A rank-based test for comparison of multidimensional outcomes

Ai Yi Liu, Qi Zhai Li, Chunling Liu, Kai Yu, Kai F. Yu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

22 Citations (Scopus)


For comparison of multiple outcomes commonly encountered in biomedical research, Huang et al. (2005) improved O'Brien's (1984) ranksum tests through the replacement of the ad hoc variance by the asymptotic variance of the test statistics. The improved tests control the type I error rate at the desired level and gain power when the differences between the two comparison groups in each outcome variable lie in the same direction; however, they may lose power when the differences are in different directions (e.g., some are positive and some are negative). These tests and the popular Bonferroni correction failed to show important significant differences when applied to compare heart rates from a clinical trial to evaluate the effect of a procedure to remove the cardioprotective solution HTK. We propose an alternative test statistic, taking the maximum of the individual rank-sum statistics, which controls the type I error rate and maintains satisfactory power regardless of the direction of the differences. Simulation studies show the proposed test to be of higher power than other tests in a certain alternative parameter space of interest. Furthermore, when used to analyze the heart rate data, the proposed test yields more satisfactory results.
Original languageEnglish
Pages (from-to)578-587
Number of pages10
JournalJournal of the American Statistical Association
Issue number490
Publication statusPublished - 1 Jun 2010
Externally publishedYes


  • Autism spectrum disorder
  • Behrens-fisher problem
  • Cardioprotective solution
  • Case-control studies
  • Growth hormones
  • Multiple outcomes
  • Nonparametrics
  • Rank-sum statistics

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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