title: A Weighted Rank-Sum Procedure for Comparing Samples with Multiple Endpoints.
abstract: 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).
authors.affiliation: Biostatistics Branch, Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, MD 20892 USA.
authors.forename: Qizhai
authors.initials: Q
authors.lastname: Li
authors.forename: Aiyi
authors.initials: A
authors.lastname: Liu
authors.forename: Kai
authors.initials: K
authors.lastname: Yu
authors.forename: Kai F
authors.initials: KF
authors.lastname: Yu