A bootstrap semiparametric homogeneity test for the distributions of multigroup proportional data, with applications to analysis of quality of life outcomes in clinical trials.

This article is concerned about the test for the difference in the distributions of multigroup proportional data, which is motivated by the problem of comparing the distributions of quality of life (QoL) outcomes among different treatment groups in clinical trials. The proportional data, such as QoL outcomes assessed by answers to questions on a questionnaire, are bounded in a closed interval such as [0,1] with continuous observations in (0,1) and, in addition, excess observations taking the boundary values 0 and/or 1. Common statistical procedures used in practice, such as t- and rank-based tests, may not be very powerful since they ignore the specific feature of the proportional data. In this article, we propose a three-component mixture model for the proportional data and a density ratio model for the distributions of continuous observations in (0,1). A semiparametric test statistic for the homogeneity of distributions of multigroup proportional data is derived based on the empirical likelihood ratio principle and shown to be asymptotically distributed as a chi-squared random variable under null hypothesis. A nonparametric bootstrap procedure is proposed to further improve the performance of the semiparametric test. Simulation studies are performed to evaluate the empirical type I error and power of the proposed test procedure and compare it with likelihood ratio tests (LRTs) under parametric distribution assumptions, rank-based Kruskal-Wallis test, and Wald-type test. The proposed test procedure is also applied to the analysis of QoL outcomes from a clinical trial on colorectal cancer that motivated our study.