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Winter Electives

Winter Electives. Molecular and Genetic Epidemiology Decision and Cost-effectiveness Analysis Grantwriting for Career Development Awards (Workshop – not for credit hours) Medical Informatics. Next Tuesday (12/5/06) 8:15 to 9:45: Journal Club 10:00 to 1:00 pm: Mitch Katz

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Winter Electives

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  1. Winter Electives • Molecular and Genetic Epidemiology • Decision and Cost-effectiveness Analysis • Grantwriting for Career Development Awards (Workshop – not for credit hours) • Medical Informatics

  2. Next Tuesday (12/5/06) • 8:15 to 9:45: Journal Club • 10:00 to 1:00 pm: Mitch Katz • Note chapters in his text book • Lunch provided • 1:30 to 2:45: Last Small Group Section • Web-based course evaluation • Bring laptop • Distribute Final Exam • Exam due 12/12 (in hands of Olivia by 4 pm) by email or China Basin 5700

  3. Confounding and Interaction: Part III • When Evaluating Association Between an Exposure and an Outcome, the Possible Roles of a 3rd Variable are: • Intermediary Variable • Effect Modifier • Confounder • No Effect • Forming “Adjusted” Summary Estimates to Evaluate Presence of Confounding • Concept of weighted average • Woolf’s Method • Mantel-Haenszel Method • Clinical/biological decision rather than statistical • Handling more than one potential confounder • Limitations of Stratification to Adjust for Confounding • the motivation for multivariable regression

  4. When Assessing the Association Between an Exposure and a Disease, What are the Possible Effects of a Third Variable? Assumption: The third variable a priori is felt to be relevant No Effect Intermediary Variable: ON CAUSAL PATHWAY I C + EM _ Effect Modifier (Interaction): MODIFIES THE EFFECT OF THE EXPOSURE Confounding: ANOTHER PATHWAY TO GET TO THE DISEASE D

  5. What are the Possible Roles of a 3rd Variable? • Intermediary Variable • Effect Modifier (interaction) • Confounder • No Effect Intermediary Variable? (conceptual decision) Report Crude Estimate no yes Effect Modifier? (numerically assess both magnitude and statistical differences) Report stratum-specific estimates no yes Confounder? (numerically assess difference between adjusted and crude; not a statistical decision) yes Report “adjusted” summary estimate Report Crude Estimate (3rd variable has no effect) no

  6. Effect of a Third Variable: Statistical Interaction Crude RR crude= 1.7 Stratified Heavy Caffeine Use No Caffeine Use RRcaffeine use = 0.7 RRnocaffeine use = 2.4 . cs delayed smoking, by(caffeine) caffeine | RR [95% Conf. Interval] M-H Weight -----------------+------------------------------------------------- no caffeine | 2.414614 1.42165 4.10112 5.486943 heavy caffeine | .70163 .3493615 1.409099 8.156069 -----------------+------------------------------------------------- Crude | 1.699096 1.114485 2.590369 M-H combined | 1.390557 .9246598 2.091201 -----------------+------------------------------------------------- Test of homogeneity (M-H) chi2(1) = 7.866 Pr>chi2 = 0.0050 Report interaction; confounding is not relevant

  7. Statistical Tests of Interaction: Test of Homogeneity (heterogeneity) • Null hypothesis: The individual stratum-specific estimates of the measure of association differ only by random variation • i.e., the strength of association is homogeneous across all strata • i.e., there is no interaction • The test statistic will have a chi-square distribution with degrees of freedom of one less than the number of strata

  8. Report vs Ignore Interaction?Some Guidelines Is an art form: requires consideration of both clinical and statistical significance

  9. If Interaction is not Present, What Next? • Case-control study of post-exposure AZT use in preventing HIV seroconversion after needlestick (NEJM 1997) Crude ORcrude = 0.61 (95% CI: 0.26 - 1.4)

  10. Post-exposure prophylaxis with AZT after a needlestick AZT Use Severity of Exposure HIV Confounding by Indication

  11. Evaluating for Interaction • Potential confounder: severity of exposure Crude ORcrude =0.61 Stratified Minor Severity Major Severity OR = 0.0 OR = 0.35

  12. Is there interaction? Is there confounding? What is the adjusted measure of association?

  13. Assuming Interaction is not Present, Form a Summary of the Unconfounded Stratum-Specific Estimates • Construct a weighted average • Assign weights to the individual strata • Summary Estimate = Weighted Average of the stratum-specific estimates • a simple mean is a weighted average where the weights are equal to 1 • which weights to use depends on type of effect estimate desired (OR, RR, RD) and characteristics of the data • e.g., • Woolf’s method • Mantel-Haenszel method

  14. Forming a Summary Estimate for Stratified Data Crude ORcrude = 0.61 Stratified Minor Severity Major Severity OR = 0.0 OR = 0.35 How would you weight these strata? According to sample size? No. of cases?

  15. Summary Estimators: Woolf’s Method • aka Directly pooled or precision estimator • Woolf’s estimate for adjusted odds ratio • where wi • wi is the inverse of the variance of the stratum-specific log(odds ratio)

  16. Calculating a Summary Effect Using the Woolf Estimator • e.g. AZT use, severity of needlestick, and HIV Crude ORcrude =0.61 Stratified Minor Severity Major Severity OR = 0.0 OR = 0.35

  17. Summary Estimators: Woolf’s Method • Conceptually straightforward • Best when: • number of strata is small • sample size within each strata is large • Cannot be calculated when any cell in any stratum is zero because log(0) is undefined • 1/2 cell corrections have been suggested but are subject to bias • Formulae for Woolf’s summary estimates for other measures (e.g., RR, RD) available in texts and software documentation • sensitive to small strata, cells with “0” • computationally messy

  18. Summary Estimators: Mantel-Haenszel • Mantel-Haenszel estimate for odds ratios • ORMH = • wi = • wi is inverse of the variance of the stratum-specific odds ratio under the null hypothesis (OR =1)

  19. Summary Estimators: Mantel-Haenszel • Mantel-Haenszel estimate for odds ratios • “relatively” resistant to the effects of large numbers of strata with few observations • resistant to cells with a value of “0” • computationally easy • most commonly used

  20. Calculating a Summary Effect Using the Mantel-Haenszel Estimator • ORMH = • ORMH = Crude ORcrude =0.61 Stratified Minor Severity Major Severity OR = 0.0 OR = 0.35

  21. Calculating a Summary Effect in Stata • epitab command - Tables for epidemiologists • see “Survival Analysis and Epidemiological Tables Reference Manual” • To produce crude estimates and 2 x 2 tables: • For cross-sectional or cohort studies: • cs variablecase variable exposed • For case-control studies: • cc variablecase variableexposed • To stratify by a third variable: • cs varcase varexposed, by(varthird variable) • cc varcase varexposed, by(varthird variable) • Default summary estimator is Mantel-Haenszel • , pool will also produce Woolf’s method

  22. Calculating a Summary Effect Using the Mantel-Haenszel Estimator • e.g. AZT use, severity of needlestick, and HIV • . cc HIV AZTuse,by(severity) pool • severity | OR [95% Conf. Interval] M-H Weight • -----------------+------------------------------------------------- • minor | 0 0 2.302373 1.070588 • major | .35 .1344565 .9144599 6.956522 • -----------------+------------------------------------------------- • Crude | .6074729 .2638181 1.401432 • Pooled (direct) | . . . • M-H combined | .30332 .1158571 .7941072 • -----------------+------------------------------------------------- • Test of homogeneity (B-D) chi2(1) = 0.60 Pr>chi2 = 0.4400 • Test that combined OR = 1: • Mantel-Haenszel chi2(1) = 6.06 • Pr>chi2 = 0.0138 Crude ORcrude =0.61 Stratified Minor Severity Major Severity OR = 0.0 OR = 0.35

  23. Calculating a Summary Effect Using the Mantel-Haenszel Estimator • In addition to the odds ratio, Mantel-Haenszel estimators are also available in Stata for: • risk ratio • “cs varcase varexposed, by(varthird variable)” • rate ratio • “ir varcase varexposed vartime, by(varthird variable)”

  24. Assessment of Confounding: Interpretation of Summary Estimate • Compare “adjusted” estimate to crude estimate • e.g. compare ORMH (= 0.30) to ORcrude (= 0.61) • If “adjusted” measure “differs meaningfully” from crude estimate, then confounding is present • e.g., does ORMH = 0.30 “differ meaningfully” from ORcrude = 0.61? • What does “differs meaningfully” mean? • a matter of judgement based on biologic/clinical sense rather than on a statistical test • no one correct answer • the objective is to remove bias • 10% change from the crude often used • your threshold needs to be stated a priori and included in your methods section

  25. Statistical Testing for Confounding is Inappropriate • Testing for statistically significant differences between crude and adjusted measures is inappropriate • e.g., when examining an association for which a factor is a known confounder (say age in the association between HTN and CAD) • if the study has a small sample size, even large differences between crude and adjusted measures may not be statistically different • yet, we know confounding is present • therefore, the difference between crude and adjusted measures cannot be ignored as merely chance. • bias must be prevented: the difference must be reported as confounding • the issue of confounding is one of internal validity, not of sampling error. • we must live with – within reason -- whatever effects we see after adjustment for a factor for which there is an a priori belief about confounding • we’re not concerned that sampling error is causing confounding and therefore we don’t have to worry about testing for role of chance

  26. Confidence Interval Estimation and Hypothesis Testing for the Mantel-Haenszel Estimator • e.g. AZT use, severity of needlestick, and HIV • . cc HIV AZTuse,by(severity) pool • severity | OR [95% Conf. Interval] M-H Weight • -----------------+------------------------------------------------- • minor | 0 0 2.302373 1.070588 • major | .35 .1344565 .9144599 6.956522 • -----------------+------------------------------------------------- • Crude | .6074729 .2638181 1.401432 • Pooled (direct) | . . . M-H combined | .30332 .1158571 .7941072 • -----------------+------------------------------------------------- • Test of homogeneity (B-D) chi2(1) = 0.60 Pr>chi2 = 0.4400 • Test that combined OR = 1: • Mantel-Haenszel chi2(1) = 6.06 • Pr>chi2 = 0.0138 • What does the p value = 0.0138 mean?

  27. Mantel-Haenszel Confidence Interval and Hypothesis Testing

  28. Mantel-Haenszel Techniques • Mantel-Haenszel estimators • Mantel-Haenszel chi-square statistic • Mantel’s test for trend (dose-response)

  29. Summary Effect in Stata – another example • e.g. Spermicide use, maternal age and Down’s Crude OR = 3.5 Age < 35 Age > 35 Stratified OR = 3.4 OR = 5.7 Is there confounding present? Which answer should you report as “final”?

  30. No Effect of Third Variable Crude ORcrude = 21.0 (95% CI: 16.4 - 26.9) Stratified Matches Present Matches Absent ORmatches = 21.0 OR nomatches = 21.0 ORadj= 21.0 (95% CI: 14.2 - 31.1)

  31. Whether or not to accept the “adjusted” summary estimate in favor of the crude? • Methodologic literature is inconsistent on this • Bias-variance tradeoff • Scientifically most rigorous approach would appear to be to create two lists of potential confounders prior to the analysis: • A List: Those factors for which you will accept the adjusted result no matter how small the difference from the crude. • Factors you know must be confounders • B List: Those factors for which you will accept the adjusted result only if it meaningfully differs from the crude (with some pre-specified difference, e.g., 10%) • Factors you are less sure about • For some analyses, may have no factors on A list. For other analyses, no factors on B list. • Always putting all factors on A list may seem conservative, but not necessarily the right thing to do in that there may be a penalty in statistical imprecision

  32. Presence or Absence of Confounding by a Third Variable?

  33. Stratifying by Multiple Potential Confounders Crude Stratified <40 smokers 40-60 smokers >60 smokers <40 non-smokers 40-60 non-smokers >60 non-smokers

  34. The Need for Evaluation of Joint Confounding • Variables that evaluated alone show no confounding may show confounding when evaluated jointly Crude Stratified by Factor 1 alone by Factor 2 alone by Factor 1 & 2

  35. Approaches for When More than One Potential Confounder is Present • Backward versus forward confounder evaluation strategies • relevant both for stratification and especially multivariable modeling (“model selection”) • Backwards Strategy • initially evaluate all potential confounders together (i.e., look for joint confounding) • conceptually preferred because in nature variables are all present and act together • Procedure: • with all potential confounders considered, form adjusted estimate. This is the “gold standard” • one variable can then be dropped and the adjusted estimate is re-calculated (adjusted for remaining variables) • if the dropping of the first variable results in a non-meaningful (eg <10%) change compared to the gold standard, it can be eliminated • procedure continues until no more variables can be dropped (i.e. are remaining variables are relevant) • Problem: • with many potential confounders, cells become very sparse and some strata provide no information

  36. Example: Backwards Selection • Research question: Is prior hospitalization associated with the presence of methicillin-resistant S. aureus (MRSA)? (from Kleinbaum 2003) • Outcome variable: MRSA (present or absent) • Primary predictor: prior hospitalization (yes/no) • Potential confounders: age (<55, >55), gender, prior antibiotic use (atbxuse; yes/no) • Assume no interaction • Which OR to report?

  37. Approaches for When More than One Potential Confounder is Present • Forward Strategy • start with the variable that has the biggest “change-in-estimate” impact • then add the variable with the second biggest impact • keep this variable if its presence meaningfully changes the adjusted estimate • procedure continues until no other added variable has an important impact • Advantage: • avoids the initial sparse cell problem of backwards approach • Problem: • does not evaluate joint confounding effects of many variables

  38. An Analysis Plan • Written before the data are analyzed • Content • Detailed description of the techniques to be used to both explore and formally analyze data • Forms the basis of “Statistical Analysis” section in manuscripts • Parameters/rules/logic to guide key decisions: • which variables will be assessed for confounding and interaction? • what p value will be used to guide reporting of interaction? • what is a meaningful difference between two estimates (e.g. 10%)? • Required for clinical trial registration • Can observational work be far behind? • Utility: A plan helps to keep the analysis: • Focused • Reproducible • Honest (avoids p value shopping)

  39. Stratification to Manage Confounding • Advantages • straightforward to implement and comprehend • easy way to evaluate interaction • Limitations • Looks at only one exposure-disease assoc. at a time • Requires continuous variables to be discretized • loses information; possibly results in “residual confounding” • Deteriorates with multiple confounders • e.g. suppose 4 confounders with 3 levels • 3x3x3x3=81 strata needed • unless huge sample, many cells have “0”’s and strata have undefined effect measures • Solution: • Mathematical modeling (multivariable regression) • e.g. • linear regression • logistic regression • proportional hazards regression

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