Epidemiology 503 Confounding

Confounding A non-causal association between a given exposure and an outcome that is observed as a result of the influence of a third variable (confounder).

Example of Confounded Association

Example of Confounded Association

Confounding in a Causal Diagram Health Status Weight Death

Properties of a Confounder Predictive of disease among the unexposed Drinking Car Crashes Associated with exposure in source population Drinking Smoking Not a downstream cause of the exposure (e.g., in the causal pathway from exposure to disease) Smoking Drinking Car Crashes

Examples of No Confounding

Why is Confounding a Problem? Because…... The estimate of association between exposure and disease includes BOTH the contribution of the exposure AND the confounder Confounding can overestimate true association (positive confounding) or underestimates true association (negative confounding) Truth E +++ D E + D E D ++ + - + + C C

Assessing Confounding in Your Data CALCULATE the CRUDE measure of association between exposure and outcome (RR or OR) ASSESS associations between a) exposure and confounder AND b) confounder and disease in non- exposed CALCULATE the strata specific RRs or ORs COMPARE crude to strata specific RRs or ORs If measure of association is the same in the strata but different than the crude then you have evidence of confounding!

Step 1: Crude association between coffee drinking and cancer. None Coffee 165 735 85 1015 Total 250 1750 Unadjusted RR= 165/(165+735) / (85)/(85+1015) =2.37 “Crude RR”

Step 2a: Is smoking associated with coffee drinking? Cf+ Cf- Total S+ 800 200 1000 S- 100 900 1100 2000 PR for Coffee Drinking Among Smokers vs. Non-Smokers: (800/1000)/(100/1000) = 8

Step 2b: Is smoking associated cancer among non-coffee drinkers? Total S+ 40 160 200 S- 45 855 900 95 1050 1100 RR for Cancer Among Smokers vs. Non-Smokers who don’t drink coffee: (40/200 )/ (45/900) = 4.0

Step 3: Is coffee associated with cancer within smoking strata? In Smokers D+ D- Total E+ 160 640 800 E- 40 200 1000 In Non-Smokers D+ D- Total E+ 5 95 100 E- 45 855 900 50 950 1000 RR Smoker Strata= (160/800)/(40/200) = 1.0 RR Non-Smoker Strata= (5/100)/(45/900) = 1.0

Step 4: Compare strata-specific RR to crude RR Smoking confounds the association between coffee and cancer because: The strata specific RR are equal (1.0) – The strata specific RR of 1.0 is NOT the same as the crude RR of 2.37 The difference between the strata specific and crude is large so we conclude that this is important confounding Some people use a 10% rule as a rough metric of “importance”

How to Report Data with Confounders If you have a confounder: DO NOT report crude OR or RR! Instead report stratum-specific OR or RR or adjusted OR or RR from regression model Other methods for summarizing strata-specific OR or RR (e.g., Mantel-Haenszel – a weighted average)