Testing and Sample Size for Polygonal One-Sided Hypotheses on Bivariate Binary Outcomes

Ziyue Liu, Menggang Yu, Yan Tong

Research output: Contribution to journalArticle


In this article, we consider hypothesis testing and computationally feasible sample size determination for bivariate binary outcomes. The hypotheses are formulated as one-sided polygons, which allow flexible trade-offs between the two outcomes. Parameters are estimated by maximizing the likelihood. Hypothesis testing for each linear constraint is performed by the Wald, score, likelihood ratio, and exact tests. The overall hypothesis is then tested using either the union-intersection or intersection-union method. We propose methods to calculate both exact power functions and asymptotic power functions. Finite sample behaviors are evaluated by numerical examples. A data example is used for illustration.

Original languageEnglish (US)
Pages (from-to)1-17
Number of pages17
JournalStatistics in Biopharmaceutical Research
Issue number1
StatePublished - Mar 1 2013



  • Bivariate binary data
  • Hypothesis testing
  • Polygonal hypothesis
  • Sample size determination

ASJC Scopus subject areas

  • Pharmaceutical Science
  • Statistics and Probability

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