1. Unit 6: Standardization and Methods to Control Confounding

2. Unit 6 Learning Objectives: 1. Understand the “design” and “analysis” methods used to control confounding. ---Randomization ---Restriction ---Matching ---Stratification ---Multivariate analysis. 2. Understand pros and cons of the methods used to control confounding.

3. Lesson 6 Learning Objectives (cont.): 3. Understand the rationale for rate adjustment (standardization). 4. Apply and interpret the technique of direct standardization. 5.Apply and interpret the technique of indirect standardization. 6. Recognize differences between direct and indirect standardization.

4. Assigned Readings: Textbook (Gordis): Chapter 4, pages 60-68 (Age adjustment) Chapter 15, pages 230-232 (More on confounding) Hennekens and Buring: Evaluating the role of confounding. In Epidemiology in Medicine, pages 304-323.

5. CONFOUNDING - REVIEW DEFINITION: A third variable (not the exposure or outcome variable of interest) that distorts the observed relationship between the exposure and outcome. Confounding is a confusion of effects that is a nuisance and should be controlled for if possible. Age is a very common source of confounding.

6. CONFOUNDING - REVIEW E D CF Confounding IS present E?CFD Confounding NOT present

7. CONFOUNDING Reason for controlling confounding: To obtain a more precise (accurate) estimate of the true association between the exposure and disease under study. As a general rule, age and gender should always be considered as potential confounders of an association.

8. CONFOUNDING POSITIVE CONFOUNDING: The confounding factor produces an estimate that is more extreme (positive or negative) than the true association. NEGATIVE CONFOUNDING: The confounding factor results in an under- estimate of the true association.

9. CONFOUNDING METHODS TO CONTROL CONFOUNDING: DESIGN: 1.Randomization 2.Restriction 3.Matching (Analysis also) ANALYSIS: 4.Stratification 5.Multivariate Analysis

10. CONTROL OF CONFOUNDING 1.RANDOMIZATION (Design): Definition:Subjects or groups of subjects are randomly assigned to a hypothesized preventive or therapeutic intervention. Pro:With sufficient sample size, virtually assures that both known and unknown confounders are controlled. Con:Sample size may not be large enough to control for confounding since many persons are unwilling to be randomized.

11. CONTROL OF CONFOUNDING 2.RESTRICTION (Design): Definition:Study participation is restricted to individuals who fall within a specified category or categories of the confounder. Pro:Straightforward, convenient, inexpensive Con:Sufficiently narrow restriction range may severely reduce the number of eligible participants Con:If restriction criteria are not sufficiently narrow, possibility of residual confounding exists

12. CONTROL OF CONFOUNDING RESTRICTION (cont.): Con:Does not permit evaluation of the association between exposure and disease for varying levels of the factor. Note:Although restriction may limit generalizability, it does not affect the internal validity of any observed association between the groups included in the study.

13. CONTROL OF CONFOUNDING 3.MATCHING (Design/analysis); Definition:All levels of the confounding factor are allowable for study inclusion, but subjects are selected in a way that potential confounders are distributed equally among the study groups. Pro:Great intuitive appeal – may provide greater analytic efficiency by insuring adequate number of cases and controls at each level of the confounder. Con:Can be difficult, time consuming, and expensive to find a comparison subjects with right set of characteristics on each matching variable.

14. CONTROL OF CONFOUNDING MATCHING (cont.): Con:Does not control potential confounding by factors other than those matched on Con:Not needed as much as in the past due to alternative techniques (e.g. multivariate analysis)

15. CONTROL OF CONFOUNDING INDICATIONS FOR MATCHING: Factors for which there would otherwise be insufficient overlap between study groups (e.g. nominal-level variables such as race). Small case series in which baseline characteristics are likely to differ between study groups. Most often employed in case-control studies.

16. CONTROL OF CONFOUNDING MATCHING (ANALYSIS); Note: Matching on several confounders can make the study groups more alike on the exposures of interest than would have occurred had independent series of cases and controls been selected. This requires use of statistical techniques that make explicit provision for the matched nature of the data (e.g. conditional odds ratio)

17. CONTROL OF CONFOUNDING STRATIFICATION (Analysis): Definition:Evaluation of the exposure/disease association within homogeneous categories or strata of the confounding variable. Pro:Intuitively appealing, straightforward, and enhances understanding of intricacies of the data Con:Impractical for simultaneous control of multiple confounders, especially those with multiple strata

18. CONTROL OF CONFOUNDING Hypothesis:Sedentary lifestyle is associated with risk of myocardial infarction (cohort study) D+D+ D-D- E+E+ 4080120 E-E- 100750850 970 RR = (40 / 120) / (100 / 850) RR = 2.83 It appears that persons with a sedentary lifestyle are 2.83 times more likely to experience myocardial infarction compared to persons without a sedentary lifestyle. BUT WHAT ABOUT SMOKING?

19. CONTROL OF CONFOUNDING D+D+ D-D- E+E+ 52530 E-E- 50525575 605 NON-SMOKERSSMOKERS D+D+ D-D- E+E+ 355590 E-E- 50225275 365 RR = (5 / 30) / (50 / 575) RR = 1.92 RR = (35 / 90) / (50 / 275) RR = 2.14 Is there evidence that smoking confounds the relationship between sedentary lifestyle and myocardial infarction?

20. CONTROL OF CONFOUNDING In general: If Strata 1 RR Strata 2 RR OR If Strata 1 RR > Crude RR < Strata 2 RR then confounding is present. CRUDE RR MI = 2.83 STRATA 1 RR NS = 1.92 STRATA 2 RR SM = 2.14

21. CONTROL OF CONFOUNDING Now, the question is: Should the stratum-specific estimates be combined to obtain an unconfounded (adjusted) estimate of the relationship between sedentary lifestyle and risk of myocardial infarction? CRUDE RR MI = 2.83 STRATA 1 RR NS = 1.92 STRATA 2 RR SM = 2.14

22. CONTROL OF CONFOUNDING Axiom: If the stratum-specific estimates are similar (homogeneous), the estimates can be combined to obtain an unconfounded (adjusted) estimate. However, if the stratum-specific estimates are sufficiently different, they should not be combined, as this would obscure useful information (lecture 7). CRUDE RR MI = 2.83 STRATA 1 RR NS = 1.92 STRATA 2 RR SM = 2.14

23. CONTROL OF CONFOUNDING Note: Statistical tests of homogeneity exist to test the similarity of the stratum-specific estimates, however, these tests are heavily affected by sample size, and often under-powered. Thus, the stratum-specific estimates should be “eyeballed.” CRUDE RR MI = 2.83 STRATA 1 RR NS = 1.92 STRATA 2 RR SM = 2.14

24. CONTROL OF CONFOUNDING Mantel-Haenszel pooled RR estimate (uniform strata): Σ a(c + d) / T RR MH = ----------------- Σ c(a + b) / T Where T = total sample in each stratum CRUDE RR MI = 2.83 STRATA 1 RR NS = 1.92 STRATA 2 RR SM = 2.14

25. CONTROL OF CONFOUNDING 5(50 + 525) / 605 + 35(50 + 225) / 365 RR MH = -------------------------------------------------- 50(5 + 25) / 605 + 50(35 + 55) / 365 4.75 + 26.431.1 =-------------- =------ =2.10 2.48 + 12.314.8 CRUDE RR MI = 2.83 STRATA 1 RR NS = 1.92 STRATA 2 RR SM = 2.14

26. CONTROL OF CONFOUNDING CRUDE RR MI = 2.83 ADJUSTED RR MH = 2.10 Axiom: The magnitude of confounding is evaluated by observing the degree of discrepancy observed between the crude and adjusted estimates. Presence of confounding should not be assessed using a test of statistical significance. Generally, when the crude estimate changes by at least 10%, meaningful confounding exists.

27. CONTROL OF CONFOUNDING MULTIVARIATE ANALYSIS (Analysis): Definition:A technique that takes into account a number of variables simultaneously. Involves construction of a mathematical model that efficiently describes the association between exposure and disease, as well as other variables that may confound or modify the effect of exposure. Examples: Multiple linear regression model Logistic regression model

28. CONTROL OF CONFOUNDING MULTIVARIATE ANALYSIS (Analysis): Multiple linear regression model: Y = a + b 1 X 1 + b 2 X 2 + …b n X n Where: n = the number of independent variables (IVs) (e.g. Exposure(s) and confounders) X 1 … X n = individual’s set of values for the IVs b 1 … b n = respective coefficients for the IVs

29. CONTROL OF CONFOUNDING MULTIVARIATE ANALYSIS (Analysis): Logistic regression model: ln [Y / (1-Y)] = a + b 1 X 1 + b 2 X 2 + …b n X n Where: Y = probability of disease n = the number of independent variables (IVs) (e.g. exposure(s) and confounders) X 1 … X n = individual’s set of values for the IVs b 1 … b n = respective coefficients for the IVs

30. CONTROL OF CONFOUNDING MULTIVARIATE ANALYSIS (Analysis): Pro:Can simultaneously control for multiple confounders when stratified analysis is impractical Pro:With the logistic regression model, beta coefficients can be directly converted to odds ratios Con:Process of efficient mathematical modeling can occur at the expense of clear understanding of the data