two specific groups, there is no substitute forsimple pairwise measures of absolute and relativedisparity.

If comparisons across multiple unorderedgroups are needed, we recommend the Between-Group Variance (BGV) as a summary of absolutedisparity and the general entropy class ofmeasures developed by Henri Theil as summarymeasures of relative disparity (more specifically,the Theil index and the Mean Log Deviation). Animportant reason for choosing the Between-GroupVariance and the entropy-based measures is thatthey are disparity measures that can bedecomposed perfectly into between-social-groupand within-social-group components, given acontinuous health outcome. This cannot be saidof other measures, such as the Gini coefficientand Atkinson’s measure (97,98). The ability of thevariance and the entropy class of disparitymeasures to decompose disparity is importantbecause it allows one to look at any number of

cross-classified social groups, whether ordered ornot. For example, race and income, or gender andeducation, can be examined jointly to assess thetrend in disparity between certain dimensions ofsociety. We could look first, for example, at thetrend in between-race disparity in cancer survivaltime and see whether the disparity is increasing ordecreasing. We then could look at the disparitybetween race-education groups over time. It maybe that, while the between-race disparity isdecreasing, educational disparities within racegroups actually are increasing. In addition, theentropy-based measures also can be decomposedto investigate the relative effects of changingsocial group distributions versus changing healthdistributions. This is important because both ofthese aspects of the population constantly arechanging over time. Understanding the relativeimpact of health changes versus compositionalchanges in social groups is important forunderstanding the prospects for intervening toeliminate health disparities. Thus, because of theirdecomposition properties, the entropy measuresmay be useful tools for describing andunderstanding the stratification of cancer-relatedhealth outcomes across time.

Our recommendation for measures of healthdisparity, for both ordered and unordered socialgroups, come from explicitly adopting thepopulation health perspective toward monitoringhealth disparities. By taking a population healthperspective, we emphasize using the totalpopulation as the reference group for measuringhealth disparity, weighting social groupsaccording to the number of individuals theyrepresent, and examining both absolute andrelative disparities in health. By doing so, we areable to account for changes in the distribution of

individuals across social groups over time, a factthat has clear population health consequences,and we also are able to express health disparities

in a way that emphasizes their overall burden onpopulation health.

64

Table 5. Summary Table of Advantages and Disadvantages of Potential Health Disparity Measures

Absolute All Reflect Social Inequality

or Reference Social SES Group A version Graphical

Disparity Measure Symbol Relative Group Groups Gradient W eighting Parameter Analogue

T otal Disparity

Inter-Individual Difference IID Variable ATBOa No No No Yes NoIndividual-Mean Difference IMD Variable Average No No No Yes No

Social Group Disparity

Absolute Difference AD Absolute Best No Yes No No YesRelative Difference RD Relative Best No Yes No No YesRegression-Based Relative Effect RRE Relative Best Yes Yes Nob No YesRegression-Based Absolute Effect RAE Absolute Best Yes Yes Nob No YesSlope Index of Inequality SII Absolute Average Yes Yes Yes No YesRelative Index of Inequality RII Relative Average Yes Yes Yes No YesIndex of Disparity IDisp Relative Best Yes No No No NoPopulation Attributable Risk PAR Absolute Best Yes No Yes No YesPopulation Attributable Risk% PAR% Relative Best Yes No Yes No NoIndex of Dissimilarity ID Absolute Average Yes No Yes No YesIndex of Dissimilarity% ID% Relative Average Yes No Yes No NoRelative Concentration Index RCI Relative Average Yes Yes Yes Yes YesAbsolute Concentration Index ACI Absolute Average Yes Yes Yes Yes YesBetween-Group Variance BGV Absolute Average Yes No Yes Yes NoSquared Coefficient of Variation CV 2 Relative Average Yes No Yes No NoAtkinson’s Measure A Relative Average Yes No Yes Yes NoGini Coefficient Gini Relative Average Yes No Yes No YesTheil Index T Relative Average Yes No Yes Yes NoMean Log Deviation MLD Relative Average Yes No Yes Yes NoVariance of Logarithms VarLog Relative Average Yes No Yes No No

aAll those better off.bIn the case of regression-with grouped data.

65

Appendix: Example Analyses

This appendix presents two examples of how tomeasure and monitor cancer-related disparitytrends using the suite of indicators andmeasurement strategy outlined in therecommendations above. The examples are takenfrom the cancer-related objectives outlined inHealthy People 2010 and are illustrative rather thansubstantive analyses. The first example assessesthe trend in the prevalence of mammographyscreening among education groups andemphasizes disparity measures for ordered socialgroups. The second example assesses the trend incolorectal cancer mortality among racial groupsand highlights the use of disparity measures forunordered social groups.

Example 1: Educational Disparity inMammography Screening, 1990–2002

This example is based on self-reported data on theuse of mammography screening from the Centersfor Disease Control and Prevention’s (CDC)Behavioral Risk Factor Surveillance Survey(BRFSS), an annual state-based telephone surveyof adults. Although perhaps not the optimalsource of data on routine cancer screeningbecause of its high rate of nonresponse, the BRFSSmay be used to approximate a nationallyrepresentative sample (99), and its annualadministration and timely reporting of resultsmake it useful for illustrating disparity trends.

Method

• Step 1: Inspect the underlying subgroup data.Figure A1 (page 66) shows the prevalence ofwomen over age 40 who reported having notreceived a mammogram in the past 2 years forfive education groups. From the chart, two thingsare immediately clear. First, all groups areimproving over time (i.e., the proportion ofwomen not having mammograms is declining),and some groups have actually achieved theHealthy People 2010 target rate of 30%. Second,there is a graded relationship between theproportion of women not having a mammogramin the past 2 years and years of education—women with fewer years of education are lesslikely to have received a mammogram in the past2 years.

• Step 2: Determine the disparity question to beanswered. For this example, we are concernedabout whether the extent of disparity inmammography screening across all educationgroups is increasing or decreasing. As a result, wewill use a summary measure of health disparity.Suppose, however, that there had been adedicated effort to increase the rate of screeningamong women with a high-school education. Wethen might be more interested in the question ofwhether the effort had narrowed the gap inscreening between women with the highest

screening rates (college-educated) and high-school-educated women. In this case, a summarymeasure might mask an important change in thisparticular subgroup, so we would use a simplepairwise comparison of the absolute and relativedifference in screening.

• Step 3: Choose a summary measure of healthdisparity. Having decided to use a summarymeasure, the choice of a measurement toolhinges on whether the social groups in questionhave a natural ordering. In the case of years ofeducation, there clearly is a natural ordering, sowe will choose the Relative Concentration Index

(RCI) as a measure of relative disparity and theAbsolute Concentration Index (ACI) as a measureof absolute disparity. Both measures arecalculated for two levels of disparity aversion,ν = 2, which gives the standard RCI and ACI (96),and ν = 4, which gives additional weight to thehealth of the lower-educated groups.

Results

For the beginning and end of the period1990–2002, Table A1 (page 68) shows theprevalence of not having a mammogram in thepast 2 years (µj) and the population proportion

66

Figure A1. Proportion of Women Age 40 and Over Who Did Not Receive a Mammogram in the Past2 Years by Educational Attainment, 1990–2002

1990

60

50

40

30

20

10

0

Per

cent

20021991 1993 1995 1997 1999 2000 2001

Figure A1. Proportion of Women Age 40 and Over Who Did Not Receive a Mammogram in the Past 2 Years by Educational Attainment, 1990-2002

Source: CDC, Behavioral Risk Factor Surveillance Surveys 1990–2002.

1992 1994 1996 1998

<8y 9–12y 12y 13–15y 16+y 2010 Target

Source: CDC, Behavioral Risk Factor Surveillance Surveys 1990–2002.

(pj) for each group. The relative ranking of eachinterval (Rj), based on the midpoint of thecumulative population distribution, is derived byapplying equation [23] above; thus, for the groupwith 9–11 years of education, the relative rankingis 0.09 + (0.5 x 0.14) = 0.17. This particulargroup’s contribution to the RCI(2) is calculatedusing equation [26] above as [2 x 0.14 x(1 – 0.17)(2–1)] – [(2/41.0) x 51.6 x 0.14 x(1 – 0.17)(2–1)] = –0.0618. Applying equation [26]across all education groups gives the overallRCI(2), which for 1990 = –0.1045. To give thisvalue some perspective, Zhang and Wang, usingincome as a measure of socioeconomic positionand using data from the National Health andNutrition Examination Survey (NHANES III) (100),report a relative Concentration Index of –0.055for obesity. Because in this case the outcome is theproportion of women not having a mammogram,the negative sign of RCI(2) indicates that thedisparity favors better-educated women. A positiveRCI(2) in this case would have indicated thatdisparity actually favors less-educated women.Additionally, the effect of increasing the aversionto disparity becomes readily apparent as the valueof the RCI in 1990 increases (from –0.10 to –0.19)when the aversion to disparity increases twofold.Our preferred measure of absolute disparity forordered social groups, the Absolute ConcentrationIndex (ACI), also is displayed in Table A1 and iscalculated from equation [27] above; for 1990ACI(2) = 41.0 x (–0.1045) = –4.2.

Comparing 1990 and 2002 it appears that, asmeasured by the standard ACI (i.e., with ν = 2),absolute disparity in mammography screeningdeclined substantially over those 12 years—a43.9% reduction. Relative disparity showed onlyslight improvement, with the HCI(2) declining

only 2.6%. Note that, with an increased aversionto disparity (ν = 4), relative disparity actuallyshows a slight increase (from –0.191 to –0.201),while absolute disparity still declines (from –7.8 to–4.7). Although this indicates virtually no changein relative disparity, Figure A2 (page 69) showsthat, when calculated annually, relative disparitywas not consistent over the entire period. As theprevalence of not having a mammogram fellfaster for the less-educated groups in the first halfof the 1990s, both absolute and relative disparitydeclined (i.e., the best possible scenario). Asscreening rates tapered off among the less-educated groups, however, relative disparityincreased in the latter half of the 1990s,eventually returning to the 1990 level by 2002.Note also that two components of the RCI andACI were changing over the period of observation:the prevalence rates and the population shares ineach education group. Most notably, the share ofthe population with less than 12 years ofeducation—the groups with the highestprevalence rates—declined from 24% (0.09 amongthose with <8 years plus 0.14 for those with 9–11years) to 14% (0.06 + 0.08). Because the RCI is apopulation-weighted index, this change alone(i.e., in the absence of any change in prevalencerates) would serve to decrease the level ofdisparity. Thus, a logical next step in analyzingthe disparity trend might be to decompose thechange in disparity to determine how much ofthe change is due to declining prevalence ratesand how much is due to upward shifting of theeducation distribution. We will not go throughthe decomposition steps here, but we would re-emphasize that such decomposition techniquesare likely to be useful in understanding thesources of changes in health disparities.

67

68

Thus, by using two summary measures ofdisparity, we can make some generalization aboutthe trend in the education-related disparity inmammography screening. Between 1990 and2002, the relative disparity between educationgroups remained essentially the same, but theabsolute disparity declined because the prevalenceof not having a mammogram declined in alleducation groups, with the largest absolutedeclines having occurred among the less-educatedgroups. Thus, we would argue that the populationhealth burden associated with the education-related disparity in mammography screening hasdecreased. This, of course, is not the best possible

scenario, but we would argue that the disparitysituation is better in 2002 than it was in 1990.

Lastly, we would re-emphasize that ourconclusion about the socioeconomic disparitytrend in mammography reflects a populationhealth perspective on health disparities. Becausewe were concerned about the disparity across alleducation groups, we chose two population-weighted summary disparity measures. The resultsobtained by the application of these measuresmay or may not be consistent with other disparitymeasures that reflect concern about a differentdimension of disparity.

Table A1. Example of Relative and Absolute Concentration Index Applied to the Change in EducationalDisparity in Mammography, 1990 and 2002

Population Cumulative

Y ears of Rate Share Share Midpoint RCI ( νν = 2) RCI ( νν = 4)

Education [µj] [pj] [pγγ

] [Rj] ( νν) ΣΣ [pj (1 – Rj )( νν – 1)

] – ( νν/ µ) ΣΣ [pj µj (1 – Rj )( νν – 1)

]

1990

<8 years 54.2 0.09 0.09 0.05 –0.0583 –0.10599–11 years 51.6 0.14 0.24 0.17 –0.0618 –0.0860

12 years 41.1 0.36 0.60 0.42 –0.0012 –0.000813–15 years 38.0 0.22 0.82 0.71 0.0093 0.001616+ years 29.0 0.18 1.00 0.91 0.0095 0.0002

T otal 41.0

Relative Concentration Index →→ –0.1025 –0.1910Absolute Concentration Index →→ –4.1963 –7.8229

2002

<8 years 33.3 0.06 0.06 0.03 –0.0452 –0.08549–11 years 33.7 0.08 0.14 0.10 –0.0610 –0.0998

12 years 24.7 0.34 0.47 0.30 –0.0214 –0.020813–15 years 22.1 0.27 0.74 0.61 0.0134 0.004216+ years 18.6 0.26 1.00 0.87 0.0144 0.0005

T otal 23.6

Relative Concentration Index →→ –0.0998 –0.2014Absolute Concentration Index →→ –2.3549 –4.7493

Note: Data is for the proportion of women over 40 who did not have a mammogram within the past 2 years and is drawn from the 1990–2002 Behavioral RiskFactor Surveillance System.

Example 2: Racial Disparity in ColorectalCancer Mortality, 1990–2002

Our second example concerns rates of colorectalcancer mortality from 1990 to 2002 among fourracial groups: American Indian/Alaska Natives,Asian/Pacific Islanders, blacks, and whites. Thedata for this example come from NCI’s SEERProgram (wwwwww..sseeeerr..ccaanncceerr..ggoovv). There are severallimitations to this example that should berecognized. First, it is not possible with currentdata to analyze longer trends for mutually

exclusive detailed racial/ethnic groups becausemany states did not have complete informationon ethnicity in death certificate data. Second,there is great heterogeneity of cancer risk amongsubgroups of American Indian/Alaska Natives andAsian/Pacific Islanders that is not reflected in thissimple example because we are forced to combinethese groups. Similar issues of lack ofhomogeneity arise in comparing groups definedby ethnicity and by various social, economic, andgeographic factors.

69

Figure A2. Trends in Education-Related Disparity and Prevalence for the Proportion of Women Age 40and Over Who Did Not Receive a Mammogram in the Past 2 Years, 1990–2002

1990

60

50

40

30

20

10

0

Pre

vale

nce

Rat

e

20021991 1993 1995 1997 1999 2000 2001*

Figure A2. Trends in Education-Related Disparity and Prevalence for the Proportion of Women Age 40 and Over Who Did Not Receive a Mammogram in the Past 2 Years, 1990-2002

Source: CDC, Behavioral Risk Factor Surveillance Surveys 1990–2002. *Note: Question not asked in 2001.

1992 1994 1996 1998

0

-2

-4

-6

-8

-10

-12

-14

Concentration Index

<8y 9–12y 12y 13–15y 16+y RCIx100 ACI

Absolute Disparity [ACI]

Relative Disparity [RCIx100]

Source: CDC, Behavioral Risk Factor Surveillance Surveys 1990–2002.*Note: Question not asked in 2001.

70

Method

• Step 1: Inspect the underlying subgroup data.Figure A3 (page 71) shows trends among thoseaged 45–64 years for colorectal cancer mortalityfor the four racial groups. Blacks have the highestrates of colorectal cancer mortality, followed bywhites, and then by American Indian/AlaskaNatives and Asian/Pacific Islanders, both of whomhave similar mortality rates that actually are nearthe 2010 age-adjusted target rate. Both blacks andwhites experienced relatively steady declines incolorectal cancer mortality rates during the 1990s(although the decline in black rates seems to slowdown after the mid-1990s), but the rates amongother groups remained somewhat steady,hovering near the 2010 target rate.

• Step 2: Determine the disparity question to beanswered. Although a number of interestingpairwise comparisons could be made, in the spiritof the Healthy People 2010 goals we are interestedin the extent to which progress is being madetoward the elimination of racial disparities incolon cancer mortality. This would be achievedwhen all groups have the same mortality rate, sowe will use a summary measure of healthdisparity to determine if racial disparities inworking-age colorectal cancer mortality areincreasing or decreasing.

• Step 3: Choose a summary measure of healthdisparity. Clearly, there is no natural orderingamong racial groups, so having decided to use asummary measure of health disparity, we will usethe Between-Group Variance (BGV) to measurethe absolute level of disparity and two entropy-based measures of relative disparity—the Theil

index (T) and the Mean Log Deviation (MLD).Although it is not necessary to use both T andMLD to measure relative health disparity, it maybe instructive to do so for reasons outlined below.

Results

Table A2 (page 72) shows the colorectal cancermortality rate (µj), the rate relative to thepopulation average rate (i.e., the mortality ratiorj), and the population share (pj) for each racialgroup in 1990 and 2001. Recall that both T andMLD are measures of average disproportionality—that is, they take the general form andmeasure the extent to which shares of populationand shares of health differ—but they use differentdisproportionality functions (i.e., different speci-fications of f(rj)). The disproportionality functionfor T is rjln(rj) and for MLD is –ln(rj) or, equiva-lently, ln(1/rj). It may not seem immediately clearwhy it might be helpful to use both measures, butit may be more clear if we use some simplealgebra to rewrite the equations. First, note thatwhen the denominator for the mortality ratio rj isthe total population rate, , where sj is theshare of mortality for racial group j. We can thenrewrite the disproportionality function f(rj) for T

as and MLD as . When we apply

the general formula for measures ofaverage disproportionality, the formula for T

becomes and MLD becomes .

Expressed in this fashion, it is clear that both Tand MLD measure the difference in (log) shares ofhealth (or ill health) and population, but T is

1n sj

pjpj ( (Σ1n pj

sjsj ( (Σ

pj f (rj )Σ j

1n sj

pj( (1npj

sj

pj

sj( (

rj x pj = sj

pj f (rj )Σ j

weighted by shares of health (or ill health, i.e., sj),whereas MLD is weighted by population shares(pj). Thus, in the context of our example T will besomewhat more influenced by groups with highmortality ratios, whereas MLD will be somewhatmore influenced by groups with large populationshares.

Applying the disproportionality functions forT and MLD listed in Table 2, in 1990 theAmerican Indian/Alaska Native segment of T iscalculated as 0.006 x 0.375 x ln(0.375) = –0.0023, and the segment of MLD is 0.006 x

[–ln(0.375)] = 0.062. The Between-Group Variance(BGV) is calculated using equation [17] above and,for the American Indian/Alaska Native segment in1990, is calculated as 0.006 (9.5 – 25.5)2 = 1.607.The racial disparity in 1990 as measured by theTheil index is 0.0124. We might then immediatelyask whether this disparity is large or small.Because there has been little use of entropy-basedmeasures in health disparities research, this is adifficult question to answer. We may get someleverage, perhaps, from the recent work byGoesling and Firebaugh (101), who used T andMLD to investigate trends in international health

71

Figure A3. Trends in Mortality from Colorectal Cancer by Race, Ages 45–64, 1990–2001

1990

40

35

30

25

20

15

10

5

0

Rat

e pe

r 10

0,00

0

20011991 1993 1995 1997 1999 2000

Figure A3. Trends in Mortality from Colorectal cancer by Race, Ages 45-64, 1990-2001

* AI/AN = American Indian/Alaska Native** API = Asian/Pacific IslanderSource: Surveillance, Epidemiology, and End Results (SEER) Program. SEER*Stat Database, National Cancer Institute,DCCPS, Surveillance Research Program, Cancer Statistics Branch, released December 2003.

1992 1994 1996 1998

AI/AN* API** Black White 2010 Target

*AI/AN = American Indian/Alaska Native**API = Asian/Pacific IslanderSource: Surveillance, Epidemiology, and End Results (SEER) Program (www.seer.cancer.gov) SEER*Stat Database, National Cancer Institute,DCCPS, Surveillance Research Program, Cancer Statistics Branch, released December 2003.

disparity in life expectancy among 169 countries.They report that in 2000 T for global disparity inlife expectancy was 0.0099 and MLD was 0.0106.We find a T of 0.0198 and MLD of 0.0186 in2002. Thus, it would appear that U.S. racialdisparities in colorectal cancer among those 45–64are similar in magnitude to cross-nationaldisparities in life expectancy, but the extent towhich the number of groups compared (4 racegroups vs. 169 countries) and the health outcome(colorectal cancer mortality rates vs. lifeexpectancy) may affect the level of disparity is anopen question. As additional analyses applyingentropy-based disparity measures within theUnited States are conducted (102), a clearer senseof how to interpret their magnitude shoulddevelop.

The results in Table A2 suggest that theabsolute racial disparity (BGV) in colorectal cancermortality rates remained approximately constantover the period in question, but the relativedisparity increased and to a slightly greater extentwhen measured with T than with MLD. The slightdifference between T and MLD results from thefact that T is somewhat more affected by highmortality ratios, and MLD is somewhat moreaffected by large population shares (88). Thus, inthe case of colorectal cancer mortality, the Theilwill be more sensitive to mortality change inblacks, and the MLD will be more sensitive tomortality change in whites. The black mortalityratio increased from 1.41 to 1.59 from 1990 to2001, but the white ratio declined only slightly,

72

Table A2. Example of Theil Index and the Between-Group Variance Applied to the Change in RacialDisparity in Colorectal Cancer Mortality, 1990 and 2001

Rate per Population Rate Relative

100,000 Share to T otal T MLD BGV Race [µj] [pj ] [rj ] [pj x rj x ln( rj )] [pj x – ln( rj )] pj [( µj – ∑µj )

2]

1990

American Indian/Alaska Native 9.5 0.006 0.375 –0.0023 0.0062 1.607Asian/Pacific Islander 14.5 0.026 0.570 –0.0084 0.0147 3.130Black 35.9 0.100 1.412 0.0486 –0.0344 10.979White 24.7 0.868 0.970 –0.0255 0.0263 0.502

T otal 25.5 0.0124 0.0128 16.219

2001

American Indian/Alaska Native 10.4 0.009 0.541 –0.0029 0.0053 0.672Asian/Pacific Islander 12.1 0.040 0.629 –0.0116 0.0184 2.018Black 30.0 0.109 1.559 0.0751 –0.0482 12.561White 18.3 0.843 0.950 –0.0410 0.0431 0.776

T otal 19.2 0.0198 0.0186 16.027

Note: Rates are age adjusted to the year 2000 population distribution and were generated by the National Cancer Institute’s SEER*Stat software, version 5.2.2.

from 0.97 to 0.95, thus favoring a relatively largerincrease in the Theil index.

Figure A4 shows the absolute and relativedisparity trends across the entire 11-year period,which indicate that the change in racial disparitywas not constant over time. Both absolute andrelative disparity declined from 1990 to 1992,after which absolute disparity rose to remain atroughly its 1990 level for the rest of the period,

while relative disparity continued to increasesteadily as mortality rates declined for all racialgroups. On the whole, then, we would take a lessfavorable view of the trend in racial disparities incolorectal cancer compared to that of education-related disparities in mammography. Therevirtually was no decline in absolute disparity, andrelative disparity increased markedly from 1990 to2002 despite an overall decline in the populationmortality rate.

73

Figure A4. Racial Disparity Trends in Working Age (45–64) Mortality from Colorectal Cancer by Race,1990–2001

1990

40

35

30

25

20

15

10

5

0

Rat

e pe

r 10

0,00

0 an

d B

GV

1991 1993 1995 1997 1999 2000

Figure A4. Racial Disparity Trends in Working-Age (45-64) Mortality from Colorectal Cancer by Race, 1990-2001

* AI/AN = American Indian/Alaska Native** API = Asian/Pacific IslanderSource: Surveillance, Epidemiology, and End Results (SEER) Program. SEER*Stat Database, National Cancer Institute,DCCPS, Surveillance Research Program, Cancer Statistics Branch, released December 2003.

1992 1994 1996 1998

AI/AN* API** Black White BGV

2001

0.025

0.020

0.015

0.010

0.005

0.000

Theil and M

LD

Theil MLD

Relative Disparity (T, MLD)

Absolute Disparity (BGV)

*AI/AN = American Indian/Alaska Native**API = Asian/Pacific IslanderSource: Surveillance, Epidemiology, and End Results (SEER) Program (www.seer.cancer.gov) SEER*Stat Database: Mortality—All COD, TotalU.S. for Expanded Races (1990–2001), National Cancer Institute, DCCPS, Surveillance Research Program, Cancer Statistics Branch,released December 2003. Underlying mortality data provided by NCHS (www.cdc.gov/nchs).

75

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