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 c ∈ 0, 1 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) t ∈ (0, 1) 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.