Abstract: In many clinical trials, it is of interest to compare more than two populations with respect to multiple correlated end-points. In this paper, we present a multivariate rank test for the comparison of R-samples (R>=2) with respect to multiple time-to-event outcomes as well as to repeated measures. We present a statistic that is a function of a linear combination of stochastic integrals and show that the large sample distribution of a vector of (R- 1)RK such stochastic integrals for K(K>1) variates and R groups is asymptotically multivariate normal. We then describe an R-sample T 2-like K-variate omnibus test similar to the Kruskal-Wallis test.
Key words and phrases: Multivariate rank test, counting processes, asymptotic distribution, stochastic integrals, random censorship model, repeated measures analysis, survival analysis.