Stratified Analysis:
Mantel-Haenszel Techniques
Instructor: 李奕慧
yihwei@mail.tcu.edu.tw
1
Lecture Overview
1.
2.
3.
4.
Review example: ”Risk factors
associated with lung cancer in Hong
Kong”
Mantel-Haenszel Technique for
Stratified Tables
Modification effect (Interaction effect)
Application: Meta-Analysis
2
Confounding factors (干擾因素）
Confounder:
Variable is associated with both the
disease and the exposure variable.
3
Method for control for confounders


1.
2.
3.
Study design:
restriction/ matching/ randomization
Statistical adjustment:
Standardization; e.g. age standardized (where
age is a confounder)
Stratified by confounder (Mantel-Haenszel test)
Incorporate the confounder into a regression
analysis as a covariate. (logistic regression
approach)
4
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
6
將性別當作分層(stratum)的因子
smoking * case * sex Crosstabulation
Count
sex
male
smoking
ex- and current smoker
nonsmoker
female
Total
smoking
ex- and current smoker
nonsmoker
Total
case
case
control
160
116
Total
276
52
212
13
96
212
6
148
424
19
106
119
113
119
219
238
Lung cancer2.sav
7
Sex-Specific OR for smoking
Risk Estimate
sex
male
female
95% Confidence
Interval
Value Lower
Upper
2.55
1.68
3.85
Odds Ratio for smoking (ex- and
current smoker / nonsmoker)
N of Valid Cases
Odds Ratio for smoking (ex- and
current smoker / nonsmoker)
424
2.31
N of Valid Cases
238
0.85
6.30
可以將男士的OR與女士的OR合併嗎？
怎麼併？
Lung cancer2.sav
8
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
smoking
Total
case
case control
173
122
52.3% 36.9%
158
209
47.7% 63.1%
331
331
100.0 100.0
%
%
ex- and current Count
smoker
% within case
nonsmoker
Count
% within case
Count
% within case
Total
295
44.6%
367
55.4%
662
100.0
%
Risk Estimate
95% Confidence Interval
Value
Odds Ratio for smoking
(ex- and current smoker /
nonsmoker)
N of Valid Cases
Lower
1.88
Upper
1.38
2.56
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
Breslow-Day
Tarone's
Chi-Squared
.031
.031
df
Asymp. Sig.
(2-sided)
1
.860
1
.860
10
整合後的OR如何？
Mantel-Haenszel Common Odds Ratio Estimate
Estimate
介於2.31~2.55之間
ln(Estimate)
ln(2.51)=0.92
Std. Error of ln(Estimate)
標準誤
Asymp. Sig. (2-sided)
p-value
Common Odds Ratio
Lower Bound
Asymp. 95%
Upper Bound
Confidence Interval
ln(Common Odds Ratio)
Lower Bound
Upper Bound
2.509
.920
.195
.000
1.711
3.678
.537
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 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.
3.
4.
Exponentiate these limits
(e0.54, e1.3)=(1.71, 3.68)
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
M-H test for common OR=1: p-value< 0.001
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Sex-Specific OR for smoking
Risk Estimate
sex
male
female
95% Confidence
Interval
Value Lower
Upper
2.55
1.68
3.85
Odds Ratio for smoking (ex- and
current smoker / nonsmoker)
N of Valid Cases
Odds Ratio for smoking (ex- and
current smoker / nonsmoker)
424
2.31
N of Valid Cases
238
0.85
6.30
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
Lung cancer2.sav
13
M-H分析的應用:Forest Plot
Odds ratio
No. of events
Study
(95% CI)
Treatment
Control
male
2.55 ( 1.68, 3.85)
160/212
116/212
female
2.31 ( 0.85, 6.30)
13/119
6/119
2.51 ( 1.71, 3.68)
173/331
122/331
Overall
.1
.5
1
2
Odds ratio
smoking better
non-smoking better
10
Sex-specific OR
Common OR
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Layer:分層
Mantel-Haenszel Statistics
15
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
Stratified Tables
fat * lungcancer * sex Crosstabulation
Count
sex
male
fat
Total
female fat
lungcancer
yes
no
161
130
51
80
212
210
69
73
50
43
119
116
moderate/high fat
low fat
moderate/high fat
low fat
Total
Total
291
131
422
142
93
235
Risk Estimate
sex
male
Odds Ratio for fat
(moderate/high fat / low fat)
N of Valid Cases
female Odds Ratio for fat
(moderate/high fat / low fat)
N of Valid Cases
95% Confidence
Interval
Value Lower Upper
1.943
1.276
2.958
422
.813
235
.481
1.373
Lung
cancer3.sav
17
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
.011
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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
Multiple 2 X 2 Tables
No interaction
With interaction
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M-H分析的應用: Meta-Analysis
Odds ratio
No. of events
Study
(95% CI)
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
0.17 ( 0.10, 0.30)
31/182
68/120
Overall
.01
.1
1
10
100
Odds ratio
Vaccine better
Placebo better
Hepatitis B.sav
21
Outcome * Vaccine * study
Crosstabulation
Count
study
Ip 1989 Outco
me
Liu
1987
Total
Outco
me
Xu
1995a
Total
Outco
me
Xu
1995b
Total
Outco
me
Total
Vaccine
vaccin place
e
bo Total
infected
7
23
30
28
11
39
not
infected
35
34
69
infected
3
21
24
24
5
29
not
infected
27
26
53
infected
7
12
19
53
18
71
not
infected
60
30
90
infected
14
12
26
46
18
64
not
infected
60
30
90
Risk Estimate
95% Confidence
Interval
study
Ip 1989
Value
Lower
Upper
OR
.120
.040
.358
OR
.030
.006
.140
OR
.198
.068
.580
OR
.457
.178
1.174
Liu 1987
Xu 1995a
Xu 1995b
22
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
Tests of Homogeneity of the Odds Ratio
Chi-Squared
Breslow-Day
Tarone's
Asymp. Sig. (2sided)
df
10.003
3
.019
9.967
3
.019
23
M-H分析的應用
Odds ratio
No. of events
Study
(95% CI)
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
0.17 ( 0.10, 0.30)
31/182
68/120
Overall
.01
.1
1
10
100
Odds ratio
Vaccine better
Placebo better
Hepatitis B.sav
24
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
Mantel-Haenszel Common Odds Ratio Estimate
Estimate
ln(Estimate)
Std. Error of ln(Estimate)
Asymp. Sig. (2-sided)
Asymp. 95%
Confidence
Interval
Common Odds
Ratio
ln(Common
Odds Ratio)
.175
-1.744
.269
.000
Lower Bound
Upper Bound
Lower Bound
Upper Bound
.103
.296
-2.271
-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.
25
Fig 2 Effect of hepatitis B vaccine on
occurrence of hepatitis B in newborn infants.
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
BMJ 2006;332:328-336
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Thank you!
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