Statistics and Its Interface

Volume 7 (2014)

Number 1

We dedicate this special issue to Dr. Gang Zheng, a great colleague and dear friend to many of us.

Rank-based tests for comparison of multiple endpoints among several populations

Pages: 9 – 18

DOI: http://dx.doi.org/10.4310/SII.2014.v7.n1.a2

Authors

Zhengbang Li (School of Mathematics and Statistics, Central China Normal University, Wuhan, China)

Aiyi Liu (Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland, U.S.A.)

Zhaohai Li (Department of Statistics, George Washington University, Washington, D.C., U.S.A.; National Cancer Institute, National Institutes of Health, Bethesda, Maryland, U.S.A.)

Qizhai Li (Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China)

Abstract

We consider comparison of multiple endpoints among several independent populations. We extend O’Brien’s and Huang et al.’s methods from comparison of two groups to two more groups, and propose three max type test statistics, $T_1$ based on normally distributed data, $T_2$ obtained from pairwise ranking, and $T_3$ derived from ranking of all populations. Numerical results show that all three test statistics maintain the desired type I error rates and achieve satisfactory power. When the normal assumption is justified, $T_1$ is slightly more powerful than $T_2$ and $T_3$. However, when the normal assumption is violated, $T_2$ and $T_3$ gain sizable power. All three tests have higher power than O’Brien’s and Huang et al.’s methods using Bonferroni correction under the considered settings. The methods are exemplified using healthy eating index data from a study examining the conformance to dietary guideline.

Keywords

max, multidimensional outcomes, rank-based statistics

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