Spring 2008

Bias, Confounding, and Effect ModificationSTAT 6395Filardo and Ng

Suppose we have observed an association between an exposure and disease in a cohort study or case-control study that:We are confident was not a biased result due to a flaw in the design or execution of the study Confounding

Suppose we have observed an association between an exposure and disease in a cohort study or case-control study that:We are confident was not a random association due to chance variation (95% confidence interval for the estimate does not include 1.0)Confounding

Suppose we have observed an association between an exposure and disease in a cohort study or case-control study that:How do we now distinguish between a noncausal association due to confounding and a causal association?Confounding

The exposure of interest is geographic areaAnnual mortality rate from prostate cancer:Region A : 50 per 100,000Region B: 20 per 100,000

Relative risk = 50/20 = 2.5

Do these data show that living in Region A is a risk factor for prostate cancer?Hypothetical example of confounding: comparison of prostate cancer mortality rate in 2 geographic areas

*per 100,000 per year

Unadjusted (crude) RR = 50/20 = 2.5Age-adjusted RR = 66.25/85 = 0.78Prostate cancer mortality rate in 2 geographic areas

Region

Age

Mid-year

Population

Prostate

Cancer Deaths

Prostate

Cancer Mortality*

A

65

800,000

490

61.25

All

1,000,000

500

50

B

65

200,000

160

80

All

1,000,000

200

20

Age as a confounderThe large discrepancy between the age-adjusted RR (0.78) and the unadjusted RR (2.5) means that age confounded the observed association between geographic area and prostate cancer mortality

Age as a confounderAge was a confounder because:Age is a risk factor for prostate cancer Age was associated with geographic regionAge is not an intermediate step in a causal pathway between residence in a geographic region and prostate cancer mortality

Age as a confounderAge is a common confounder in observational epidemiology because it is associated with many diseases and many exposuresAs distinct from a biased association, which is erroneous, the confounded association between geographic region and prostate cancer mortality, though not causal, is real

Geographic areaProstatecancerAgeCausal association (?)RR(unadj)=2.5RR(adj)=0.78+ association+associationAge confounded the relationship between geographic area and prostate cancer

Case-control study: alcohol consumption and lung cancerOR(unadj) = (390x175)/(325x110) = 1.91Note:90% of the 500 cases in the study were smokers 25% of the 500 controls in the study were smokers 80% of the smokers drank

Cases

Controls

Total

Drinkers

390

325

715

Non-

Drinkers

110

175

285

Total

500

500

1,000

OR = (360x25)/(100x90) = 1.00Case-control study: alcohol consumption and lung cancer table for Smokers

Cases

Controls

Total

Drinkers

360

100

460

Non-

Drinkers

90

25

115

Total

450

125

575

OR = (30x150)/(225x20) = 1.00Case-control study: alcohol consumption and lung cancer table for NON Smokers

Cases

Controls

Total

Drinkers

30

225

255

Non-

Drinkers

20

150

170

Total

50

375

425

OR = (450x375)/(125x50) = 27.0Smoking and lung cancer

Cases

Controls

Total

Smokers

450

125

575

Non-

smokers

50

375

425

Total

500

500

1,000

Alcohol consumption and smokingOR = (460x170)/(255x115) = 2.67

Smokers

Non-

smokers

Total

Drinkers

460

255

715

Non-

drinkers

115

170

285

Total

575

425

1,000

Alcohol consumption and lung cancer (summary)Unadjusted OR = 1.91Stratify by smoking status (2 strata -- smokers and nonsmokers)OR = 1 for the relationship between alcohol consumption and lung cancer among both smokers and non smokers

Smoking-adjusted OR (weighted average of the stratum-specific ORs) = 1.00

Smoking confounded the relationship between alcohol consumption and lung cancerLarge discrepancy between the smoking-adjusted OR (1.00) and the unadjusted OR (1.91) shows smoking was a confounder

Smoking confounded the relationship between alcohol consumption and lung cancerSmoking was a confounder because: Smoking is a strong risk factor for lung cancer

Smoking is associated with alcohol consumption

Smoking is not an intermediate step in a causal pathway between alcohol consumption and lung cancer

AlcoholconsumptionLungcancerSmokingCausal association = NOOR(unadj)=1.91OR(adj)=1.00+ association+associationSmoking confounded the relationship between alcohol consumption and lung cancer

Confounding: definition Confounding is a distortion of the association between exposure and outcome brought about by the association of another, extraneous exposure (confounder) with both the disease and the exposure of interest

Confounding: definitionAs distinct from a biased association, which is erroneous, a confounded association, though not causal, is real

Properties of confoundersA confounder must be associated with the exposure under study

AlcoholconsumptionLungcancerElectomagneticfieldsCausal association (?)RR(unadj)=RR(adj) ?associationExposure to electromagnetic fields cannot confound the relationship between alcohol consumption and lung cancerProperties of confounders

Properties of confounders For an extraneous exposure to be a confounder, it is necessary, but not sufficient to just be associated with the exposure of interest

AlcoholconsumptionLungcancerRead meatCausal association (?)RR(unadj)=RR(adj) Red meat consumption cannot confound the relationshipbetween alcohol consumption and lung cancer+ associationProperties of confounders

Properties of confoundersA confounder must also be a risk factor for the disease

AlcoholconsumptionLungcancerSmokingCausal association = NOOR(unadj)=1.91OR(adj)=1.00+ association+associationSmoking confounds the relationship between alcohol consumption and lung cancerProperties of confounders

Properties of confounders A confounder cannot be an intermediate variable in the causal pathway between the exposure of interest and the disease

Willingness to get HIV testingA: Predictors / Confounders HIV-related knowledge

Direct effect on HIV-related knowledge Direct effect on willingness to get HIV testing Mediated effect of A on willingness to get HIV testing

Properties of confounders

ExposureDiseaseConfounderCausal association ?+ / - association+ / -associationProperties of confounders

Avoiding confounding with appropriate study designRandomizationRestrictionMatching

Randomizationdone in experimental studies ONLYSubjects are randomly allocated between n groups ...ensuring that known and unknown potential confounder distributions are similar across groups

Restriction Restrict the selection criteria for subjects to a single category of an exposure that is a potential confounder in the cohort study of alcohol consumption and lung cancer, restrict the cohort to persons who have never smoked.

Enhances internal validity, but could hurt external validity

MatchingIn a case-control study, selection of controls who are identical to, or nearly identical to, the cases with respect to the distribution of one or more potential confounding factors Matching is intuitively appealing, but its implications, particularly in case-control studies, are much more complicated than one might at first suppose

Assessing the presence of confounding during analysisIs the potential confounder related to both the exposure and the disease?Stratification: Is the unadjusted OR or RR similar in magnitude to the ORs or RRs observed within strata of the potential confounder?Adjustment: Is the unadjusted OR or RR similar in magnitude to the OR or RR adjusted for the presence of the potential confounder?

Assessing the presence of confounding during analysisIs the potential confounder related to both the exposure and the disease?Confounding is judged to occur when the adjusted and unadjusted values differ meaningfully.

Pandey DK et al. Dietary vitamin C and beta-carotene and risk of death in middle-aged men. The Western Electric study.Concurrent cohort studyHypothesis: intake of vitamin C and beta carotene (both anti-oxidants) are protective against all-cause mortality Potential confounder: cigarette smoking

Unadjusted mortality rates and RRs according to vitamin C/beta-carotene intake index*deaths per 1,000 person-years

Index

Deaths

Person-

years

Mortality

Rate*

RR

Low

195

10,707

18.2

1.00

Medium

163

10,852

15.0

0.82

High

164

11,376

14.4

0.79

Percentage distribution of vitamin C/beta-carotene intake index by smoking status at baseline

Intake Index (%)

Current

Smoking

Low

Medium

High

No

29.3

35.3

35.4

Yes

35.0

31.1

33.9

Mortality rates and RRs by current smoking at baseline*deaths per 1,000 person-years

Current

Smoking

Deaths

Person-

years

Mortality

Rate*

RR

No

165

14,854

11.3

1.00

Yes

357

18,401

19.4

1.72

Mortality rates and RRs for vitamin C/beta-carotene intake index, stratified by current smoking at baseline*deaths per 1,000 person-years

Current

Smoking

Intake

Index

Mortality

Rate*

RR

No

Low

13.4

1.00

Medium

10.7

0.80

High

10.3

0.77

Yes

Low

21.4

1.00

Medium

18.9

0.88

High

17.8

0.83

Unadjusted and smoking-adjusted mortality RRs according to vitamin C/beta carotene intake index*Adjusted for smoking using the direct method with the total cohort as the standard population

RR

Low

Medium

High

Un-

adjusted

1.00

0.82

0.79

Adjusted*

1.00

0.85

0.81

Vitamin C/beta-caroteneMortalitySmokingCausal association (?)Medium intake:RR(unadj)=0.82RR(adj)=0.85

High intake:RR(unadj)=0.79RR(adj)=0.81

- association+associationSmoking did not confound the association between vitamin C/beta carotene intake and all-cause mortality

Methods of adjusting for (controlling for) confounding in the analysisAdjustment methods based on stratificationMathematical models (multivariable analysis)

Adjustment methods based on stratificationStratify by the confounderCalculate a single estimate of effect across the strata (adjusted OR or adjusted RR), which is a weighted average of the RRs or ORs across the strata

Adjustment methods based on stratificationStratify by the confounderCalculate the RR or OR for the association between the exposure and disease within each stratum of the confounder

3 methods of obtaining a weighted averageDirect adjustment (used in cohort studies) -- weights are based on the distribution of the confounder in a standard population

3 methods of obtaining a weighted averageIndirect adjustment (mainly used in occupational retrospective cohort studies) -- weights are based on the distribution of the confounder in the study population

3 methods of obtaining a weighted averageMantel-Haenszel method (most common adjustment method based on stratification; used in case-control or cohort studies) -- weights are approximately proportional to the reciprocals of the variances of the ORs or RRs within each stratum

Shapiro S et al. Oral-contraceptive use in relation to myocardial infarction a case-control studyHypothesis: recent use of oral contraceptives is associated with risk of myocardial infarctionCases: 234 premenopausal women with a definite first myocardial infarction (median age 43)Controls: 1,742 premenopausal women admitted for musculoskeletal conditions, trauma, abdominal conditions, and many miscellaneous conditions (median age 36)

Hospital-based case-control studyOR(unadj) = (29x1607)/(135x205) = 1.7

Cases

Controls

OC

29

135

No OC

205

1607

Age is a likely confounderAge is a risk factor for myocardial infarctionAge is negatively associated with oral contraceptive use

Assess for confounding by agePerform a stratified analysis by age

Compare the Mantel-Haenszel adjusted OR with the unadjusted ORMantel-Haenszel age-adjusted OR = 4.0Unadjusted OR = 1.7

Limitations of adjustment methods based on stratificationThere is often more than one potential confounderAllow adjustment only for categorical variables; continuous variables must be categorizedStratification methods are usually limited to adjustment for one or two confounders with a small number of categories each

Multivariable modelsSimultaneous adjustment for multiple potential confounders, including continuous variablesPotential confounders are included as variables in the model along with the exposure under studyCommonly used modelsLogistic regression: case-control and cohort studiesCox proportional hazards model: cohort studiesPoisson regression: cohort studies

Definition: variation in the magnitude of the association between an exposure and a disease (variation in the RR or OR) across strata of another exposureAre the odds ratios regarding the association between OC use and MI heterogeneous across the smoking status strata?Effect Modification (Interaction) - Oral contraceptives and myocardial infarction example

Oral contraceptives and myocardial infarction: stratified analysis by smokingEffect modification has an underlying biologic basis; it is not merely a statistical phenomonon.

Smoking

(cigarettes per day)

OC

Cases

Controls

OR

0

Yes

3

51

0.4

No

79

566

1-24

Yes

4

52

1.7

No

34

754

25+

Yes

22

32

2.1

No

92

287

Other effect modification examplesMenopausal status modifies the association between obesity and breast cancerThe association between gender and hip fracture is modified by ageNutrition modifies the association between HIV infection and progression of latent tuberculosis infection to active tuberculosis

Effect modification example: Lyon et al. Smoking and carcinoma in situ of the uterine cervixOR(unadj) = (130x198)/(45x87) = 6.6

Cases

Controls

Smokers

130

45

Non-smokers

87

198

Effect modification example: Lyon et al. Smoking and carcinoma in situ of the uterine cervixOR(unadj) = (130x198)/(45x87) = 6.6Mantel-Haenszel age-adjusted OR = 6.3p-value for heterogeneity

Confounding vs. Effect ModificationConfounding: Confounding is a distortion of the RR or OR that should be adjusted for

Effect modification: Effect modification is a property of a putative causal association. It is a finding to be detected and estimated, not a bias to be avoided or confounding to be adjusted forAn effect modifier may or may not itself be a confounder

Confounding vs. Effect Modification cohort study exampleThe unadjusted RR for the association between Exposure A and Disease X is 9.7How does age affect the relationship between Exposure A and Disease X? 4 hypothetical scenarios

*Iexp(A) /Inonexp(A)RR(unadj) = 9.7RR (adj) = 10.1Confounding vs. Effect Modification cohort study exampleAge is neither a confounder nor an effect modifier

Age

RR*

20-29

9.8

30-39

10.7

40-49

9.3

50-59

11.4

60-69

10.1

70-79

9.1

Note: When there is effect modification, we cannot summarize the relationship between Exposure A and Disease X with a single number [RR(adj)]Confounding vs. Effect Modification cohort study example*Iexp(A) /Inonexp(A)RR(unadj) = 9.7RR(adj) = 10.1Age is an effect modifier, but not a confounder

Age

RR*

20-29

15.7

30-39

17.3

40-49

12.8

50-59

9.1

60-69

3.2

70-79

2.4

*Iexp(A) /Inonexp(A)RR(unadj) = 9.7RR(adj) = 4.3Confounding vs. Effect Modification cohort study exampleAge is a confounder, but not an effect modifier

Age

RR*

20-29

5.4

30-39

2.8

40-49

4.7

50-59

3.5

60-69

4.1

70-79

4.5

*Iexp(A) /Inonexp(A)RR(unadj) = 9.7RR(adj) = 4.3

Confounding vs. Effect Modification cohort study exampleAge is a confounder and an effect modifier

Age

RR*

20-29

8.6

30-39

8.5

40-49

6.2

50-59

4.1

60-69

2.0

70-79

2.5

Case-control study of alcohol consumption, smoking, and oral cancerOR(unadj) = (80x125)/(40x40) = 6.25

Alcohol

Cases

Controls

Yes

80

40

No

40

125

Case-control study of alcohol consumption, smoking, and oral cancerOR(unadj) = (84x120)/(45x36) = 6.22

Smoking

Cases

Controls

Yes

84

45

No

36

120

Case-control study of alcohol consumption, smoking, and oral cancerUnadjusted OR = 6.25 Smoking-adjusted OR = 4.0

Smoking is a confounder of the relationship between alcohol consumption and oral cancer and no effect modification

Smoker

Alcohol

Cases

Controls

OR

No

No

20

100

Yes

16

20

4.0

Yes

No

20

25

Yes

64

20

4.0

Case-control study of alcohol consumption, smoking, and oral cancerUnadusted OR = 6.22 Alcohol-adjusted OR = 4.0

Alcohol consumption is a confounder of the relationship between smoking and oral cancer and no effect modification

Alcohol

Smoker

Cases

Controls

OR

No

No

20

100

Yes

20

25

4.0

Yes

No

16

20

Yes

64

20

4.0

ORs for the joint effect of smoking and alcohol consumption on risk of oral cancer

Smoker

Alcohol

Cases

Controls

OR

No

No

20

100

Ref

Yes

16

20

4.0

Yes

No

20

25

4.0

Yes

64

20

16.0

Assessment of effect modification (summary)Stratify by the potential effect modifierCalculate the RR or OR for the association between the exposure and disease within each stratum of the potential effect modifier

Assessment of effect modification (summary)Assess the degree of heterogeneity of the RRs or ORs across the strata by inspectionCalculate a p-value for heterogeneity however, remember that formal test for heterogeneity are conservative and they might fail to detect effect modification