HOW TO USE DATA TO GET “THE

RIGHT ANSWER”

Donna Spiegelman Departments of Epidemiology, Biostatistics, Nutrition and Global Health Harvard School of Public Health stdls@hsph.harvard.edu

2

Triumphs of Modern Epidemiology • Alcohol and esophageal cancer • Hep B virus and liver cancer • HPV and cervical cancer • H. pylori and peptic ulcer • Folic acid and neural tube defects • Asbestos and lung cancer, mesothelioma • Aniline dye and bladder cancer • Vinyl chloride and angiosarcoma of the liver • Nickel and nasal cancer • Radon and lung cancer • Aspirin and MI • Dalkon Shield IUD and PID ...

http://www.epimonitor.net/Triumphs_in_Epidemiology.htm (55 entries) http://monographs.iarc.fr/ENG/Classification/ (113 human

carcinogens)

3

Definition of junk science: “It is a hodgepodge of biased data, spurious inference, and logical legerdemain, patched together by researchers whose enthusiasm for discovery and diagnosis far outstrips their dredging, wishful thinking, truculent dogmatism, and, now and again, outright fraud.”

The Start of Junk Science??

4

The Junkyard Dogs “Unfortunately, and increasingly today, one can find examples of junk science that compromise the integrity of the field of science and, at the same time, create a scare environment where unnecessary regulations on industry in particular, are rammed through without respect to rhyme, reason, effect or cause.”

—Michael A. Miles, former CEO of the Phillip Morris tobacco company

6

More Controversial: “Weak Effects”

• Air pollution and all-cause mortality, CVD mortality

• Low dose exposure to radon and lung cancer

• Low dose exposure to lead and neurotoxicity in children

• Passive cigarette smoking and lung cancer

• Alcohol and breast cancer

• Oral contraceptives and breast cancer

• Types of fat and cardiovascular disease

Population Attributable Risk and Weak Effects: Still Important!

Exposure Prevalence (%)

10 40 80

1.2 2 7 14

RR 1.5 5 17 29

2.0 17 44 66

“Weak Associations” (NEJM 1990) Rylander

“Studies … a relation between exposure to environmental tobacco smoke and lung cancer must take into account other …factors and the possibility that exposure to environmental tobacco smoke may be confounded. This has not been considered in the majority of such studies. Until this has been done, the claim of causality between environmental tobacco smoke and lung cancer remains uncertain.”

Angell

“There is no question that epidemiologic studies of risk factors for disease are of growing interest and importance, both for individuals and for the public health. It is important, however, to remember the pitfalls in interpreting them and to be cautious in advising patients on the basis of single or conflicting studies. This is particularly true of studies that purport to show only weak associations between exposures and disease.”

9

The research (and the researcher) that Philip Morris did not want you to see

(Ragnar) Rylander was at that time at another Swedish university and had previously undertaken assignments for both Lorillard (another tobacco company) and Philip Morris. He was to be “officially … carried on the books as a consultant to FTR [Fabriques de tabac réunies, a Philip Morris subsidiary] and would be paid by FTR”.

By means of material from internal industry documents it can be revealed that one company, Philip Morris, acquired a research facility, INBIFO, in Germany and created a complex mechanism seeking to ensure that the work done in the facility could not be linked to Philip Morris. In particular it involved the appointment of a Swedish professor as a ‘co-ordinator’, who would synthesise reports for onward transmission to the USA. Various arrangements were made to conceal this process

Relation between Philip Morris and

INBIFO

Source: Diethelm et al. Lancet 2005

10

RCTs vs. observational studies

• ß-carotene and lung cancer

• HRT and CVD incidence and mortality

• VIOXX

• Dietary fat and breast cancer

- Standard designs & analysis sometimes not

adequately controlling for

- confounding

- information bias

- selection bias

Wrong answer?

- Agreed: We can be doing a better job

- Not agreed: HOW

Confounding – What do we do?

“industry standard” END of mainstream epi methods

collect data on known & suspected time-varying confounders

MSMs, G-causal algorithm

Design Analysis

Match on key confounders

Matched

Randomize Intent-to-treat

Restrict Simple (crude)

Collect data on known & suspected confounders (time-invariant)

Multivariate models

13

Confounding – Outstanding problems

• unknown confounders

Fact: ~ 47% of US breast cancer incidence explained by known risk factors (Madigan et al., JNCI, 1987:1681-1695)

𝑟𝑟2 in most epi regressions (blood pressure, serum hormones) 20%-40% (Pediatric Task Force on BP Control in Children, Pediatrics, 2004; Hankinson, personal communication)

Undiscovered genes?

Unimagined environmental factors?

Complex non-linear interactions?

Solution to confounding by unknown risk factors:

randomization VERY limited applicability

Outstanding questions:

a few strong risk factors or many weak ones?

many rare ones or a few common ones?

modeling of scenarios: do biases cancel?

NEW IDEAS NEEDED

15

Solution to confounding by unknown risk factors

• Instrumental variables (𝑉𝑉)

• Very hard to find; validity based on empirically unverifiable assumption of E[𝐷𝐷 𝑉𝑉,𝐶𝐶1] = 𝐸𝐸[𝐷𝐷 𝑉𝑉,𝐶𝐶]

• 𝐷𝐷 = 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜, 𝐶𝐶 = other risk factors for 𝐷𝐷

• 𝑋𝑋 = the exposure of interest

• 𝐶𝐶1.= measured risk factors, 𝐶𝐶2=unmeasured risk factors

• Large power loss if 𝐶𝐶𝑜𝑜𝑟𝑟𝑟𝑟 𝐶𝐶2,𝑉𝑉 is low

• Also requires empirically unverifiable assumption that E[𝐷𝐷 𝑉𝑉,𝑋𝑋,𝐶𝐶] = 𝐸𝐸[𝐷𝐷 𝑋𝑋,𝐶𝐶]

Solution to confounding by unknown risk factors

Regression discontinuity: A regression discontinuity design (RDD) is a quasi-experimental pretest-posttest design that elicits the causal effects of interventions by assigning a cutoff or threshold above or below which an intervention is assigned. By comparing observations lying closely on either side of the threshold, it is possible to estimate the local Average treatment effect in environments in which randomization was unfeasible.

17

Effects of unknown confounders References

“The impact of residual and unmeasured confounding in epidemiological studies: a simulation study”, Davey-Smith and colleagues, Am J Epidemiol 2007; 166:646-655

Marshall and Hastrup, Am J Epidemiol, 1999; 150:88-96, 1996; 143: 1069-1078

“Poppers, Kaposi’s sarcoma, and HIV infection: empirical evidence of a strong confounding effect?”, Morabia, Prev Med 1995; 24:90-95.

Unmeasured confounding by known or suspected risk factors: We can use the data to get ‘the right answer’ to improve the validity of new studies’!

Design: two-stage (Reilly & Salim, http://www.meb.ki.se/~marrei/software/

Stage 1 𝐷𝐷𝑖𝑖 ,𝑋𝑋𝑖𝑖,𝐶𝐶1𝑖𝑖 , 𝑖𝑖 = 1, … ,𝑛𝑛

Stage 2 𝐷𝐷𝑖𝑖 ,𝑋𝑋𝑖𝑖,𝐶𝐶1𝑖𝑖 ,𝐶𝐶2𝑖𝑖 , 𝑖𝑖 = 1, … ,𝑛𝑛2 or

𝑋𝑋𝑖𝑖 ,𝐶𝐶1𝑖𝑖 ,𝐶𝐶2𝑖𝑖 , 𝑖𝑖 = 1, … ,𝑛𝑛2

So that 𝐷𝐷𝑖𝑖 ,𝑋𝑋𝑖𝑖 ,𝐶𝐶1𝑖𝑖 , . , 𝑖𝑖 = 𝑛𝑛2 + 1, … ,𝑛𝑛1 + 𝑛𝑛2

𝑛𝑛1 ≫ 𝑛𝑛2

Analysis: MLE of 2-stage likelihood References:

Reilly M, 1996; Weinberg & Wacholder, 1990; Zhao & Lipsitz, 1992;

Robins et al., 1994; + many others

Cain & Breslow, AJE, 1988

𝑓𝑓 𝐷𝐷 𝑋𝑋,𝐶𝐶1,𝐶𝐶2; 𝛽𝛽) pdf of complete data

Pr 𝐼𝐼 𝐷𝐷,𝑋𝑋,𝐶𝐶1), 𝐼𝐼 = 1, 0 otherwise --- selection model for stage 2

𝑓𝑓 𝐷𝐷, 𝐼𝐼 𝑋𝑋,𝐶𝐶1; 𝛽𝛽,𝜃𝜃) =

Pr 𝐼𝐼 𝐷𝐷,𝑋𝑋,𝐶𝐶1) ∫ 𝑓𝑓 𝐷𝐷 𝑋𝑋,𝐶𝐶1, 𝑜𝑜2) 𝑓𝑓 𝑜𝑜2 𝑋𝑋,𝐶𝐶1) 𝑑𝑑𝑜𝑜2𝑐𝑐2

likelihood of 2-stage design =

Stage 1

� log[𝑓𝑓 𝐷𝐷 𝑋𝑋,𝐶𝐶1; 𝛽𝛽,𝜃𝜃]

Stage 2

� log [𝑓𝑓 𝐷𝐷 𝑋𝑋,𝐶𝐶1,𝐶𝐶2; 𝛽𝛽)]

Stage 2

� log [𝑓𝑓 𝐶𝐶2 𝑋𝑋,𝐶𝐶1; 𝜃𝜃)]

+

+

(Steenland & Greenland, AJE 2004;160:384-392)

𝑓𝑓 𝐷𝐷 𝑋𝑋,𝐶𝐶); 𝑋𝑋 = silica, 𝐶𝐶 = smoking

𝑓𝑓 𝐷𝐷 𝑋𝑋) = �𝑓𝑓 𝐷𝐷 𝑋𝑋,𝐶𝐶 = 𝑠𝑠) Pr 𝐶𝐶 = 𝑠𝑠 𝑋𝑋)𝑆𝑆

𝑠𝑠=1

Pr 𝐶𝐶 = 𝑠𝑠 𝑋𝑋 = 𝑟𝑟) = 𝑃𝑃𝑟𝑟𝑠𝑠 where �𝑃𝑃𝑟𝑟𝑠𝑠 = 1𝑠𝑠

Likelihood (silica + 1987 smoking data + US smoking data + ACS lung cancer & smoking data)

silica study 1987 silica smoking data

= ∑ log [𝑓𝑓 𝐷𝐷𝑖𝑖 𝑋𝑋𝑖𝑖)] + ∑ [∑ ∑ 𝑙𝑙𝑜𝑜𝑙𝑙𝑃𝑃𝑟𝑟𝑠𝑠 𝐼𝐼 𝑋𝑋𝑖𝑖=𝑟𝑟 𝐼𝐼 𝐶𝐶𝑖𝑖=𝑠𝑠𝑆𝑆𝑠𝑠=1 ]𝑅𝑅

𝑟𝑟=1𝑛𝑛2𝑖𝑖=1

𝑛𝑛1𝑖𝑖=1

( )

( )3 4

1 1 1log | , 0

iI C sn nS

os i i ii s i

P f D C X =

= = =

+ + = ∑ ∑ ∑

• assume distribution of smoking during entire period ~ 1987 distribution

could treat as known

𝑛𝑛1silica workers in retrospective cohort study

𝑛𝑛2 silica workers in 1987 smoking prevalence study

𝑛𝑛3 NHIS participants on general population smoking rates in 1986

𝑛𝑛4 ACS prospective cohort data on smoking & lung cancer

r=1,…, R levels of exposure

s=1,…, S levels of smoking

U.S ACS

Example: Kyle Steenland – retrospective cohort study of lung cancer in relation to occupational silica exposure

Obstacles

• software? Design software available;

Offsets or weights in PROC GENMOD or PROC PHREG can be used for analysis

• training?

• funding?

Result: The right answer? A better answer?

Is it worth it?

22

Information Bias

• “We believe of the two of the major methodological issues raised in epidemiological studies of occupational exposures, that is, confounding and exposure misclassification, the latter is of far greater concern” –

• Blair A, Stewart P, Lubin JH, Forastiere F. Methodological issues regarding confounding and exposure misclassification in epidemiological studies of occupational exposures. American Journal Of Industrial Medicine. Mar 2007;50(3):199-207.

Information Bias What do we usually do?

NOTHING!

What can we do?

Design Analysis

main study/validation study measurement error methods

MS/EVS, MS/IVS, IVS misclassification methods

MS/ERS, MS/IRS, IRS References:

Carroll, Ruppert, Stefanski, 1995, Chapman + Hall

Rosner et al., AJE, 1990, 1992

Spiegelman, “Reliability studies”

“Validation studies”

Robins et al., JASA, 1994

Encyclopedia of Biostatistics

Example FRAMINGHAM HEART STUDY

MAIN STUDY

- 1731 men free of CHD

(non-fatal MI, fatal CHD)

At exam 4

- Followed for 10 years for CHD

Incidence (163 events, cumulative incidence = 9.4%)

REPRODUCIBILITY STUDY

- 1346 men with all risk factors

information at exams 2+3 (subgroup of 1731 men)

- Risk factors in main study: Age, BMI, Serum Cholesterol, Serum Glucose, Smoking, SBP

- Risk factors in reproducibility study: Serum Cholesterol, BMI, Serum Glucose, SBP, Smoking

Example: (from Rosner, Spiegelman, Willett; AJE, 1992)

Framingham Heart Study

Reliability study: (n = 1346 men)

Subject i’s

observed valve at time j

Subject i’s true mean

Reliability Coefficients

CHOL 75%

GLUC 52%

BMI 95%

SBP 72%

𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑖𝑖𝑖𝑖𝐺𝐺𝐶𝐶𝐺𝐺𝐶𝐶𝑖𝑖𝑖𝑖𝐵𝐵𝐵𝐵𝐼𝐼𝑖𝑖𝑖𝑖𝑆𝑆𝐵𝐵𝑃𝑃𝑖𝑖𝑖𝑖

=

𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑖𝑖𝐺𝐺𝐶𝐶𝐺𝐺𝐶𝐶𝑖𝑖𝐵𝐵𝐵𝐵𝐼𝐼𝑖𝑖𝑆𝑆𝐵𝐵𝑃𝑃𝑖𝑖

+ 𝜺𝜺𝑖𝑖𝑖𝑖 ,𝑉𝑉𝑉𝑉𝑟𝑟 𝜺𝜺𝑖𝑖𝑖𝑖 = � ,𝑤𝑤𝐸𝐸 𝜺𝜺𝑖𝑖𝑖𝑖 = 𝟎𝟎

𝜎𝜎𝐵𝐵2

𝜎𝜎𝐵𝐵2 + 𝜎𝜎𝑊𝑊2 = 𝑅𝑅𝐼𝐼

Assumptions 1. Measurement error model

2. Disease incidence model

log𝐷𝐷𝑖𝑖

1 − 𝐷𝐷𝑖𝑖= 𝛽𝛽0 + 𝛽𝛽1′𝑿𝑿𝒊𝒊 + 𝛽𝛽2′𝑪𝑪𝒊𝒊

3. • Pr (𝐷𝐷𝑖𝑖) is small

• Measurement error independent of disease status

4. Reliability substudy “representative” of main study

𝒁𝒁𝒊𝒊𝒊𝒊 = 𝑿𝑿𝒊𝒊 + 𝜺𝜺𝒊𝒊𝒊𝒊, 𝐸𝐸 𝜺𝜺𝒊𝒊𝒊𝒊 = 𝟎𝟎;𝑉𝑉𝑉𝑉𝑟𝑟 𝜺𝜺𝑖𝑖𝑖𝑖 = 𝚺𝚺𝑾𝑾 within 𝐸𝐸 𝑿𝑿𝒊𝒊 = 𝝁𝝁𝒙𝒙;𝑉𝑉𝑉𝑉𝑟𝑟 𝑿𝑿𝒊𝒊 = 𝚺𝚺𝑩𝑩 between

The Procedure ― For one variable measured with unbiased, additive error

𝑍𝑍 = 𝑋𝑋 + 𝜀𝜀, where 𝐶𝐶𝑜𝑜𝑟𝑟𝑟𝑟 𝑋𝑋, 𝜀𝜀 = 0 {simplest case}

Step 1. Run a logistic regression of 𝐷𝐷 on 𝑍𝑍, 𝑪𝑪 in main study

𝑙𝑙𝑜𝑜𝑙𝑙𝑖𝑖𝑜𝑜[Pr 𝐷𝐷 = 1 𝑍𝑍,𝐺𝐺)] = 𝛽𝛽0 + 𝛽𝛽1 𝑍𝑍 + 𝛽𝛽2′𝑪𝑪

Measured with error

Measured without

error (≥1)

Step 2. Estimate reliability coefficient from reliability substudy (𝑛𝑛2 subjects, 𝑟𝑟 replicates)

Need same # of replicates per subject

where

𝜎𝜎�𝑍𝑍2= �

(𝑍𝑍𝑖𝑖� − �̅�𝑍. . )2

𝑛𝑛2 − 1, 𝜎𝜎�𝜀𝜀

2= ��(𝑍𝑍𝑖𝑖𝑖𝑖 − 𝑍𝑍𝑖𝑖� )2

𝑛𝑛2(𝑟𝑟 − 1)

𝑟𝑟

𝑖𝑖=1

𝑛𝑛2

𝑖𝑖=1

𝑛𝑛2

𝑖𝑖=1

within-person variance (estimated)

TOTAL

𝑅𝑅𝐼𝐼� =𝜎𝜎�𝑋𝑋

2

𝜎𝜎�𝑋𝑋2 + 𝜎𝜎�𝜀𝜀

2 , 𝜎𝜎�𝑋𝑋2 = 𝜎𝜎�𝑍𝑍

2 − 𝜎𝜎�𝜀𝜀2/𝑟𝑟

Step 3. Correct.

*1 1ˆ ˆ ˆ/ IRβ β=

corrected uncorrected

( ) ( )

( )21* 1

1 4

ˆVar ˆ ˆVar Varˆ ˆ II I

RR R

β ββ = +

MAIN STUDY RELIABILITY STUDY

This contributes much less.

( ) ( )( ) ( )

( ) ( )

22

22 2

ˆ ˆ2 1 1 1 1ˆVar

1 1I I

In r R r R

Rr r n n

− − + − =− − (Donner, Intl Stat

Review, 1986) 95% C.I. for odds ratio:

( )

±∆ *

1*1 rVa961 ββ ˆˆ.ˆexp

∆= biological meaningful comparison, e.g. 90% percentile – 10% percentile

Results: 10-year cumulative incidence of CHD (163 events / 1731 men)

Uncorrected Corrected CHOL 2.21 (1.43, 3.39) 2.91 (1.62, 5.24)

Δ= 100 mg/dl

GLUC 1.27 (0.97, 1.66) 1.75 (0.87, 3.52)

Δ= 34 mg/dl

BMI 1.64 (1.04, 2.58) 1.49 (0.92, 2.43)

Δ= 9.7 kg/m2

SBP 2.80 (1.85, 4.24) 3.93 (2.19, 7.05)

Δ= 49 mmHg

SMOKE 1.70 (1.17, 2.47) 1.69 (1.16, 2.47)

Δ= 30 cig/day

AGE (45-54) 2.05 (1.27, 3.33) 1.89 (1.16, 3.07)

AGE (55-64) 3.21 (1.95, 5.29) 2.85 (1.72, 4.74)

AGE (65-69) 4.30 (2.06, 8.98) 3.73 (1.67, 8.35)

𝐶𝐶𝑅𝑅� (95% CI)

General framework for estimation and inference in failure time regression models

- Main study/validation study studies

The data:

𝐷𝐷𝑖𝑖 ,𝑇𝑇𝑖𝑖 ,𝑋𝑋𝑖𝑖 ,𝐶𝐶𝑖𝑖 , 𝑖𝑖 = 1, … ,𝑛𝑛1 main study subjects

(𝐷𝐷𝑖𝑖 ,𝑇𝑇𝑖𝑖 , 𝑥𝑥𝑖𝑖 ,𝑋𝑋𝑖𝑖 ,𝐶𝐶𝑖𝑖), 𝑖𝑖 = 𝑛𝑛1 + 1, … ,𝑛𝑛1 + 𝑛𝑛2 validation study subjects

where 𝑇𝑇𝑖𝑖 = survival time 𝐷𝐷𝑖𝑖 = 1 if case at 𝑇𝑇𝑖𝑖, 0 o.w. 𝑥𝑥𝑖𝑖 = perfect exposure measurement 𝑋𝑋𝑖𝑖 = surrogate exposure measurement for 𝑥𝑥 𝐶𝐶𝑖𝑖 = other perfectly measured covariate data

- assume sampling into validation study is at random

Liao and Spiegelman, In progress

(𝑥𝑥) (𝑋𝑋)

Effect of radon exposure on lung cancer mortality rates:

UNM uranium miners Mortality RR(95% CI)

• > 30% attenuation in �̂�𝛽1

• policy implications for risk assessment

�̂�𝛽1 𝑆𝑆𝐸𝐸� 𝑥𝑥 10−3 Δ = 100 WLM 500 WLM

Uncorrected 3.52 (0.658) 1.4 (1.3, 1.6) 5.8 (3.1, 11)

EPL 5.00 (1.00) 1.7 (1.4, 2.0) 12 (4.6, 32)

Nutritional epidemiology (over 100): Tworoger SS, Eliassen AH, Rosner B, Sluss P, Hankinson SE. Plasma prolaction concentrations and risk of premenopausal breast cancer. Cancer Research, 2004;64:6814-6819.

Hankinson SE, Willett WC, Michaud DS, Manson JE, Colditz GA, Longcope C, Rosner B, Speizer FE. Plasma prolaction levels and subsequent risk of breast cancer in postmenopausal women. Journal of the National Cancer Institute 1999; 91:629-634.

Smith-Warner SA, Spiegelman D, Adami H, Beeson L, van den Brandt P, Folsom A, Fraser G, Freudenheim J, Goldbohm R, Graham S, Kushi L, Miller A, Rohan T, Speizer FE, Toniolo P, Willett WC, Wolk A, Zeleniuch-Jacquotte A, Hunter DJ. Types of dietary fat and breast cancer: a pooled analysis of cohort studies. International Journal of Cancer 2001; 92:767-774.

Holmes MD, Stampfer MJ, Wolf AM, Jones CP, Spiegelman D, Manson JE, Coldditz GA. Can behavioral risk factors explain the difference in body mass index between African-American and European-American women? Ethnicity and Disease 1999; 8:331-339.

Rich-Edwards JW, Hu F, Michels K, Stampfer MJ, Manson JE, Rosner B, Willett WC. Breastfeeding in infancy and risk of cardiovascular disease in adult women. Epidemiology, 2004; 15:550-556.

Koh-Banerjee P, Chu NF, Spiegelman D, Rosner B, Colditz GA, Willett WC, Rimm EB. Prospective study of the association of changes in dietary intake, physical activity, alcohol consumption, and smoking with 9-year gain in wais circumference among 15,587 men. Am J Clin Nutr 2003; 78:719-727.

Koh-Banerjee P, Franz M, Sampson L, Liu S, Jacobs Jr. DR, Spiegelman D, Willett WC, Rimm EB. Changes in whole grain, bran and cereal fiber consumption in relation to 8-year weight gain among men. Am J Clin Nutr, 2004; 5:1237-1245.

Environmental epidemiology Keshaviah AP, Weller EA, Spiegelman D. Occupational exposure to methyl tertiary-butyl ether in relation to key health symptom prevalence: the effect of measurement error correction. Environmetrics, 2002; 14:573-582. Thurston SW, Williams P, Hauser R, Hu H, Hernandez-Avila M, Spiegelman D. A comparison of regression calibration methods for measurement error in main study/internal validation study designs. Journal of Statistical Planning and Inference, 2005; 131:175-190.

Fetal lead exposure in relation to birth weight; MS/IVS; bone lead vs. cord lead (r=0.19)

Spiegelman D, Valanis B. Correcting for bias in relative risk estimates due to exposure measurement error: A case study of occupational exposure to antineoplastics in pharmacists. American Journal of Public Health. Mar 1998;88(3):406-‐412. Weller EA, Milton DK, Eisen EA, Spiegelman D. Regression calibration for logistic regression with multiple surrogates for one exposure. Journal of Statistical Planning and Inference, 2007; 137:449-461.

Metal working fluids exposure in relation to lung function; MS/EVS; job characteristics vs. personal monitors (r=0.82)

Horick N, Milton DK, Gold D, Weller E, Spiegelman D. Household dust endotoxin exposure and respiratory effects in infants: correction for measurement error bias. Environmental Health Perspectives, 2006; 114:135-140. Li R, Weller EA, Dockery DW, Neas LM, Spiegelman D. Association of indoor nitrogen dioxide with respiratory symptoms in children: the effect of measurement error correction with multiple surrogates. Journal of Exposure Analysis and Environmental Epidemiology, 2006; 16:342-350.

Software is available! • http://www.hsph.harvard.edu/donna-spiegelman/software/

SAS macros for regression calibration (Rosner et al., AJE, 1990, 1992; Spiegelman et al., AJCN, 1997; Spiegelman et al, SIM, 2001)

in main study/validation study designs

• STATA (Carroll et al. SIMEX, regression calibration)

So why are methods under-utilized? No validation data

Insufficient training of statisticians & epidemiologists

Either/or about assumptions

Quantitative correction for selection bias:

Design Analysis

main study/’selection’ study ML

SPE E-E

Note: large overlap w/ missing data literature when 𝐷𝐷 is missing, potential for selection bias

References for ignorable missingness:

Little & Rubin, Wiley, 1986 Scharfstein et al., 1998 Rotnitzky et al., 1997 Robins et al., 1995

ML

SPE E-E

Basic idea:

Let 𝐼𝐼 = 1 if selected, 0 otherwise,

Pr (𝐼𝐼 | 𝐸𝐸,𝑪𝑪) = selection probability

Selection study has data on those not in main study 𝐷𝐷𝑖𝑖,𝐸𝐸𝑖𝑖,𝑪𝑪𝑖𝑖 𝑜𝑜𝑟𝑟 (𝐶𝐶𝑖𝑖,𝐺𝐺𝑖𝑖 ), 𝑖𝑖 = 1, … ,𝑛𝑛2)

Surrogates for D,

risk factors for D

IPW: 𝑃𝑃𝑟𝑟−1 (𝐼𝐼𝑖𝑖 = 1 | 𝐷𝐷𝑖𝑖 ,𝐸𝐸𝑖𝑖,𝑪𝑪𝑖𝑖) = 𝑤𝑤𝑖𝑖

Use PROC GENMOD w/ robust variance + weights 𝑤𝑤𝑖𝑖 , 𝑖𝑖 = 1, … ,𝑛𝑛1

REPEATED SUBJECT = ID / TYPE = IND;

Mail, phone, house visit to get data

For dependent censoring, (a.k.a. biased loss to follow-up)

Without the second stage, must assume that Pr 𝐼𝐼𝑖𝑖 𝑜𝑜 = 1 𝐸𝐸𝑖𝑖 𝑜𝑜 ,𝑪𝑪𝑖𝑖 𝑜𝑜 ,𝑇𝑇𝑖𝑖 ,𝐷𝐷𝑖𝑖) = Pr 𝐼𝐼𝑖𝑖 𝑜𝑜 = 1 𝑇𝑇𝑖𝑖 ,𝐸𝐸𝑖𝑖 𝑜𝑜 ,𝑪𝑪𝑖𝑖(𝑜𝑜))

𝑤𝑤𝑖𝑖 𝑜𝑜 = [Pr 𝐼𝐼𝑖𝑖 𝑜𝑜 = 1 𝐸𝐸𝑖𝑖 𝑜𝑜 ,𝑪𝑪𝑖𝑖 𝑜𝑜 ,𝑇𝑇𝑖𝑖 ,𝐷𝐷𝑖𝑖 = 0]−1

Two-stage designs and analysis for adjusting for selection bias

• Schomaker et al. Statist Med 2013; “Non-ignorable loss to follow-up: correcting mortality estimates based on additional outcome ascertainment”

• Geng et al., JAMA 2008; “Sampling based approach to determining outcomes of patients lost of follow-up in antiretroviral therapy scale-up programs in Africa”

• Geng et al. PLOS One, 2011; “Retention in care and connection to care among HIV-infected patients on antiretroviral therapy in Africa: estimation via a sampling-based approach”

Factor Unadjusted Adjusted* Odds Ratio 95% CI p-value Odds Ratio 95% CI p-value

Age (per 10 years)

1.87 0.95–3.71 0.07 1.08 1.00–1.17 0.05

Distance (per 10 kilometer)

1.30 1.04–1.62 0.02 1.45 1.11–1.90 0.01

Male sex 0.90 0.25–3.27 0.87 Pre-therapy CD4+ T cell value (per 50 cells)

1.05 0.77–1.42 0.78

Calendar date of last visit (per year)

2.05 0.82–5.13 0.13 4.35 1.23–15.36 0.02

Methods EXIST for efficient study design and valid data analysis when standard design with standard analysis gives the wrong answer

Conclusions -

- Barriers to utilization

• software gaps

• software unfriendly, no QC

• inadequate training of students + practitioners (Epi & Biostat)

• are two-stage designs fundable @ NIH?

- Why do epidemiologists routinely adjust for one source of bias only?

(confounding by measured risk factors)