11.3 - Safety and Efficacy (Phase II) Studies: The Mantel-Haenszel Test for the Odds Ratio

Sometimes a safety and efficacy study is stratified according to some factor, such as clinical center, disease severity, gender, etc. In such a situation, it still may be desirable to estimate the odds ratio while accounting for strata effects. The Mantel-Haenszel test for the odds ratio assumes that the odds ratio is equal across all strata, although the rates, \(p_1\) and \(p_2\), may differ across strata. This procedure calculates the odds ratio within each stratum and then combines the strata estimates into one estimate of the common odds ratio. For example,

Stratum	\(p_1\)	\(p_2\)	\(\theta\)
1	0.50	0.25	3.00
2	0.40	0.18	3.00
3	0.30	0.12	3.00
4	0.20	0.08	3.00

SAS® Example

Using PROC FREQ for conducting a Mantel-Haenszel test

A company performed a multi-center safety and efficacy study at six sites, with a binary outcome (success/failure), for comparing placebo and treatment.

***********************************************************************
* This is a program that illustrates the use of PROC FREQ for         *
* conducting a Mantel-Haenszel test within the setting of a multi-    *
* center clinical trial.                                              *
***********************************************************************;

proc format;
value centfmt  1='Phoenix'
               2='Denver'
               3='Miami'
               4='New York'
               5='Atlanta'
               6='Chicago';
value groupfmt 0='Placebo'
               1='Treatment';
value respfmt  0='Failure'
               1='Success';
run;

data one;
input center group response count;
format center centfmt. group groupfmt. response respfmt.;
cards;
1 0 0 24
1 0 1  8
1 1 0 20
1 1 1 12
2 0 0 44
2 0 1 28
2 1 0 40
2 1 1 32
3 0 0 25
3 0 1  5
3 1 0 20
3 1 1 10
4 0 0 14
4 0 1 16
4 1 0 12
4 1 1 18
5 0 0 32
5 0 1 20
5 1 0 24
5 1 1 28
6 0 0 45
6 0 1  5
6 1 0 32
6 1 1 18
;
run;

proc freq data=one;
tables center*group*response/cmh;
exact comor;
weight count;
title "Example of the Mantel-Haenszel Test Applied to a Multi-Center Trial";
run;

SAS PROC FREQ yields an estimated odds ratio of 1.84 with an approximate 95% confidence interval is (1.28, 2.66).

The exact 95% confidence interval is (1.26, 2.69). The exact and asymptotic confidence intervals are nearly identical due to the large sample size across the six clinical centers.

\(H_0 \colon θ = 1\) is rejected at the 0.05 significance level (\(p = 0.0013\), which is consistent with the 95% confidence interval not containing 1.0. (Later in this chapter we discuss the construction of the Mantel-Haenszel test statistic.)

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