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

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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