1. Confounding Biost/Stat 579 David Yanez Department of Biostatistics University of Washington July 7, 2005

2. Information Bias Measurement Errors Non-differential –Error in assessing exposure or disease is similar between study groups –Measure of effect tends toward 1 Differential –Error in assessing exposure (or disease) differs in different study groups –May increase or decrease measure of effect

3. Information Bias Non-differential Misclassification –Hypothetical Case-Control study 6040 60 D E ˉ E D ˉ OR = 60*60/40*40 = 2.25 100 4832 5268 D E ˉ E D ˉ 100 Percent Exposure Misclassification: 20% 20% OR = 48*64/36*52 = 1.96

4. Information Bias Differential Misclassification –Hypothetical Case-Control study 6040 60 D E ˉ E D ˉ OR = 60*60/40*40 = 2.25 100 5732 4368 D E ˉ E D ˉ 100 Percent Exposure Misclassification: 5% 20% OR = 57*68/43*32 = 2.81

5. Confounding The Idea: Confounding is a confusion of effects. Definition: The apparent effect of the exposure of interest is distorted because the effect of an extraneous factor is mistaken for or mixed with the actual exposure effect.

6. Confounding Properties of a Confounder: A confounder, C, must be causally related to the outcome, Y, OR associated with some predictor that is causally related to Y. C must be associated with the predictor of interest, X, in the source population. C must not be affected by X or Y. The confounder cannot be an intermediate step in the causal path between X and Y.

7. Confounding Sources of confounding –Randomized clinical trials Random differences between groups Randomized clinical trials reduce confounding effect by balancing known and unknown confounding factors –Observational Studies Random differences between groups Factors associated with the exposure of interest

8. Confounding Causal Diagram Confounder PredictorOutcome Non-causal Causal Confounder PredictorOutcome

9. Country of Residence and Mortality CountryMortality (per 1000) Costa Rica3.8 Venezuela4.4 Mexico4.9 Canada7.3 U.S.8.7

10. Age CountryMortality Confounding Non-causal Causal Ecologic study to determine whether country of residence is associated with mortality. Average age may be different among countries.

11. Country of Residence and Age-Adjusted Mortality CountryAdjusted Mortality (per 1000) Costa Rica3.7 Venezuela4.6 Mexico5.0 Canada3.2 U.S.3.6

12. Confounding Case-control study to determine whether vitamin C intake is associated with colon cancer. Diet/lifestyle Vitamin CCancer Non-causal Causal People who take vitamin C may eat a healthier diet and live a healthier lifestyle

13. Confounding Design –Restriction –Matching Individual matching Group matching –Randomization Analysis –Stratified analysis –Adjustment Age-adjustment Regression analysis

14. Confounding Detection –Biologic model or underlying theory should allow you to specify potential confounders in advance of study/analysis –Assess for confounding in a systematic way Known of potential confounding factors Other factors not previously known to be confounding factor

15. Stratified Analysis ij kl i+j k+l i+kj+l D E ˉ E D ˉ ef gh e+f g+h e+gf+h D E ˉ E D ˉ OR 1 = eh/fg OR 2 = il/kj ab cd a+b c+d a+cb+d D E ˉ E D ˉ OR c = ad/bc Stratum 1 2

16. OR c = ad/bc OR a = f(OR 1, OR 2 ), Mantel Haenszel procedure If OR c = OR a no evidence of confounding If OR c ≠ OR a, evidence of confounding Confounding

17. Stratified Analysis 30 18 7082 48 152 100 D E ˉ E D ˉ OR c = ad/bc = 1.95 2510 2510 35 50 20 D E ˉ E D ˉ 8 4572 13 117 5080 D E ˉ E D ˉ OR 1 = eh/fg = 1.0 OR 2 = il/kj = 1.0 Age < 40 Age ≥ 40 200 130 70 5

18. Stratified Analysis 200800 50950 1000 2501750 D E ˉ E D ˉ OR c = ad/bc = 4.75 40560 10590 600 501150 D E ˉ E D ˉ 160240 40360 400 200600 D E ˉ E D ˉ OR 1 = eh/fg = 6.0 OR 2 = il/kj = 4.2 Stratum 1 2 2000 800 1200

19. Stratified Analysis OR c = ad/bc = 1.95 30 18 7082 48 152 100 D E ˉ E D ˉ 200 50 20 5080 70 130 100 D < 40 ≥ 40 D ˉ 200 35 13117 70 130 48 152 E 200 Is Confounder associated with Disease? Is Confounder associated with Exposure? OR = 4 ≥ 40 < 40 E ˉ OR = 9

20. Confounding Analytic Criteria for Confounding –The crude estimate of effect differs from the adjusted estimate of effect Steps to assess confounding –Calculate crude measure of effect (means, reg. Coeff., RR, OR) –Stratify and calculate stratum-specific measures of effect, or –Fit regression that adjusts for the potential confounders –Examine whether effects are similar. –Statistical significance should not be used as a criterion for assessing confounding.