stratified analysis: mantel-haenszel techniques instructor: 李奕慧 [email protected] 1
TRANSCRIPT
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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