1. Stratified Analysis: Mantel-Haenszel Techniques Instructor: 李奕慧 yihwei@mail.tcu.edu.tw 1

2. Lecture Overview 1. Review example: ”Risk factors associated with lung cancer in Hong Kong” 2. Mantel-Haenszel Technique for Stratified Tables 3. Modification effect (Interaction effect) 4. Application: Meta-Analysis 2

3. Confounding factors ( 干擾因素） Confounder: Variable is associated with both the disease and the exposure variable. 3

4. Method for control for confounders Study design: restriction/ matching/ randomization Statistical adjustment: 1. Standardization; e.g. age standardized (where age is a confounder) 2. Stratified by confounder (Mantel-Haenszel test) 3. Incorporate the confounder into a regression analysis as a covariate. (logistic regression approach) 4

5. Restriction Example 研究主旨：二手煙 (ETS, exposure) 與罹患肺癌 (disease) 的關係 confounder: 研究對象本身是否抽煙 為了避免干擾只分析 ETS 對 nonsmoker 的影響 5

6. Stratified Analysis 6

7. 將性別當作分層 (stratum) 的因子 smoking * case * sex Crosstabulation Count sex case Total casecontrol malesmokingex- and current smoker160116276 nonsmoker5296148 Total212 424 femalesmokingex- and current smoker13619 nonsmoker106113219 Total119 238 Lung cancer2.sav 7

8. Sex-Specific OR for smoking Risk Estimate sexValue 95% Confidence Interval LowerUpper male Odds Ratio for smoking (ex- and current smoker / nonsmoker) 2.551.683.85 N of Valid Cases424 female Odds Ratio for smoking (ex- and current smoker / nonsmoker) 2.310.856.30 N of Valid Cases238 Lung cancer2.sav 可以將男士的 OR 與女士的 OR 合併嗎？ 怎麼併？ 8

9. Don’t do! 完全忽略性別 (confounder) OR=1.88 距離 2.31 或 2.55 都很遠, smoking * case Crosstabulation case Total casecontrol smoking ex- and current smoker Count173122295 % within case52.3%36.9%44.6% nonsmokerCount158209367 % within case47.7%63.1%55.4% TotalCount331 662 % within case100.0 % Risk Estimate Value 95% Confidence Interval LowerUpper Odds Ratio for smoking (ex- and current smoker / nonsmoker) 1.881.382.56 N of Valid Cases662 9

10. 男、女的 OR 很接近嗎？可以將 男女的 OR 整合嗎？ H 0 : OR m = OR f = OR (common odds ratio) 抽煙對男、女性罹癌的風險是否有差異？ Test of the Homogeneity of Odds Ratio (OR 的同質性檢定 ) Tests of Homogeneity of the Odds Ratio Chi-Squareddf Asymp. Sig. (2-sided) Breslow-Day.0311.860 Tarone's.0311.860 10

11. 整合後的 OR 如何？ Mantel-Haenszel Common Odds Ratio Estimate Estimate 介於 2.31~2.55 之間 2.509 ln(Estimate) ln(2.51)=0.92.920 Std. Error of ln(Estimate) 標準誤.195 Asymp. Sig. (2-sided) p-value.000 Asymp. 95% Confidence Interval Common Odds RatioLower Bound1.711 Upper Bound3.678 ln(Common Odds Ratio)Lower Bound.537 Upper Bound1.302 The Mantel-Haenszel common odds ratio estimate is asymptotically normally distributed under the common odds ratio of 1.000 assumption. So is the natural log of the estimate. 11

12. Confidence Interval and Testing for common OR 1. Obtain confidence interval for ln(OR) ln(OR)  1.96*SE 0.92  1.96*0.195 (0.38) (0.92-0.38, 0.92+0.38)=(0.54, 1.3) 2. Exponentiate these limits (e 0.54, e 1.3 )=(1.71, 3.68) 3. 當控制性別後，抽煙者罹患肺癌的風險是不抽 煙者的 1.7~3.7 倍 4. M-H test for common OR=1: p-value< 0.001 12

13. Sex-Specific OR for smoking Risk Estimate sexValue 95% Confidence Interval LowerUpper male Odds Ratio for smoking (ex- and current smoker / nonsmoker) 2.551.683.85 N of Valid Cases424 female Odds Ratio for smoking (ex- and current smoker / nonsmoker) 2.310.856.30 N of Valid Cases238 Lung cancer2.sav 男性 OR 信賴區間較窄，標準誤較小，給予較大 的權重。女性的 CI 較寬，標準誤較大，給予較 小的權重。 Common OR=2.51 13

14. M-H 分析的應用 :Forest Plot Sex-specific OR Common OR 14

15. Layer: 分層 Mantel-Haenszel Statistics 15

16. 如果不能整合，怎麼辦？ Table 4: Impact of fatty food consumption on lung cancer risk by Gender Male Female 16

17. Stratified Tables fat * lungcancer * sex Crosstabulation Count sex lungcancer Total yesno malefatmoderate/high fat161130291 low fat5180131 Total212210422 femalefatmoderate/high fat6973142 low fat504393 Total119116235 Risk Estimate sexValue 95% Confidence Interval LowerUpper male Odds Ratio for fat (moderate/high fat / low fat) 1.9431.2762.958 N of Valid Cases422 female Odds Ratio for fat (moderate/high fat / low fat).813.4811.373 N of Valid Cases235 Lung cancer3.sav 17

18. 可以將男女的 OR 整合嗎？ H 0 : OR m = OR f = OR (common odds ratio) 脂肪攝取對男、女性罹癌的風險是否有差異？ 如有差異，則表示此危險因子，在男女性的表 現是不一樣的，不能將兩者整合。 Tests of Homogeneity of the Odds Ratio Chi-SquareddfAsymp. Sig. (2-sided) Breslow-Day6.4981.011 Tarone's6.4971.011 18

19. Interaction or modification If the stratum-specific odds ratios ( say lung cancer) are different across the 2 (or g) strata, then there is an interaction between Exposure (fat consumption) and Confounder (gender), and the Confounder is an effect modifier ( 修飾因子 ). 脂肪攝取與性別會交互影響肺癌的發生風 險 19

20. Multiple 2 X 2 Tables No interaction With interaction 20

21. M-H 分析的應用 : Meta-Analysis Hepatitis B.sav 21

22. Outcome * Vaccine * study Crosstabulation Count study Vaccine Total vaccin e place bo Ip 1989 Outco me infected72330 not infected 281139 Total353469 Liu 1987 Outco me infected32124 not infected 24529 Total272653 Xu 1995a Outco me infected71219 not infected 531871 Total603090 Xu 1995b Outco me infected141226 not infected 461864 Total603090 Risk Estimate studyValue 95% Confidence Interval LowerUpper Ip 1989 OR.120.040.358 Liu 1987 OR.030.006.140 Xu 1995a OR.198.068.580 Xu 1995b OR.457.1781.174 22

23. Tests of Homogeneity of the Odds Ratio Chi-Squareddf Asymp. Sig. (2- sided) Breslow-Day10.0033.019 Tarone's9.9673.019 H0: OR1=OR2=OR3=OR4 檢定 4 個研究的 OR 是否相同 P=0.019 表示這 4 個 OR 差異很大 23

24. M-H 分析的應用 Hepatitis B.sav 24

25. Mantel-Haenszel Common Odds Ratio Estimate Estimate.175 ln(Estimate)-1.744 Std. Error of ln(Estimate).269 Asymp. Sig. (2-sided).000 Asymp. 95% Confidence Interval Common Odds Ratio Lower Bound.103 Upper Bound.296 ln(Common Odds Ratio) Lower Bound-2.271 Upper Bound-1.218 The Mantel-Haenszel common odds ratio estimate is asymptotically normally distributed under the common odds ratio of 1.000 assumption. So is the natural log of the estimate. Common OR: 整合後的 OR =0.18, 95%CI (0.10- 0.30) 檢定整合後的 OR=1, p=0.000 25

26. Fig 2 Effect of hepatitis B vaccine on occurrence of hepatitis B in newborn infants. BMJ 2006;332:328-336 Test for heterogeneity 檢定 RR1=RR2=RR3=RR4 是否相等 Test for overall effect 檢定整合後的 RR 是否等於 1 26

27. Thank you! 27