Multiple testing of interval composite null hypotheses using randomized p-values

Abstract

Equivalence tests are statistical hypothesis testing procedures that aim to establish practical equivalence rather than the usual statistical significant difference. These testing procedures are frequent in “bioequivalence studies," where one would wish to show that, for example, an existing drug and a new one under development have comparable therapeutic effects. In this article, we propose a two-stage randomized (RAND2) p-value that depends on a uniformly most powerful (UMP) p-value and an arbitrary tuning parameter c∈[0,1]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c\\in [0,1]$$\\end{document} for testing an interval composite null hypothesis. We investigate the behavior of the distribution function of the two p-values under the null hypothesis and alternative hypothesis for a fixed significance level t∈(0,1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t\\in (0,1)$$\\end{document} and varying sample sizes. We evaluate the performance of the two p-values in estimating the proportion of true null hypotheses in multiple testing. We conduct a family-wise error rate control using an adaptive Bonferroni procedure with a plug-in estimator to account for the multiplicity that arises from our multiple hypotheses under consideration. The various claims in this research are verified using a simulation study and real-world data analysis.