Testing Simultaneous Marginal Homogeneity in Clustered Matched-Pair Multinomial Data

Abstract

For matched-pair data with a multinomial reponse, the Stuart-Maxwell test (1955, 1970) and the Bhapkar test (1966) are commonly used to test the marginal homogeneity. However, in medical research, many studies for assess- ing safety consider multiple multinomial endpoints to detect the treatment ef- fects. To test the simultaneous marginal homogeneity (SMH) in such clustered matched-pair multinomial data, three overall tests are proposed. Furthermore, when the outcome is ordinal, three ordinal statistics which test SMH against stochastic ordering are proposed. To evaluate the performance of our methods, we generated a total of 5000 clustered matched-pair data sets, considering number of endpoints = 2; 3; 4 and sample size ranging from 25 to 200. Then our methods are applied to these 5000 datasets and the empirical size and power are compared. The simulation shows that the Score-type tests perform well with respect to nominal size and power even with small sample size. For ordinal endpoints, the ordinal statistic provides uniformly larger power than the one which does not utilize the ordinal feature.