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

Abstract

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.