A Weighted Rank-Sum Procedure for Comparing Samples with Multiple Endpoints.

For comparing the distribution of two samples with multiple endpoints, O'Brien (1984) proposed rank-sum-type test statistics. Huang et al. (2005) extended these statistics to the general nonparametric Behrens-Fisher hypothesis problem and obtained improved test statistics by replacing the ad hoc variance with the asymptotic variance of the rank-sum statistics. In this paper we generalize the work of O'Brien (1984) and Huang et al. (2005) and propose a weighted rank-sum statistic. We show that the weighted rank-sum statistic is asymptotically normally distributed, permitting the computation of power, p-values and confidence intervals. We further demonstrate via simulation that the weighted rank-sum statistic is efficient in controlling the type I error rate and under certain alternatives, is more powerful than the statistics of O'Brien (1984) and Huang et al.(2005).