PH 241: Chapter 16 Nicholas P. Jewell University of California Berkeley April 17-26, 2006

1. PH 241: Chapter 16 Nicholas P. Jewell University of California Berkeley April 17-26, 2006

2. Frequency Matching • Situation: Stratification factors have few distinct levels • Goal: To maintain balance on the marginals of planned strata so that precision is not lost when stratification is used to reduce confounding • Implementation: Perform mini studies at each stratification level

3. Pancreatic Cancer and Coffee Drinking, Stratified by Sex Balance: 2.2:1 Balance: 1.4:1 Original balance: 1.75 controls for every case Frequency matching: select 265 female and 378 male controls so that balance is approximately 1.75:1 in both strata

4. Frequency Matching: Analysis • For example, in case-control studies, we can no longer estimate P(E |D) etc, only P(E |D,C ) where C is the matching factor • Are therefore committed to stratification on C • Can no longer evaluate the association between C and D in case-control studies • Can still use logistic regression so long as C is always appropriately entered into the model

5. Pair Matching • Matching factors have a very high number of discrete levels • Pair Matching • One case, one control at any given common level of matching factors (Case-Control) • One exposed, one unexposed at any given common level of matching factors (Cohort)

6. Types of Matched Pair Case-Control Data

7. Summarization of Matched Pair Case-Control Data Classification of Pairs, not individuals

8. Matched Pair Case-Control Data on Spontaneous Abortions and CHD Matched on age and location of residence

9. Exposure Patterns in the Four Types of Matched Pair Case-Control Data

10. Odds Ratio with Matched Pair Case-Control Data • Pr(pair has exposed case | discordant)

11. Odds Ratio with Matched Pair Case-Control Data • If no interaction: • Pr(pair has exposed case | discordant) • For example OR = 1 & P = 0.5 • Estimation: • Known as conditional maximum likelihood • Testing:

12. Matched Pair Case-Control Data on Spontaneous Abortions and CHD Confidence intervals:

13. Cochran-Mantel-Haenszel Procedures for Pair-Matched Data Cochran-Mantel-Haenszel test statistic: Mantel-Haenszel Estimator: Small-sample OR estimator:

14. 1:M Matching • Can use conditional maximum likelihood or Cochran-Mantel-Haenszel procedures (no longer exactly the same)

15. Further Assessment of Confounding and Interaction • Further confounders (non matching factors) • Stratify further on new confounders • Quick loss of precision • Interaction • Straightforward if interested in interaction of E with a matching factor • If the additional covariate is a non-matching factor, further stratification limits power to estimate interactive effects

16. Logistic Regression Model for Matched Data • Too many unknown parameters for regular maximum likelihood • Use conditional maximum likelihood (conditioning on the • exposure pattern in the matched pair) Use conditional likelihood (which only depends on b) just as a conventional likelihood (ML estimates, SEs, Wald test, LR tests)

17. Coding for Matched Study of Pregnancy History and CHD

18. Matched Study of Pregnancy History and CHD: Fitted Logistic Regression Models

19. Matched Study of Birth Order and RDS: Fitted Logistic Regression Models Caution: natural matched pairs Matched Cohort study of RDS in twins 221 twins: matched on everything common to twins! Birth order is known risk factor—can it be explained by other factors? OR = 31/8 = 3.9 McNemar’s test statistic = 13.6, P = 0.0002 X is birth order (1 is second born); Y is delivery mode (1 is vaginal)