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PH 240A: Chapter 9 Steve Shiboski University of California Berkeley (Slides by Nick Jewell)

PH 240A: Chapter 9 Steve Shiboski University of California Berkeley (Slides by Nick Jewell). CHD and Behavior Type, Stratified by Body Weight. Pancreatic Cancer and Coffee Drinking, Stratified by Sex. 2 x 2 Table Notation for i th Stratum.

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PH 240A: Chapter 9 Steve Shiboski University of California Berkeley (Slides by Nick Jewell)

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  1. PH 240A: Chapter 9 Steve Shiboski University of California Berkeley (Slides by Nick Jewell)

  2. CHD and Behavior Type, Stratified by Body Weight

  3. Pancreatic Cancer and Coffee Drinking, Stratified by Sex

  4. 2 x 2 Table Notation for ith Stratum

  5. Testing of Independence Based on Stratified Tables • H0:OR1=OR2= . . . =ORI = 1 • HA1: at least one ORj differs from 1 • Do a c2test for each stratum • Multiple testing issue • Low power • Add the c2test statistic from each stratum to give a c2test with I degrees of freedom • Low power

  6. Variation of Stratum-Specific Odds Ratio x x x ORi x Typical HA2 x x x x H0 1 1 2 I Stratum Indicator HA2:OR1=OR2= . . . =ORI

  7. Cochran-Mantel-Haenszel test • In ith stratum, if D and E are independent • E(ai) = Ai=(ai+bi)(ai+ci)/ni • Var(ai)=Vi =(ai+bi)(ci+di)(ai+ci)(bi+di)/ni2(ni-1) • Look at deviations ai-Ai and their accumulation

  8. CHD and Behavior Type, Stratified by Body Weight

  9. Cochran-Mantel-Haenszel Test Statistic Calculations for CHD Data

  10. Cochran-Mantel-Haenszel Test Statistic Calculations for CHD Data

  11. Woolf Estimator (and CI) for Common Odds Ratio • Average the log Odds Ratio estimates from the separate strata • Weight the average with weight inversely proportional to variability (high variance stratum estimates get low weight in the average and vice-versa)

  12. Woolf Estimator (and CI) for Common Odds Ratio • Sampling Distribution: assuming no interaction

  13. Mantel-Haenszel Estimator • Average the Odds Ratio estimates from each stratum

  14. Woolf and Mantel-Haenszel Estimator Calculations for CHD Data

  15. Summary of Findings for WCGS • Pooled results for Behavior Type • c2test statistic is 39.9 • OR estimate = 2.34 (1.79—3.11) • Var of estimate of log(OR) = 0.01956 • Adjusting Results for Body Weight • Cochran-Mantel-Haenszel c2test statistic is 37.6 • Woolf OR estimate = 2.26 (1.72—2.98) • Mantel-Haenszel estimate = 2.32 (1.76—3.06) • Var of estimates of log(OR) = 0.01960 (Woolf) • Little confounding seen from body weight

  16. Pancreatic Cancer and Coffee Drinking, Stratified by Sex

  17. Summary of Findings for Coffee Drinking and Pancreatic Cancer • Pooled results for Coffee Drinking • c2test statistic is 16.6 • OR estimate = 2.75 (1.66—4.55) • Adjusting Results for Sex • Cochran-Mantel-Haenszel c2test statistic is 14.5 • Woolf OR estimate = 2.51 (1.53—4.13) • Mantel-Haenszel estimate = 2.60 (1.57—4.32) • Little confounding seen from sex

  18. Balance at Stratum Level Var of estimate of log(OR) = 0.01956 (SD = 0.141) Var of log(ORW) = 0.01960 (SD = 0.140)

  19. Balance at Stratum Level: Case-Control Study of Pancreatic Cancer

  20. Stratification by Hypothetical C

  21. Increase in Variability Associated with Stratification • Loss of balance (on D) more common in case-control studies • Loss of precision not usually a problem with stratification on a single variable, but can quickly become an issue with stratification on several variables • Think of how many strata are need with 5 (10) binary confounding variables

  22. Increase in Variability Associated with Stratification • Two remedies to loss of precision associated with excessive stratification • Make modeling assumptions about relationship of confounders to D • Regression models (logistic regression) • Maintain balance after stratification by design • Matched designs

  23. Warning: Woolf’s Method • Woolf’s Method approximations fail when every stratum has small sample size (OK when some strata have large sample sizes) • Mantel-Haenszel estimator still works well in these situations (perhaps use exact CIs)

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