EP 521, 2007, Vol I, part 4 Copyright © 2006, Trustees of the University of Pennsylvania 1 §2.3 Stratification and matching in design Matching/stratification: Definitions “Matching” -- linking a few people by means of their characteristics (age and gender) for example. There can be 1 to 1 or 1 to 2 or , …, 1 to m matching in both case-control or cohort studies. “Stratification” – The same idea but with larger groups of patients, and this might be n to m matching. The only difference is the thickness of the strata. We have considered some methods for adjusting for confounding in analysis. Mantel Haenszel methods stratify on (or condition on) the potential confounder. What about stratifying in the design. What are the advantages and disadvantages? When might we want to stratify in the design? What data patterns should we look out for? What are the consequences of not stratifying in the design/ and or analysis? EP 521, 2007, Vol I, part 4 Copyright © 2006, Trustees of the University of Pennsylvania 2 §2.3.1 Stratification in design -- Issues 1. Distinguish implications of stratification for (a) cohort vs (b) case control study. a. in a cohort study, distribution of exposed serves as the prespecified distribution (match smokers to nonsmokers by age) b. in a case-control study, distribution of cases serves as the prespecified distribution (match cancer patient to noncancer control) 2. Distinguish rationale for stratification/matching (a) confounding – The perceived reason "The widely held belief that matching is a panacea for confounding has resulted in its misuse in many epidemiologic research studies, especially case-control studies." (Kleinbaum et al pg. 378.) (b) efficiency -- The real reason. Efficiency means more statistical power for a given sample size. If we are comparing two groups we want to ensure that we have members in each strata of potential covariates, so that we can adjust for the covariates. Example: Consider age as a covariate. If we do not match or stratify on age we cannot ensure that we will have case and controls (exposed and unexposed) in each age group.EP 521, 2007, Vol I, part 4 Copyright © 2006, Trustees of the University of Pennsylvania 3 3. Can stratify in analysis regardless of study design. 4. If design is stratified, analysis usually should be stratified. Generally, ignoring stratification biases toward null in CC study. 5. Design stratification sometimes improves (statistical) efficiency, especially if design (matching) factor and disease are strongly associated. Lose efficiency when stratifying factor and exposure (E) are strongly associated in CC study. 6. Cannot examine association between design factor and disease because must stratify on design factor. We must result in regression methods to avoid this barrier. 7. Can also stratify the analysis on other factors (in addition to stratifying in the analysis on design strata). If condition analyses on non-design factors (MH methods, conditional logistic regression), lose ability to assess main effects of these factors. Are we interested in only the exposure or treatment of interest? Or, are we also interested in the association of the potential confounder with the outcome? 8. Some applications of matching is good practice – genetics, for example, where need to use EP 521, 2007, Vol I, part 4 Copyright © 2006, Trustees of the University of Pennsylvania 4 match as proxy for many potential confounders. Reason for twins studies. Family studies. Using the family as a proxy for a large group of genetic factors, we can control for them simply by matching in the design (and in the analysis)EP 521, 2007, Vol I, part 4 Copyright © 2006, Trustees of the University of Pennsylvania 5 §2.3.2: Types of stratification and matching Separate analyses. Some authors conduct a separate analysis by race, gender, age, … and they term this procedure “stratification”. This term is ambiguous in this setting. Say what you mean, and mean what you say when trying to write your Methods section. Stratification: means developing strata for either sampling (in the design) or in analysis. Example: you want to look at males and females in equal numbers. So, you sample 100 M and 100 F, regardless of the population of M and F. Matching – A form of stratification. Can be either in the design or the analysis. Matching: "...the pairing of one or more controls to each case on the basis of their similarity with respect to several variables." -Schlesselman EP 521, 2007, Vol I, part 4 Copyright © 2006, Trustees of the University of Pennsylvania 6 Types of Matching (Blocking) 1. Caliper matching: Pick a “control” (x2) that is close to the case (x1) such that | x1 - x2 | < c, where c is a constant, e.g., age +/- 2 years; age +/- 0 years But Rothman indicates on page 282 that this results in a small amount of bias. 2. Frequency or categorical matching (Woodward pp 269-70) e.g., Create age categories: 20 or less, 21 - 30, 31 - 40, 41 or greater Then pick controls from the same category as contains the case or cases Problem of highest and lowest categories, which are unbounded. Good matches more difficult. A person 60 could be “matched” with someone age 41. Advantages: (1) Helps to ensure that control sample has same type of persons as case sample (both have M and F patients age 70+). If lacking, then cannot compare effect of M v F on outcome. (2) Advantage over pair matching – can lose a case or a control without losing the corresponding patient. 3. Pair matching - This is common – 1 to 1 matching or, in general n to m matchingEP 521, 2007, Vol I, part 4 Copyright © 2006, Trustees of the University of Pennsylvania 7 §2.3.3.1 Matching induces confounding in Case Control studies Example: Frequency matching in CC study Rothman (2nd ed) Table 10.5 The population table (the entire cohort): Males Females E+ E- E+ E- D+ 450 10 50 90 D- 89550 9990 9950 89910 Total 90000 10000 10000 90000 OR=5.02 OR=5.02 Pr(D)= 460/100000 Pr(D)=140/100000 45090,0005.01010,000RR == 5010,0005.09090,000RR == RD=0.005-0.001= 0.004 RD = 0.005 – 0.001 = 0.004 Pr(D|E-) = 0.001 Pr(D|E-) 0.001EP 521, 2007, Vol I, part 4 Copyright © 2006, Trustees of the University of Pennsylvania 8 Combined M + F in the