Transcript Mantel-Haenszel Common Odds Ratio Estimate

Stratified Analysis:
Mantel-Haenszel Techniques
Instructor: 李奕慧
[email protected]
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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
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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


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)
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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
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Stratified Analysis
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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
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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
可以將男士的OR與女士的OR合併嗎？
怎麼併？
Lung cancer2.sav
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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 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
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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
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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
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Sex-specific OR
Common OR
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Layer:分層
Mantel-Haenszel Statistics
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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 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
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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
.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

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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
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
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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
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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
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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
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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.
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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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