# Cocran-Mantel-Haenszel Test

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```					    Cocran-Mantel-Haenszel Test

•  A method to adjust odds ratios or relative
risks

• Yields a summary odds ratio or relative
risk
From the Task List under Describe
select Table Analysis
Select Race, Sex and CAD from the
Under Tables drag CAD to the top and
Sex to the left side
Next under Tables drag Race to the middle
of the table with Sex and CAD
For Cell Statistics select Row
percentages and Cell frequencies
Under Table Statistics/Association select
Chi-square tests and CMH statistics
The first table gives the results for race
equal to AP
Table 1 of SEX by CAD

Frequency Controlling for RACE=AP
0       1
F          169     218     387
43.67   56.33

M          283     370     653
43.34   56.66

Total      452     588     1040
Other results are the Relative Risks and the
Chi-Square results for the first table

Estimates of the Relative Risk (Row1/Row2)
Type of Study                   Value     95% Confidence Limits
Case-Control (Odds Ratio)       1.0136    0.7865       1.3061
Cohort (Col1 Risk)              1.0076    0.8732       1.1627
Cohort (Col2 Risk)              0.9942    0.8902       1.1102

Statistic          DF           Value         Prob
Chi-Square       1         0.0108            0.9171
• A table has only one odds ratio regardless
of the coding of the variables
• If your outcome of interest (in this example
CAD) is 1 (or yes) for column2, use the
Col 2 risks for a cohort study
• If your outcome of interest is in column 1
use the Col 1 risks for a cohort study
The second table gives the results for race
equal to C
Table 2 of SEX by CAD
Frequency    Controlling for RACE=C
Row Pct
0          1
F              86         98      184
46.74      53.26

M              163        280     443
36.79      63.21

Total          249        378     627

Statistic       DF Value       Prob
Chi-Square 1        5.3699 0.0205
Relative Risks and the Chi-Square results
for the second table

Estimates of the Relative Risk (Row1/Row2)

Type of Study                    Value     95% Confidence Limits

Case-Control (Odds Ratio)        1.5074    1.0643        2.1351

Cohort (Col1 Risk)               1.2703    1.0435        1.5464

Cohort (Col2 Risk)               0.8427    0.7232        0.9818

Statistic             DF    Value         Prob
Chi-Square            1     5.3699        0.0205
The third table gives the results for race
equal to C
Table 3 of SEX by CAD
Frequency Controlling for RACE=O
Row Pct
)          0       1
F          57       49     106
53.7     46.2
7        3
M          96       111    207
46.3     53.6
8        2
Total      153      160    313

Statistic   DF Value     Prob
Chi-Square 1    1.5349 0.2154
Relative Risks and the Chi-Square results
for the third table

Estimates of the Relative Risk (Row1/Row2)

Type of Study                    Value     95% Confidence Limits

Case-Control (Odds Ratio)        1.3450    0.8411        2.1509

Cohort (Col1 Risk)               1.1595    0.9218        1.4584

Cohort (Col2 Risk)               0.8621    0.6773        1.0973

Statistic         DF     Value        Prob
Chi-Square        1      1.5349       0.2154
The summary tables gives the combined
Relative Risks for the three tables

Estimates of the Common Relative Risk (Row1/Row2)
Type of Study   Method            Value    95% Confidence Limits
Case-Control    Mantel-Haenszel   1.1895   0.9861     1.4349
(Odds Ratio)    Logit             1.1905   0.9866     1.4365
Cohort          Mantel-Haenszel   1.1019   0.9937     1.2219
(Col1 Risk)     Logit             1.1052   0.9967     1.2255
Cohort          Mantel-Haenszel   0.9265   0.8518     1.0077
(Col2 Risk)     Logit             0.9297   0.8548     1.0110
The p-value is called Prob; for nominal data
the 3 statistics listed will be the same.

Cochran-Mantel-Haenszel Statistics (Based on Table Scores)

Statistic   Alternative Hypothesis        DF   Value         Prob

1           Nonzero Correlation           1    3.2979        0.0694

2           Row Mean Scores Differ        1    3.2979        0.0694

3           General Association           1    3.2979        0.0694
The test for homogeneity tests if the results
for the three races are the same

Breslow-Day Test for
Homogeneity of the Odds Ratios

Chi-Square           3.5773
DF                   2
Pr > ChiSq           0.1672

The Pr > ChiSq = 0.1672 is greater than 0.05; we can’t reject the
hypothesis that the results for the three races are the same.
Summary of results
Relative
Category      Risk       95% CI      P-value
Race=AP       0.99      0.89, 1.11    0.92

Race=C       0.84      0.72, 0.98    0.02

Race=0       0.86      0.68, 1.10    0.22

Summary       0.93      0.85, 1.01    0.07

Chi-sq                               0.17
homogeneity
Relative risks (RRs) of death by sex
CAD     DM CHF      RR      95% CI P-value
No     No   No     1.63   0.97, 2.78 0.07
No     No   Yes    1.22   0.67, 2.23 0.51
No     Yes Yes     1.87   0.78, 4.40 0.14
Yes     No   No     1.44   0.69, 2.99 0.33
Yes     No   Yes    1.02   0.54, 1.93 0.95
Yes     Yes  No     1.76   0.71, 4.38 0.21
Yes     Yes Yes     1.02   0.59, 1.78 0.93
Summary              1.32   1.04, 1.68 0.02
Chi-sq homogeneity                     0.89

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 views: 25 posted: 11/24/2011 language: English pages: 19