Homogeneity Test with a Generalized Mantel-Haenszel Estimator forL2 ×KContingency Tables

Abstract

A conditional test for the homogeneity of the odds ratios in L 2 × K ( K > 2) tables is developed based on a multiple hypergeometric distribution. The test is a generalization of the Breslow-Day test (1980) and is useful in sparse tables. For computational feasibility, the conditional maximum likelihood estimator is replaced by a consistent but inefficient estimator in the test statistic. If this is the case, it is shown that the asymptotic distribution is not chi squared, as has been noticed by Tarone (1985) in the case of 2 × 2 tables. Following Tarone we develop a correction method so that the statistic follows an asymptotic chi-squared distribution. An algorithm is developed for calculating the homogeneity test with a generalized Mantel-Haenszel estimator.