confounding & effect modification

Smokers

Non-Smokers

Age

Age

Confounding

&

Effect Modification

Confounding

&

Effect Modification

Yes No

Heart Disease

20 108 128 15.6%Yes

30 64 94 31.9%No

RR (95% CI)= 0.5 (0.3-0.8)p = 0.004

Vigorous Exercise

Incidence

Weighing the Risk of CAD

Sedentary

Active

Active Sedentary Active Sedentary

Age Age

Age

Age

Unequal Age Distribution Exaggerates the Benefit of Exercise

Active

Sedentary

Age

Age

Equal Ages Provide aFairer Comparison

Confounding occurs when the study groups differ with respect to other factors that influence the outcome.

ConfoundingConfounding

The true effect of the exposure on likelihood of disease is distorted because it is mixed up with another factor that is associated with the disease.

Older people exercise less.

physical inactivity heart disease

age

?

What is the relationship after removing the distorting effect of confounding by age?

Older people have more risk of heart disease.

(Latin: “confundere” : to mix together)

In order for confounding to occur the extraneous factor must be associated with both the risk factor being evaluated and the outcome of interest.

physical inactivity coronary artery disease

fluidintake

Even if fluid intake differs, it will not confound this relationship, since it doesn’t affect CAD.

?

However, if the age distributions of the groups being compared are the same, there will be no confounding.

physical inactivity heart disease

age

?

Older people have more risk of heart disease.

Confounding occurs when the study groups differ with respect to other factors that influence the outcome. This distorts the association you are trying to evaluate.

The comparison of cancer death rates in Alaska & Florida was distorted by the older age distribution in Florida. This was dealt with by calculating “age-adjusted” rates which removed the effect of age differences.

ConfoundingConfounding

Florida

AlaskaAge

Age

Confounding Can Exaggerate Differences…Confounding Can Exaggerate Differences…

Confounding may account for

all or part of an apparent association.

0

200

400

600

800

0

200

400

600

800

0

200

400

600

800

Apparent difference(Crude, Unadjusted)

True difference (Adjusted) True difference (Adjusted)

…or Confounding Can Cause Differences to Be Underestimated

…or Confounding Can Cause Differences to Be Underestimated

Confounding may account for all or part of an apparent association.

0

200

400

600

800

0

200

400

600

800

Apparent difference(Crude, Unadjusted)

Difference after Adjusting

The comparison of CAD was distorted by the fact that sedentary subjects may be older.

Goal: determine the association between activity and heart disease after removing the distorting effect of age.

Sedentary

ActiveAge

Age

Confounders are other risk factors that confuse the relationship you want to study, so you want to remove their effect.

Other Differences BetweenExercisers and Non-exercisers

Other Differences BetweenExercisers and Non-exercisers

Active SedentaryAge 46 + 1.4 59 + 1.5Body Fat % 15 + 4.5 22 + 5.6Dietary fat % 29 + 5.0 42 + 7.0Current smokers 5% 24%Hypertension 8% 17%Diabetes mellitus 2% 9%

Family history of CHD 25% 5%Males 60% 40%

Sedentary

ActiveAge

Age

Diabetes

Diabetes

Fam Hx

Fam Hx

Confounders are other risk factors or preventive factors for the outcome of interest.

Ways to Control for ConfoundingWays to Control for Confounding

In the Design:• Restriction• Matching (also need matched analysis)• Randomization (don’t need to know

what the confounders are)

In the Analysis:• Stratification• Multivariate Analysis

Simple and effective, but There will be residual confounding if

restriction is not narrow enough. Limits sample size. Can’t evaluate restricted variable. Limits ability to generalize findings.

We could restrict our study on exercise to non-smoking, non-diabetic, white males age 20-40.

RestrictionRestriction

Simple and effective, but Expensive, time-consuming Limits sample size You can’t evaluate the matched factor.

MatchingMatching

Very Useful For:- complex multifaceted variables (e.g., environment, heredity)- case-control with few cases, but many controls (e.g., DES)

Subjects are allocated to treatment groups by a random method that gives an equal chance of being in any treatment group.

With adequate numbers of subjects, it insures baseline comparability of groups.

Provides control for both known and unknown confounders.

Randomization (in a clinical trial)Randomization (in a clinical trial)

If differences between young and old confuse the relationship between physical activity and coronary artery disease, then look at the relationship separately in the young and the old.

Control of Confounding (in analysis)

Stratification

Control of Confounding (in analysis)

Stratification

• Older people tend to exercise less.• Older people have a greater risk of heart disease.

physical inactivity coronary artery disease

age?

Heart Diseaseyes no

48 800

69 625Crude RR = 0.57

yesActive no

Heart Diseaseyes no

25 600

11 225

RR = 0.86

yesActive no

23 200

58 400

RR = 0.81

yesActive no

Heart Diseaseyes no

Young subjects (<45) Older subjectsStratified Analysis

The stratum-specific RRs differ from crude, but are similar to each other (confounding). There’s a benefit of activity, but not as great as the crude RR suggested.

Confounding in a Cohort Study

Confounding in a Cohort Study

Ie=0.10

Io=0.13

Ie=0.040

Io=0.047

Mantel-Haenszel chi-square test: tests significance of the adjusted RR.

A pooled average of the stratum-specific RRs.RRmh = 0.84 (adjusted for confounding by age)

Heart Diseaseyes no

25 600

11 225

RR = 0.86

yesActive no

23 200

58 400

RR = 0.81

yesActive no

Heart Diseaseyes no

Young subjects (<45) Older subjects

Summarizing Results of Stratified AnalysisSummarizing Results of Stratified Analysis

Mantel-Haenszel Equations Calculate:

RR=0.5

35-39 40-44 45-49 50-54 55-59 60-64

RR: 0.72 0.81 0.80 0.79 0.83 0.77

Multiple Strata to Control for Confounding by AgeMultiple Strata to Control for Confounding by Age

Exercise + -

Heart Disease + -

(Crude RR)

(Stratum-specific Relative Risks)

Pooled estimate: RRmh= 0.79)

Multiple Strata to Control for Confounding by Two Factors (or more)

Multiple Strata to Control for Confounding by Two Factors (or more)

Exercise + -

Heart Disease + -

Family History Family Historyof Heart Disease Negative

Males Females Males Females

Heart Diseaseyes no

51 800

76 600Crude RR = 0.57

yesActive no

Heart Diseaseyes no

35 315

60 290

RR = 0.58 (0.40 - 0.86)

yesActive no

11 339

9 341

RR = 1.22 (0.51 - 2.91)

yesActive no

Heart Diseaseyes no

Men WomenStratified Analysis

The effect of exercise on heart disease is different in men and women. Effect modification is present if the stratum-specific estimates of association differ from each other!

Effect Modificationin a Cohort Study


Heart Diseaseyes no

51 800

76 600Crude RR = 0.57Crude RR = 0.57

yesActive no

Heart Diseaseyes no

35 315

60 290

RR = 0.58 (0.40 - 0.86)

yesActive no

11 339

9 341

RR = 1.22 (0.51 - 2.91)

yesActive no

Heart Diseaseyes no

Men WomenStratified Analysis



Possible explanations:1) The effect of exercise on risk of heart disease is different in men and women, i.e. there is a physiologic difference. (Effect modification)

2) Inadequate sample size & imprecise estimates.

Effect ModificationEffect Modification

“Interaction” or “Synergism”When the magnitude of association (effect) is modified by another factor.

Example: The association between smoking and lung cancer is modified by asbestos exposure.

Without Asbestos With Asbestos

Smoking

Lung Cancer

Y

Y N

NSmoking

Lung Cancer

Y

Y N

N

RR = 20 RR = 64

Is there an association between smoking and lung cancer?

50-59 year olds 60-69 year olds

Smoking

Lung Cancer

Y

Y N

NSmoking

Lung Cancer

Y

Y N

N

RR = 20RR = 21

Smoking

Lung Cancer

Y

Y N

N

RR = 26

Heart Diseaseyes no

54 800

69 600

Crude RR = 0.61 yesActive no

Heart Diseaseyes no

RR = 0.80 (0.50 - 1.10)

yesActive no

28 200

58 400

RR = 0.97 (0.57 - 1.37)

yesActive no

Heart Diseaseyes no

26 600

11 200

Young OldStratified Analysis

Stratum-specific estimates of association differ from crude estimate and also differ from each other!

BothEffect

Modification&

Confounding

Stratified Analysis: SummaryStratified Analysis: Summary

Purposes:• Identify & control for confounding• Identify effect modification

Possibilities:1) No confounding or effect modification2) Confounding only3) Effect modification only4) Both effect modification & confounding

When the stratum-specific estimates differ:Report the stratum-specific estimates of association and the 95% confidence interval for each.

Do NOT combine the stratum-specific estimates into a pooled estimate.

Like confounding, effect modification can be evaluated by stratification.

BUTEffect modification is a biological phenomenon that should be carefully described (not adjusted for).

Effect ModificationEffect Modification

• If crude and stratum-specific estimates of RR are similar, there is no confounding or effect modification

• If stratum-specific estimates differ appreciably from each other then effect modification is occurring & should be described by reporting all stratum-specific estimates separately.

• If stratum-specific RRs differ from crude, but are similar to one another, then confounding has occurred, and an adjusted estimate should be calculated (Mantel-Haentzel).

“Eyeball” the Results

The 10% Rule

Dietary Fiber and Colon Cancer

A case-control study was done to look for an association between low dietary fiber and risk of colon cancer.

Crude analysis:OR= 3.1 95% CI: 1.2-4.2

Stratified by dietary fat content:

Canceryes no

OR = 1.2 (0.50 - 1.90)

yesLow Fiber no

yesLow Fiber no

Canceryes no

High Fat Low Fat

OR = 1.1 (0.60 - 1.95)

CHD No CHD Totals IncidenceHigh BMI 220 9,780 10,000 .022Low BMI 83 9,917 10,000 .0083

Crude RR = 2.65

Is High BMI Associated with CHD?


RR = 1.94

Given: Age is associated with both high BMI & risk of CHD.


RR = 1.54

1) Is age a confounder in this study?2) Is there effect modification?

Young

Old

Crude

A Cohort StudyA Cohort Study

The Problem of Multiple Confounding FactorsThe Problem of Multiple Confounding FactorsStratify by:• gender• age (5 categories)• smoking status (never, former, current)

males females

5 ages 5 ages

3 levels of smoking for each age & gender group

30 different sub-strata!!!(some with very small # of subjects)

Crude RR = 6.75

RR = 9.54 RR = 4.90

5 45

12 576

yes70+ no

Deathyes no

Deathyes no

8 16

13 359

yes70+ no

No Safety (Unrestrained) Various Safety

Stratified Analysis

MVCMVC

13 61

25 935

Deathyes no

yes70+ no

74

960

17.6%

2.6%

33.1%

3.5%

10 %

2 %

RRmh=7.22(7.22-6.75)/6.75 = 0.07 =7%

To evaluate confounding, you can use Mantel-Haenszel method to compute a pooled average, then see if this differs from crude RR by >10%

The Problem of Multiple Confounding FactorsThe Problem of Multiple Confounding FactorsStratify by:• gender• age (5 categories)• smoking status (never, former, current)

males females

5 ages 5 ages

3 levels of smoking for each age & gender group

30 different sub-strata!!!(some with very small # of subjects)

Multiple Variable Regression Analysis to

Control for Confounding

Multiple Variable Regression Analysis to

Control for Confounding

Multiple Variable AnalysisMultiple Variable Analysis

• Analytical techniques that adjust for several variables simultaneously.

• Mathematical models describe association between:

Disease Exposure (main risk factor of interest) Confounders (other risk factors)

• Efficient control of multiple confounding factors (even when stratification would fail).

Simple Linear Regression (with a continuous dependent [Y] variable)

Simple Linear Regression (with a continuous dependent [Y] variable)

*

*

* *

* **

X-axis: Height (inches)

Y-axis:

Body Weight(pounds)

50 60 70 80

160

150

140

130

100

80

Y = a + b Xwgt = 80 + 2 (hgt)

Multiple Linear RegressionMultiple Linear Regression

An extension of simple linear regression

Y = a + b1X1 + b2X2 + b3X3 . . . bnXn

Multiple independent (predictor) variables

x

x

x

x

x

x

xx

xx

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0 2 4 6 8 10

x

x

x

x

x

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x

x

x

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xx

x

x

x

BodyMassIndex

30

28

26

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22

20

“Diet Score”

x

x

x

x

x

x

xx

xx

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x

x

x

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x

x

x

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0 2 4 6 8 10

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x

x

x

x

x

x

x

x

x

xx

x

x

x

BodyMassIndex

30

28

26

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“Diet Score”

What if older people tend to have higher BMIs?

x

x

x

x

x

x

xx

xx

x

x

x

x

x

x

x

x

x

0 2 4 6 8 10

x

x

x

x

x

x

x

x

x

x

xx

x

x

x

BodyMassIndex

30

28

26

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22

20

“Diet Score”

What if older people tend to have higher BMIs?

And what if males tend to have higher BMIs than females?

x

x

x

x

x

x

xx

xx

x

x

x

x

x

x

x

x

x

0 2 4 6 8 10

x

x

x

x

x

x

x

x

x

x

xx

x

x

x

Males

FemalesMales

Females

AGE > 20

AGE < 20

30

28

26

24

22

20

BodyMassIndex

“Diet Score”

x

x

x

x

x

x

xx

xx

x

x

x

x

x

x

x

x

x

0 2 4 6 8 10

BodyMassIndex

x

x

x

x

x

x

x

x

x

x

xx

x

x

x

Males

FemalesMales

Females

AGE > 20

AGE < 20

30

28

26

24

22

20

“Diet Score”

BMI = 18.0 + 1.5 (diet score) + 1.6 (if male) + 4.2 (if adult)

Multiple Linear Regression(with a continuous dependent [Y] variable)

Multiple Linear Regression(with a continuous dependent [Y] variable)

Y = a + b1 X1 + b2 X2 + b3 X3

BMI is dependent on several factors (age, gender, & diet), each of which has an independent effect on BMI.

BMI is dependent on several factors (age, gender, & diet), each of which has an independent effect on BMI.

x

x

x

x

x xx

xx

x

xx

x

x

x

xx

0 2 4 6 8 10

BodyMassIndex

x

Females

30

28

26

24

22

20

“Diet Score”

Males

A similar question:

How is body weight related to height and age?

Wgt

Height (inches)

Age

0

10

15

20

25

30

35

50 60 70 80

10

20

30

40

50

60

*

*

*

*

*

*

*

*

*

Wgt

.

Hei

ght (

inch

es)

Age

*

*

*

*

*

*

**

*

At any given height, an increase in age is associated with a further increase in weight.

Y = a + b1X1 + b2X2

Weight = 10 + 1.5 x Height [in] + 0.5 x Age [yrs]

Wgt

Height (inches)A

ge

0

10

15

20

25

30

35

50 60 70 8010

2

0

30

4

0

50

“Independent Effect”

By “independent” effect, I mean independent of confounding by other risk factors.

Or, after I have “taken into account” or “adjusted for” the effect of possible confounders, the “independent” factor still has a significant impact on the outcome.

Some outcomes are dichotomous, not continuous.

e.g. Lived or died

Developed CHD or not

Obese or non-obese

Colon cancer (Y/N)

Problem

x

x

x

x

x

x

xx

xx

x

x

x

x

x

x

x

x

x

0 2 4 6 8 10

x

x

x

x

x

x

x

x

x

x

xx

x

x

x

BodyMassIndex

30

28

26

24

22

20

“Diet Score”

The “Crude” (Unadjusted) Association

p = 0.15

OR = 2.14

High BMI

High Diet Score

15

6 6

7Yes

No

Yes No

Confounding?

Obeseyes no

yes

no

yes

no

Obeseyes no

Young Old

Males Females Males Females

Could Stratify….

Something Similar to Multiple Linear Regression?

e.g.The relationship between “diet score” and BMI (high versus low)...

while simultaneously taking into account (adjusting for) differences in age and gender??

1 0 2 02 0 2 03 0 3 04 1 6 .145 1 3 .256 1 2 .337 4 7 .368 5 4 .569 7 4 .6410 7 2 .7811 7 1 .8812 11 1 .9213 5 0 1.0014 2 0 1.0015 1 0 1.00

# with # with ProbabilityDiet Score High BMI Low BMI of High BMI

Likelihood = Probability of an event occurring(Odds) Probability of the event not occurring

If probability of an event occurring = “Y”,

then Likelihood (odds) = Y

(1-Y)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 2 4 6 8 10 12 14 16

Diet Score

Pro

ba

bili

ty o

f H

igh

BM

I (Y

)Probability of High BMI for Different Diet Scores

0

1020

30

4050

60

0 5 10 15

Diet Score

Lik

elih

oo

d o

f H

igh

BM

I

-1.5000

-1.0000

-0.5000

0.0000

0.5000

1.0000

1.5000

2.0000

2.5000

0 5 10 15 20

Diet Score

Lo

g(L

ike

liho

od

of

Hig

h B

MI)

Likelihood[Odds]

Log(Likelihood)[Log(Odds)]

Y (1-Y)

Log = b0 + b1X1 + b2X2 + b3X3 + ... + bnXn

The Logistic Function

Y = probability of high BMI

Y/ (1-Y) = likelihood of high BMI

dietscore(0/1)

agegroup(0/1)

sex(0/1)

Multiple Logistic Regression(with a categorical dependent [Y] variable)

Multiple Logistic Regression(with a categorical dependent [Y] variable)

Log(Likelihood)

x

x

x

x

x

x

xx

xx

x

x

x

x

x

x

x

x

x

0 2 4 6 8 10

x

x

x

x

x

x

x

x

x

x

xx

x

x

x

BodyMassIndex

30

28

26

24

22

20

“Diet Score”

The “Crude” (Unadjusted) Association

p = 0.15

OR = 2.14

High BMI

High Diet Score

15

6 6

7Yes

No

Yes No

Model: Log(Odds of High BMI) = High diet score Older age grp. Male

values: (High BMI= 0 or 1) (0/1) (0/1) (0/1)

Variable b p-value ORX1: High diet score 2.6011 0.03 13.5X2: Older age group 2.1919 0.07 8.9X3: Male gender 1.2527 0.13 3.5

(Adjusted)

(Association between High diet score and High BMI after adjusting for confounders (age group & gender)

Multiple Logistic RegressionMultiple Logistic Regression

(dichotomousoutcome)

(dichotomousoutcome)

ConfoundersConfounders

Alcohol Consumption

HDL levelHeart

disease

Not just a step in a causal chain.

2-3 glasses of wine/dayversus

No alcohol

Association Between Alcohol Consumption & CHD

Coronary Heart Disease

RR = 0.70

After adjusting for HDL (high density lipoproteins):

RR = 0.98

Does Exercise Decrease Heart Disease?Does Exercise Decrease Heart Disease?

Exercisers vs. Sedentary: Crude RR = 0.53

RR Factor (adjusted) 95% CI pExercise .75 .63 - .97 .02Age>40 4.3 3.8 - 4.8 .001Smoking 5.2 4.9 - 5.5 .001BMI>28 2.3 1.4 - 4.2 .04Hypertension 2.1 1.8 - 2.4 .001Diabetes 5.4 5.0 - 5.8 .001+ Family History 2.2 1.2 - 3.2 .03Use of multivitamins0.8 0.6 - 1.2 .09

Results of Logistic Regression Analysis:

So, Does Exercise Prevent Heart

Disease?

So, Does Exercise Prevent Heart

Disease?

“In epidemiologic studies, physical activity hasbeen associated with a decrease in the risk ofcoronary heart disease, but data on womenhave been sparse.”

What kind of study would you do?

“We prospectively examined the associationsbetween the score for total physical activity,walking, and vigorous exercise and the incidence of coronary events ….”

Who would you choose for subjects?

Study Population“The Nurses’ Health Study was initiated in 1976, when 121,700 female registered nurses 30 to 55 years old who were residing in 11 large U.S. states completed a mailed questionnaire on their medical history and lifestyle. Every two years, follow-up questionnaires have been sent to obtain updated information on potential risk factors and to identify newly diagnosed cases of coronary heart disease or other illnesses. For the primary analyses in the present study, the base-line data were those gathered in 1986, when detailed information on physical activity was first collected, and the duration of follow-up was eight years. After women who reported a diagnosis of cardiovascular disease or cancer at base line were excluded, the population for analysis was made up of 72,488 women 40 to 65 years old in 1986.”

How would you assess the exposure (exercise)?

Assessment of Physical Activity“Detailed information on physical activity was first collected in1986 and was updated in 1988 and 1992. Participants were asked to report the average amount of time spent per week during the previous year in walking or hiking outdoors (including walking to work or while playing golf ), jogging (at a speed slower than 10 minutes per mile [6 minutes per kilometer]), running (at 10 minutes per mile or faster), bicycling (including the use of a stationary bicycle), swimming laps, playing tennis or squash, or participating in calisthenics, aerobics, or aerobic dance; in addition, the women were asked to report the average number of flights of stairs they climbed each week. Women also reported their usual walking pace: easy or casual (<2.0 miles per hour [mph] [3.2 km per hour]), average (2.0 to 2.9 mph [3.2 to 4.6 km per hour]),brisk (3.0 to 3.9 mph [4.8 to 6.2 km per hour]), or very brisk(»4.0 mph [6.4 km per hour]).”

“Using a standardized classification of the energy costs of physical activities,8 we calculated a weekly metabolic-equivalent (MET) score for total physical activity, vigorous activity (»6 MET per hour), nonvigorous activity(<6 MET per hour), and walking (2.5 to 4.5 MET per hour, depending on the pace). One MET is the caloric need per kilogram of body weight per hour of activity, divided by the caloric need per kilogram per hour at rest. Physical-activity scores were expressed as MET-hours per week. Validation of the questionnaire for assessing physical activity has been described previously in a similar cohort9; the overall correlation between physical activities reported on the questionnaire and those recorded in four one weekdiaries was 0.62, and the correlation was 0.79 for activitiesreported on the questionnaire and those recalled after one week.9”

How would you assess the outcome of interest (heart disease)?

Ascertainment of End PointsThe primary end points for this study were coronary events(defined as nonfatal myocardial infarction or death due to coronary disease) that occurred after the return of the 1986 questionnaire and before June 1994. We requested permission to review the medical records of women who reported a nonfatal myocardial infarction on a follow-up questionnaire. Study physicians who had no knowledge of the women’s self-reported risk factors reviewed the records. Nonfatal myocardial infarction was confirmed if data in the medical records met World Health Organization criteriafor this condition — namely, symptoms and either diagnosticelectrocardiographic changes or elevated cardiac-enzyme levels.10

In this prospective cohort study, what is a potentially important bias and how would you deal with it?

“Follow-up information for nonfatal infarction was obtained for more than 95 percent of the potential person-time of follow-up.

Deaths were reported by family members or the Postal Service or were ascertained through state registries or the National Death Index. We estimate that follow-up for deaths was more than 98 percent complete.”

How would you approach the statistical analysis?

What key comparisons would you make?

“Person-time for each participant was calculated from the date of her return of the 1986 questionnaire to the date of an incident coronary event, death from any cause, or June 1, 1994, whichever came first.

The relative risk of a coronary event was computed as the incidence of the event in each quintile group for MET score, divided by the incidence in the lowest quintile group, with adjustment for five-year age categories.”

What are some possible confounding factors for this study?

How would you suggest they deal with these?

“We used … logistic regression to adjust simultaneously for potential confounding variables, including age (in five-year categories), period during the study (four two-year periods), smoking status (never smoked, previously smoked, or currently smokes 1 to 14, 15 to 24, or »25 cigarettes per day), body-mass index… , alcohol consumption (0, 1 to 4, 5 to 14, or »15 g per day), menopausal status (premenopausal, postmenopausal without hormone-replacement therapy, postmenopausal with previous hormone-replacement therapy, or postmenopausal with current hormone-replacement therapy), history of diabetes, history of hypercholesterolemia, history of hypertension,parental history of myocardial infarction before the age of60 years, use of multivitamin supplements, use of vitamin E supplements, and use of aspirin….”

Was there potential confounding by any of these factors?

N Engl J Med 1999;341:650-8.

Low Fiber Diet Colon Cancer??

Model 1Variable OR p-valueLow fiber diet 3.1 0.02

Model 3Variable OR p-valueLow fiber diet 1.2 0.45High fruit & veggies 0.6 0.01Dietary fat>40% 4.7 0.001

Model 2Variable OR p-valueLow fiber diet 2.1 0.07High fruit & veggies 0.3 0.002

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