MODULE 2: Exercise solution
1. Apply the Mantel-Haenszel analysis of sex stratified for smoking and smoking stratified for sex
First, we test for the marginal coherences and find the marginal OR (Crosstabs|Statistics|Risk)
Test for marginal coherences
Table 1.
χ2
p-value
ORMARGINAL
CHD × sex
26,307
<0,001
0,493 (0,375 – 0,648)
CHD × smoking
3,261
0,071 (not significant!) 1,279 (0,979 – 1,672)
Now the mantel-Haenszel analysis
CHD and sex stratified for smoking:
Table 2
Breslow-Day
Test: 2,468
p-value: 0,116
ORnon-smoker
0,610 (0,416 – 0,894)
ORsmoker
0,379 (0,239 – 0,600)
ORMH
0,492
MH-test (p-value)
<0,001
Conclusion:

Breslow-Day: H0 about homogeneity of the OR (smoker vs. non-smoker) is accepted  no
interaction/effect modification.. It therefore makes sense to use the calculated ORMH.

Interpretation of ORMH: women have about half the risk for CHD than men, when adjusted
for smoking.

Mantel Haenszel test for conditional independence: the H0 about conditional independence
(ORMH = 1) is rejected  coherence between CHD and sex when adjusted for smoking.

Smoking is a confounder, and you can now compare the ORMH with the ORmarginal and
thereby see the confounder effect. Here the effect is very small, i.e. 0,493 vs. 0,492, but the
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association between CHD and sex is a little weaker after adjusting for smoking (the OR has
moved closer to 1 after adjusting for smoking).
CHD and smoking stratified for sex:
Table 3
Breslow-Day
Test: 2,453
p-value: 0,117
ORmale
1,245 (0,860 – 1,802)
ORfemale
0,773 (0,483 – 1,237)
ORMH
1,034
MH-test (p-value)
Test: 0,024
0,876
Conclusion:

Breslow-Day: H0 about homogeneity of the OR (male vs. female) is accepted  no
interaction/effect modification. It therefore makes sense to use the calculated ORMH.

Interpretation of ORMH: Non-smokers have about 3 % larger risk for CHD than smokers
when adjusted for sex.

BUT: Mantel Haenszel test for conditional independence: the H0 about conditional
independence (ORMH = 1) is accepted  NO coherence between CHD and sex when
adjusted for smoking.
2. Compare the risk for CHD in the 4 age groups
Logistic regression is to be used as the data no longer can be constructed in a 2×2 table.
Comparison of the risk for CHD between the age groups:
Table 4
Age
Wald-test, p-value
β
OR (Exp(β))
45-48 (ref. group)
> 0,0001
0
1
2
49-52
0,304
0,212
1,236 (0,825 – 1,853)
53-56
0,042
0,420
1,522 (1,016 – 2,278)
57-62
> 0,0001
0,860
2,364 (1,614 – 3,464)
Conclusion

Wald-test: The overall Wald-test (Wald test for the ref. group) is significant  coherence
between CHD and age. The p-value for the age subgroup 49-52 is insignificant  the risk
for CHD for people aged 49-52 is not different from the risk of the ref. group (aged 45-48)

The risk for CHD increases with age.
3. Logistic regression analysis of the risk for CHD with different explanatory variables
Sex
o Interpretation: Women have about half the risk for CHD than men.
Sex and smoking
o Interpretation:

Sex: Women have about half the risk for CHD than men.

Smoke: Non-smokers have 3 % greater risk for CHD than non-smokers. But
remember: Smoking is not significant!
Age
o OR: see table 4.
o Interpretation: People aged 49-52 have about 24 % greater risk of CHD than the
reference group (people aged 45-48). Those aged 53-56 have about 52 % greater risk
for CHD than the reference group. Ect.
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o Remember to look at the p-value to be sure of significance!
Sex, smoking and age
o Interpretation:

Smoke: Non-smokers have about 16 % greater risk for CHD than smokers
(not significant)

Sex: women have about half the risk for CHD than men

Age: People aged 57-62 have about 2 ½ times greater risk for CHD than
people aged 45-48. Ect.
4. Estimate in a logistic regression analysis the effect of SBP with and without adjusting for sex
and age
New variable: SPBny:
≤140 = 0
141 – 180 = 1
> 180 = 2
Effect of SBP:
Isolated effect of SBP:
o People with a SBP between 141-180 have almost a two-fold greater risk for CHD than the
reference group (SBP ≤140). People with a SBP > 180 have 3,6 times greater risk for CHD
than the reference group
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Effect of SBP adjusted for sex and age:
o When adjusted for sex and age, people with a SBP between 141-180 have about a two-fold
greater risk for CHD than the reference group (SBP ≤140). People with a SBP > 180 have
about 4 times greater risk for CHD than the reference group
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