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
           Task Roles
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
      Row Pct   SEX(SEX) CAD(CAD)          Total
                           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
                          SEX(SEX)       CAD(CAD)           Total
                                         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
                      SEX(SEX CAD(CAD)             Total
                      )          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
     adjusting for CAD, DM, and CHF
 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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posted:11/24/2011
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