A CLASS OF EFFICIENT NONPARAMETRIC K-SAMPLE TESTS FOR MULTIVARIATE COUNTING-PROCESSES WITH FRAILTIES

A K-sample testing problem is studied for multivariate counting profes ses with time-dependent frailty. Asymptotic distributions and efficien cy of a class of non-parametric test statistics are established for ce rtain local alternatives. The concept of efficiency is to show that fo r every non-parametric test in this class, there is a parametric submo del for which the optimal test has the same asymptotic power as the no n-parametric one. The theory is applied to analyse a diabetic retinopa thy study data set. A simulation study is also presented to illustrate the theory.