Procedures for testing the homogeneity of relative difference in sparse data

Abstract

To quantify the excess effect of an experimental treatment over a placebo group in clinical trials, we often consider use of the relative difference, defined as the proportion of patients who would respond to the experimental treatment among those who would not otherwise if they were assigned to the placebo group. To control the effects due to confounders on the response of interest, we frequently employ stratified analysis in practice. Before obtaining a summary estimate of the relative difference, it is desirable to assess whether this measure is constant across strata. Based on the beta-binomial model, we develop simple procedures for testing the homogeneity of relative difference for sparse data in which we have many strata but few patients per stratum. Using Monte Carlo simulations, we demonstrate that the proposed test procedures can generally perform well with respect to type I error in a variety of situations. We further evaluate and study the power of these test procedures. Finally, we note some robustness in using the test procedures proposed here.