Stratified Analysis:

Mantel-Haenszel Techniques

Instructor: 李奕慧

yihwei@mail.tcu.edu.tw

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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

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Confounding factors (干擾因素）

Confounder:

Variable is associated with both the disease and the exposure variable.

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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)

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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

Stratified Analysis

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將性別當作分層 (stratum) 的因子

smoking * case * sex CrosstabulationCount

sexcase

Totalcase controlmale smoking ex- and current smoker 160 116 276

nonsmoker 52 96 148Total 212 212 424

female smoking ex- and current smoker 13 6 19

nonsmoker 106 113 219Total 119 119 238

Lung cancer2.sav7

Sex-Specific OR for smokingRisk Estimate

sex Value

95% Confidence Interval

Lower Uppermale Odds Ratio for smoking (ex- and

current smoker / nonsmoker)2.55 1.68 3.85

N of Valid Cases 424female Odds Ratio for smoking (ex- and

current smoker / nonsmoker)2.31 0.85 6.30

N of Valid Cases 238

Lung cancer2.sav

可以將男士的 OR 與女士的 OR 合併嗎？怎麼併？

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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 Crosstabulationcase

Totalcase controlsmoking ex- and current

smokerCount 173 122 295% within case 52.3% 36.9% 44.6%

nonsmoker Count 158 209 367% within case 47.7% 63.1% 55.4%

Total Count 331 331 662% within case 100.0

%100.0

%100.0

%

Risk Estimate

Value

95% Confidence Interval

Lower Upper

Odds Ratio for smoking (ex- and current smoker / nonsmoker)

1.88 1.38 2.56

N of Valid Cases 662

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男、女的 OR 很接近嗎？可以將男女的 OR 整合嗎？ H0: ORm = ORf = 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-Squared dfAsymp. Sig.

(2-sided)

Breslow-Day .031 1 .860

Tarone's .031 1 .86010

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 Ratio Lower Bound 1.711

Upper Bound 3.678

ln(Common Odds Ratio) Lower Bound .537

Upper Bound 1.302

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.

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Confidence Interval and Testingfor common OR1. 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

(e0.54, e1.3)=(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

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Sex-Specific OR for smokingRisk Estimate

sex Value

95% Confidence Interval

Lower Uppermale Odds Ratio for smoking (ex- and

current smoker / nonsmoker)2.55 1.68 3.85

N of Valid Cases 424female Odds Ratio for smoking (ex- and

current smoker / nonsmoker)2.31 0.85 6.30

N of Valid Cases 238

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

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M-H 分析的應用 :Forest Plot

Odds ratio smoking better non-smoking better

.1 .5 1 2 10

Study

Odds ratio

(95% CI)

No. of events

Treatment Control

male 2.55 ( 1.68, 3.85) 160/212 116/212

female 2.31 ( 0.85, 6.30) 13/119 6/119

Overall 2.51 ( 1.71, 3.68) 173/331 122/331

Sex-specific OR

Common OR

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Layer: 分層

Mantel-Haenszel Statistics15

如果不能整合，怎麼辦？Table 4:

Impact of fatty food consumption on lung cancer risk by Gender

Male

Female

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Stratified Tablesfat * lungcancer * sex Crosstabulation

Count

sexlungcancer

Totalyes nomale fat moderate/high fat 161 130 291

low fat 51 80 131Total 212 210 422

female fat moderate/high fat 69 73 142low fat 50 43 93

Total 119 116 235

Risk Estimate

sex Value

95% Confidence Interval

Lower Uppermale Odds Ratio for fat

(moderate/high fat / low fat)1.943 1.276 2.958

N of Valid Cases 422female Odds Ratio for fat

(moderate/high fat / low fat).813 .481 1.373

N of Valid Cases 235Lung cancer3.sav

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可以將男女的 OR 整合嗎？ H0: ORm = ORf = 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-Squared df Asymp. Sig. (2-sided)

Breslow-Day 6.498 1 .011

Tarone's 6.497 1 .01118

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

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Multiple 2 X 2 Tables

No interaction With interaction

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M-H 分析的應用 : Meta-Analysis

Hepatitis B.sav

Odds ratio Vaccine better Placebo better

.01 .1 1 10 100

Study

Odds ratio

(95% CI)

No. of events

Treatment Control

Ip (1989) 0.12 ( 0.04, 0.36) 7/35 23/34

Liu (1987) 0.03 ( 0.01, 0.14) 3/27 21/26

Xu (1955) 0.20 ( 0.07, 0.58) 7/60 12/30

Xu (1995) 0.46 ( 0.18, 1.17) 14/60 12/30

Overall 0.17 ( 0.10, 0.30) 31/182 68/120

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Outcome * Vaccine * study Crosstabulation

Count

study

Vaccine

Totalvaccin

eplace

boIp 1989 Outco

meinfected 7 23 30not infected

28 11 39

Total 35 34 69Liu 1987

Outcome

infected 3 21 24not infected

24 5 29

Total 27 26 53Xu 1995a

Outcome

infected 7 12 19not infected

53 18 71

Total 60 30 90Xu 1995b

Outcome

infected 14 12 26not infected

46 18 64

Total 60 30 90

Risk Estimate

study Value

95% Confidence Interval

Lower UpperIp 1989

OR .120 .040 .358

Liu 1987OR .030 .006 .140

Xu 1995aOR .198 .068 .580

Xu 1995bOR .457 .178 1.174

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Tests of Homogeneity of the Odds Ratio

Chi-Squared dfAsymp. Sig. (2-

sided)

Breslow-Day 10.003 3 .019

Tarone's 9.967 3 .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

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M-H 分析的應用

Hepatitis B.sav

Odds ratio Vaccine better Placebo better

.01 .1 1 10 100

Study

Odds ratio

(95% CI)

No. of events

Treatment Control

Ip (1989) 0.12 ( 0.04, 0.36) 7/35 23/34

Liu (1987) 0.03 ( 0.01, 0.14) 3/27 21/26

Xu (1955) 0.20 ( 0.07, 0.58) 7/60 12/30

Xu (1995) 0.46 ( 0.18, 1.17) 14/60 12/30

Overall 0.17 ( 0.10, 0.30) 31/182 68/120

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Mantel-Haenszel Common Odds Ratio Estimate

Estimate .175

ln(Estimate) -1.744Std. Error of ln(Estimate) .269Asymp. Sig. (2-sided) .000

Asymp. 95% Confidence Interval

Common Odds Ratio

Lower Bound .103Upper Bound .296

ln(Common Odds Ratio)

Lower Bound -2.271Upper 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

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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

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Thank you!

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