Confounding and effect modification Epidemiology 511 W. A. Kukull November

Confounding “A function of the complex interrelationships between various exposures and disease”. Occurs when the disease - exposure association under study is “mixed” with the effect of another factor

Example (after Rothman, 1998) Is frequent beer consumption is associated with rectal cancer ? Beer consumption is associated with consumption of pizza Is pizza consumption a confounder? –Is pizza, by itself, causally associated with Ca? if yes, then its a confounder; otherwise not

Beer and Rectal Ca OR= 0.67 ( )

Pizza consumption ? YesNo Beer No Beer Rectal CaControl Rectal CaControl

Confounding (after Rothman, 1998) Confounding factor must be risk factor for disease (causally associated) Confounding factor must be associated with exposure in the source (study) population Confounding factor must not be affected by exposure or disease –it cannot be the result of exposure –it cannot be an intermediate step in causal path

Confounding (after Koepsell & Weiss, 2003) A factor that occurs only as a consequence of the exposure cannot distort (confound) the disease- exposure association. To be a confounder, the factor would have to give rise to the exposure or be associated with something that did. “No matter how strongly a variable is related to exposure status, if it is not also related to the occurrence of the disease in question, it cannot be a confounder.”

Confounder – Exposure – Disease: some finer distinctions (Koepsell & Weiss, 2003) A confounder can be an actual cause of disease. A confounder can be associated with a cause of disease that, in the context of the study, cannot be measured. (e.g., genotype) A variable can be a confounder if it is related to the recognition of the disease even if it has no relationship to the actual occurrence of disease. (e.g., frequency of screening tests for disease)

Exposure Disease Confounder = non causal = causal Confounding ?

Age Distribution (conf) Country (exp) Mortality ?

General Health (conf) Sexual Activity (exp) Mortality ?

Other Meds (conf) Ca Channel Blockers (exp) GI Bleeding ?

Diet, SES Lifestyle (conf) Vitamin C Intake (exp) Colon Cancer ?

Low Fat Diet (exp) Cholesterol (conf ?) Heart disease ? Consequence of exposure

Weight Loss (conf ?) Smoking Lung Ca ? Consequence of disease

Quetelet Index Abdominal skinfold (conf ?) Type II Diabetes ? Skinfold is a surrogate measure of body mass

Red Meat diet Colon Ca Tax Id Number (conf ?) No plausible association with disease ?

Confounder or consequence? Studying decreased risk of MI and due to moderate alcohol consumption Higher HDL cholesterol is independently associated with lower risk of MI HDL increases as a result of moderate alcohol use Is HDL a Confounder?

Controlling confounding in the design of a study Randomization: ensures known and unknown confounders are evenly distributed in study groups Restriction: Limit subjects to one category of a confounder –e.g. if sex confounds, use only men; Matching: equalize groups on confounder (must follow matched analysis)

Evaluating Confounder disease and exposure Construct tables for –confounder and disease –confounder and exposure Examine odds ratios (or effect estimate) –are the associations “strong” –are they likely to be “causal”

Stratification in analysis: adjusting for confounding Computing the crude OR from a 2x2 table Stratification breaks the crude table into separate 2x2 tables for each level of the confounding factor –analogous to “standardization” –many factors and many levels can cause tables with empty cells

Is there Confounding? Do stratum specific RR estimates differ from Crude estimate? Does “adjusted” RR estimate differ from Crude estimate –Mantel-Haenszel –Multivariate modeling differences of >10% in RR when factor is included in the model, indicate confounding present

Confounding in stratified analyses stratify by the potential confounder compute stratum-specific OR estimates If uniform but different from crude OR then confounding is probably present: –calculate adj. OR (e.g., use Mantel-Haenszel) If NOT uniform across strata then “effect modification” (interaction) may be present –Report stratum specific estimates; do not adjust

Is toluene exposure associated with Diabetes? DiabetesCTRL Exposed to Toluene Not Exposed Crude OR = 1.95 ( )

Does the Age confound the diabetes – toluene association? <40> 40 diabetesctrldiabetesctrl Tolu. Not Tolu. Not OR(1) = 1.0 ( ) OR(2) = 1.0 ( )

Why? Age confounds because it is associated with diabetes, regardless of toluene exposure Toluene exposed No Toluene Diab Ctrl DiabCtrl >40 <40 >40 < OR = 4.0 ( ) OR = 4.0 ( )

Stratification example 1 Crude OR = 1.95 OR in each age group is 1.0 –when the strata OR’s are the roughly equal -- but different from the Crude OR-- it indicates confounding Age is a confounder We should adjust for Age in the analysis –Mantel-Haenszel adjusted OR (you will not need to memorize the formula)

ETOH and MI MINo MI Alcohol Yes No OR= 2.26 { }

non smokers smokers MICtrl MICtrl ETOH Yes No Yes No OR=1.0 ( ) OR = 1.0 ( ) Stratify by smoking

Physical Activity and Stroke StrokeNo Stroke P. A. High Low OR= 0.64 { }

Men Women StrokeCtrl StrokeCtrl P.A. Hi Lo Hi Lo OR= 0.53 ( ) OR = 1.19 ( ) Stratify by Gender

Controlling Confounding in the Analysis: Adjusted odds ratio Stratified analysis (examine strata OR) –Mantel-Haenszel adjusted OR : a weighted average of stratum specific OR’s  (ad / N) divided by  (bc / N) = OR mh –Where N= total subjects in each sub table ab cd N1N1 a b c d N2N2

Mantel-Haenszel Adjusted OR (a 1 d 1 )/N 1 + (a 2 d 2 )/N (b 1 c 1 )/N 1 + (b 2 c 2 )/N OR mh = ^

Trisomy 21 and spermicide use: Case-Control Study Down’sCtrl Sp + Sp - OR=

Stratify by Maternal Age < Down CtrlDown Ctrl Sp + Sp - Sp + Sp OR=

Mantel-Haenszel Adjusted OR (a 1 d 1 )/N 1 + (a 2 d 2 )/N (b 1 c 1 )/N 1 + (b 2 c 2 )/N OR mh = ^ [(3)(1059) / (1175)] + [(1)(86) / (95)] [(9)(104) / (1175)] + [(3)(5) / (95)] = = 3.8

Multivariate Statistics Linear: y = b 0 + b 1 x 1 + b 2 x b k x k Logistic: exp (b) gives you adjusted OR log(odds) = b 0 + b 1 x 1 + b 2 x b k x k for b 1 coded as a [0,1] variable, the OR x1 = e b1 (adjusted for all other x i ) Cox : exp (b) gives you adjusted RR log(haz) = b 0 + b 1 x 1 + b 2 x b k x k

Logistic Regression Coding Variables Continuous x causes b to be interpreted as: increase in log odds per unit change in x Interaction of two variables is represented by a single product term: x 1 x 2 (with only one b) –interpretation of models which include interaction and continuous terms can be tricky –Consult a friendly Biostatistician

Recognizing Confounding in logistic regression models Logistic Regression: –ln[Y/(1-Y)] = a + b 1 X 1 + b 2 X 2 + … b n X n –e (b i ) = OR (xi) (per unit change in X i ) –does b xi change when X k factor(s) are added? –Does crude OR differ from adjusted OR? –does model “log-likelihood” change (score test)

Logistic coefficients and OR’s e b = OR

Interaction (Effect Modification) Statistical, Biological and Social semantic meanings differ. Does the RR estimate “differ” at each level of a third variable? Homogeneity of RR Biological reasoning: is there something about the third factor that changes the way the Exposure-Disease association works?

Crude table Stratification Example: Crude table Hepatocellular carcinoma CaseControl Hepatitis C Virus infection Yes No Crude OR = 9.2 ( )

Stratify by HBV infection Are the stratum specific odds ratios statistically different? HBV- HepC+ - - CaseCtrlCaseCtrl HBV OR(1)= 25.9 (4.2 - * )OR(2)= 6.0 ( ) M-H “adjusted odds ratio” OR= 8.1 ORs are not statistically different: should we adjust or report strata ORs???

Stratification Example 2: HBV, HepC and Liver Ca The OR’s in the HBV strata look quite different –Does this indicate “effect modification”? –Effect modification is a finding in the data that needs to be elaborated; it is a natural phenomena that exists independently –Confounding is a nuisance that needs to be eliminated (by adjusting, matching, restriction, etc.)

Effect Modification (also known as “interaction”) When the measure of effect differs between strata –Can apply to RR or risk difference (AR) measures Presumed additive or multiplicative effect model depends on biology of disease and factor Synergy: when effect exceeds that expected under the chosen model –RR (A+B) >> RR (A) + RR (B) –RR (A x B) >> RR (A) x RR (B)

Schematic of additive model for case control data (Szklo & Nieto, 2000) BL “A” “Z” “A” Excess joint increase Additive model effects: Expected = OR(A) + OR(Z) OR= Expected Observed

RR estimates in strata: “guidelines” for heterogeneity [Szklo & Nieto 2000]

Is there an association between risk factor (X) and disease (Y)? YES Is it affected by Bias? No Estimate magnitude and direction of effect on RR Are STRATUM RR’s different from“crude”RR? YES Stratum RRs are similar to each other: Confounding : Adjust for stratum factor Stratum RRs are statistically different from each other: Interaction/effect modification report strata RRs, don’t adjust Yes No No confounding by Strata factor Stratified analysis flow chart

Considerations Collect data on potential confounders –if you don’t get it you can’t control for it Try to reason what the potential effect of confounding might be –Magnitude and direction (as with bias) –Coffee drinking and MI: smoking may be a positive confounder because smokers are at increased risk of MI

Generally speaking... A “strong” association is less likely to be explained by confounding than a weak one For an observed association to be the sole result of confounding by another factor: –the factor must have a stronger association with disease than the one observed –if RR= 10.0 for smoking and Lung ca, then a confounder would need RR> 10.0

Logistic Regression Allows simultaneous adjustment for several confounders (also allows “interactions”) –multiple variables to predict disease status (dichotomous outcome) Odds ratios can be obtained directly from the regression coefficients “Standard” method seen in most case- control study analyses (matched and unmatched analyses)

Conclusion What is confounding? –How do we recognize, evaluate and control it? What is effect modification? –How do we recognize and evaluate it? –Why is it important? –[also know as “interaction”, “effect measure modification”, etc.]