Tests of homogeneity for the relative risk in multiply-matched case-control studies

We examine several tests of homogeneity of the odds ratio in the analysis of 2 x 2 tables arising from epidemiologic 1:R matched case-control studies. The T4 and T5 statistics proposed by Liang and Self (1985, Biometrika 72, 353-358) are unable to detect obvious inhomogeneity in two numerical examples and in simulation studies. The null hypothesis is rejected by the chi-square statistic of Ejigou and McHugh (1984, Biometrika 71, 408-411) and by a new proposed method whose significance level must be simulated.