Statistics and Its Interface

Volume 2 (2009)

Number 2

A weighted rank-sum procedure for comparing samples with multiple endpoints

Pages: 197 – 201

DOI: http://dx.doi.org/10.4310/SII.2009.v2.n2.a9

Authors

Qizhai Li (Biostatistics Branch, Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, Maryland, U.S.A.)

Aiyi Liu (Biostatistics and Bioinformatics Branch, National Institute of Child Health and Human Development, Bethesda, Maryland, U.S.A.)

Kai Yu (Biostatistics Branch, Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, Maryland, U.S.A.)

Kai F. Yu (Biostatistics and Bioinformatics Branch, National Institute of Child Health and Human Development, Bethesda, Maryland, U.S.A.)

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 ranksum 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).

Keywords

asymptotic normality, Behrens-Fisher problem, case-control, clinical trials, multiple endpoints, rank-sum statistics, weights

2010 Mathematics Subject Classification

60K35

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