Intermediate methods in observational epidemiology 2008 Confounding - I

Mortality 18% 30% Deaths Intervention No intervention % InterventionNo intervention Experimental (n=2000) Observational (n= 2000) OBSERVATION VS. EXPERIMENT Absent, mortality = 10% Present, mortality = 50% Confounding variable:

Confounding variable Less common in the group that undergoes the intervention Increased mortality (“outcome”) (DUAL) ASSOCIATION OF CONFOUNDING VARIABLE WITH BOTH OUTCOME AND INDEPENDENT VARIABLE

Mortality according to the intervention, stratified by the confounder Confounding variable: Intervention:NNo. of deaths Mortality PresentYes % No % AbsentYes % No % % 30% Intervention No intervention No. Deaths: Mortality: Absent, mortality = 10% Present, mortality = 50% Confounding variable: One of the solutions to eliminate confounding: stratify

Israeli Study, see Kahn & Sempos, pp. 105 OR= 1.88 Is the association causal? Is it due to a third (confounding) variable (e.g., age)? BP MI ? Age A variable is only a confounder if dual association is present

OR= 3.0 OR= 3.4 Does age meet the criteria to be a confounder? Yes

Age Increased odds of systolic hypertension (“exposure”) Increased odds of myocardial infarction (“outcome”) (DUAL) ASSOCIATION OF AGE WITH BOTH SYSTOLIC HYPERTENSION AND MYOCARDIAL INFARCTION

Confounder Exposure Outcome CONFOUNDING EFFECT … and not in the causality pathway between exposure and outcome: Confounder Exposure Outcome

Blood Pressure MI Risk Is it appropriate to calculate an adjusted OR? NO Odds Ratios not homogeneous Assumption when doing adjustment: Homogeneity of odds ratios (no multiplicative interaction).

Ways to assess if confounding is present: Strategy 1:Does the variable meet the criteria to be a confounder (relation with exposure and outcome)? Strategy 2: If the effect of that variable (on exposure and outcome) is controlled for (e.g., by stratification or adjustment) does the association change?

Ways to control for confounding During the design phase of the study: –Randomized trial –Matching –Restriction During the analysis phase of the study: –Stratification –Adjustment Stratified methods –Direct method –Mantel-Haenszel adjustment of Odds Ratios Regression methods

Matching in Case-Control Studies

Matching in a Case-Control Study Objective: To achieve comparability between cases and controls with regard to confounding variables Technique: For each case, choose a control without the case disease, of the same or similar age, at same service, same sex, etc.

Example of Matched Case-Control Study Cases: aplastic anemia seen in Baltimore from Controls: patients with non-hematologic/nonmalignant disorders, matched to cases on age (± 5 years), sex, ethnic background and hospital of admission Hypothesis: subclinical HBV is associated with Aplastic Anemia

Matched case-control study 42 yr old black woman 40 yr old white male 57 yr old white woman 55 yr old white woman 48 yr old black men 44 yr old AA woman- diab. 37 yr old white male- MI 60 yr old white woman- AP 55 yr old white woman- lupus 49 yr old AA men- meningioma Cases of Aplastic AnemiaControls (Patients)* (*Admitted to the same hospital as index case with other diseases)

PAIRS Cases smokernonsmoker Controls smoker nonsmoker Pair No.CaseControl 1smokernonsmoker 2smokernonsmoker 3 smoker 4 nonsmoker smoker 8 nonsmoker 9 10smoker Pairs of Cases and Controls Individually Matched by Age and Sex

PAIRS Cases smokernonsmoker Controls smoker nonsmoker Pair No.CaseControl 1smokernonsmoker 2smokernonsmoker 3 smoker 4 nonsmoker smoker 8 nonsmoker 9 10smoker Pairs of Cases and Controls Individually Matched by Age and Sex

PAIRS Cases smokernonsmoker Controls smoker nonsmokerXXXX Pair No.CaseControl 1smokernonsmoker 2smokernonsmoker 3 smoker 4 nonsmoker smoker 8 nonsmoker 9 10smoker Pairs of Cases and Controls Individually Matched by Age and Sex

PAIRS Cases smokernonsmoker Controls smokerX nonsmokerXXXX Pair No.CaseControl 1smokernonsmoker 2smokernonsmoker 3 smoker 4 nonsmoker smoker 8 nonsmoker 9 10smoker Pairs of Cases and Controls Individually Matched by Age and Sex

PAIRS Cases smokernonsmoker Controls smokerX nonsmokerXXXXX X X Pair No.CaseControl 1smokernonsmoker 2smokernonsmoker 3 smoker 4 nonsmoker smoker 8 nonsmoker 9 10smoker Pairs of Cases and Controls Individually Matched by Age and Sex

PAIRS Cases smokernonsmoker Controls smokerXX nonsmokerXXXXX X X Pair No.CaseControl 1smokernonsmoker 2smokernonsmoker 3 smoker 4 nonsmoker smoker 8 nonsmoker 9 10smoker Pairs of Cases and Controls Individually Matched by Age and Sex

= 4/2= 2.0 Odds Ratio for Matched Case-Control Studies Favors hypothesis Against hypothesis PAIRS Cases smokernonsmoker Controls smoker12 nonsmoker43

Risk Factors for Brain Tumors in Subjects Aged <20 years: A Case-Control Study (Gold et al, Am J Epidemiol 1979;109:309-19) Exploratory study of risk factors for brain tumors Subjects < 20 yrs old Cases: primary malignant brain tumors in Baltimore in Normal controls: chosen from birth certificates on file, and matched on cases by sex, date of birth (±1 year) and race Interviews with parents of children

Risk Factors for Brain Tumors: Birthweight 3818<3629 g g Controls’ birthweight <3629 g3629+ g Cases’ birth weight Exposed: g Unexposed: <3629 g Odds Ratio= 18/7= 2.6 (Gold et al, Am J Epidemiol 1979;109:309-19)

A few notes on “Matching” Most frequently used in case-control studies Frequency vs. individual matching Advantages: –Intuitive, easy to explain –Guarantees certain degree of comparability in small studies –Efficient (if matching on a strong confounder) –Particularly useful when outpatients are studied, and sample size is relatively small (e.g., <100 cases and <100 controls) Example: Case-control study of risk factors for emphysema: –For each newly diagnosed case of emphysema seen in an Outpatient Unit, select the next (control) patient without diabetes, with an age ± 2 years, of the same sex, and educational status Disadvantages: –Costly, usually logistically complicated –Inefficient if matching on a weak confounder –Questionable representativiness of control group (limits its use for other case-control comparisons) –Cannot study the matching variable (and additive interaction) –Possibility of residual confounding

Further issues for discussion Types of confounding Confounding is not an “all or none” phenomenon Residual confounding Confounder might be a “constellation” of variables or characteristics Considering an intermediary variable as a “confounder” for examining pathways Statistical significance and confounding

Types of confounding Positive confounding When the confounding effect results in an overestimation of the effect (i.e., the crude estimate is further away from 1.0 than it would be if confounding were not present). Negative confounding When the confounding effect results in an underestimation of the effect (i.e., the crude estimate is closer to 1.0 than it would be if confounding were not present).

Relative risk Type of confounding: Positive Negative TRUE, UNCONFOUNDED OBSERVED, CRUDE x x x x X ?

Confounding is not an “all or none” phenomenon A confounding variable may explain the whole or just part of the observed association between a given exposure and a given outcome. Crude OR=3.0 … Adjusted OR=1.0 Crude OR=3.0 … Adjusted OR=2.0 Residual confounding Controlling for one of several confounding variables does not guarantee that confounding be completely removed. Residual confounding may be present when: - the variable that is controlled for is an imperfect surrogate of the true confounder, - other confounders are ignored, -the units of the variable used for adjustment/stratification are too broad -the confounding variable is misclassified The confounding variable may reflect a “constellation” of variables/characteristics –E.g., Occupation (SES, physical activity, exposure to environmental risk factors) –Healthy life style (diet, physical activity)

Residual Confounding: Relationship Between Natural Menopause and Prevalent CHD (prevalent cases v. normal controls), ARIC Study, Ages Years, ModelOdds Ratio (95% CI) 1Crude4.54 (2.67, 7.85) 2Adjusted for age: Vs. 55+ (Mantel-Haenszel) 3.35 (1.60, 6.01) 3Adjusted for age: 45-49, 50-54, 55-59, (Mantel- Haenszel) 3.04 (1.37, 6.11) 4Adjusted for age: continuous (logistic regression) 2.47 (1.31, 4.63)

Confounding is not an “all or none” phenomenon A confounding variable may explain the whole or just part of the observed association between a given exposure and a given outcome. Crude OR=3.0 … Adjusted OR=1.0 Crude OR=3.0 … Adjusted OR=2.0 Residual confounding Controlling for one of several confounding variables does not guarantee that confounding be completely removed. Residual confounding may be present when: - the variable that is controlled for is an imperfect surrogate of the true confounder, - other confounders are ignored, -the units of the variable used for adjustment/stratification are too broad -the confounding variable is misclassified The confounding variable may reflect a “constellation” of variables/characteristics –E.g., Occupation (SES, physical activity, exposure to environmental risk factors) –Healthy life style (diet, physical activity)

Treating an intermediary variable as a confounder (i.e., ignoring “the 3 rd rule”) Under certain circumstances, it might be of interest to treat an hypothesized intermediary variable acting as a mechanism for the [risk factor-outcome] association as if it were a confounder (for example, adjusting for it) in order to explore the possible existence of additional mechanisms/pathways.

Scenario 1: The relationship of obesity to mortality is confounded by hypertension, i.e., the relationship is statistical but not causal Confounding factor or part of the chain of causality? Obesity Mortality Hypertension confounder exposure outcome Example: relationship of obesity to mortality

Scenario 2: The relationship of obesity to mortality is causal and mediated by hypertension mediator Obesity Mortality Hypertension exposure outcome Confounding factor or part of the chain of causality? Example: relationship of obesity to mortality

Scenario 3: In addition to being mediated by hypertension, the causal relationship of obesity to mortality is direct Obesity Mortality Hypertension mediator exposure outcome Confounding factor or part of the chain of causality? Example: relationship of obesity to mortality

Scenario 4: In addition to being mediated by hypertension, the causal relationship of obesity to mortality is mediated by other mechanisms Hypertension mediator Obesity Mortality exposure outcome Obesity Other mechanisms, e.g., diabetes Confounding factor or part of the chain of causality? Example: relationship of obesity to mortality

The different scenarios are not mutually exclusive! Hypertension mediator Obesity Mortality exposure outcome Obesity Other mechanisms, e.g., diabetes Confounding factor or part of the chain of causality? Example: relationship of obesity to mortality

Obesity and Mortality Relative Risk Unadjusted2.5 Adjusted for age, gender and ethnic background2.0 Adjusted for age, gender, ethnic background and systolic blood pressure (SBP) 1.3

Obesity and Mortality Relative Risk Unadjusted2.5 Adjusted for age, gender and ethnic background2.0 Adjusted for age, gender, ethnic background and systolic blood pressure (SBP) 1.3 For positive associations (exposures associated with a RR> 1.0):

Statistical significance as criteria to assess the presence of confounding E.g., a confounder might be ruled out in a case-control study solely because there is no statistically significant difference in the levels of the confounder comparing cases and controls. Exposure Case-cont ? Confounder BAD IDEA! If the confounder is strongly associated with the exposure, even a small difference between cases and controls (not statistically significant because of limited sample size) may still induce confounding… and vice versa E.g., Study of menopause as predictor of myocardial infarction. Even a small difference in age between cases and controls (e.g., 1 year, NS) may result in confounding due to the strong association between age and “exposure” (menopause).

% post-menopausal Age (years)5556 Odds Ratio= 60/40 ÷ 50/50 = 1.5 Example: Menopause as a risk factor

% post-menopausal Age (years)5556 casescontrols Odds Ratio= 60/40 ÷ 50/50 = 1.5