Optimal Tests for Combining p-Values

Abstract

Combining information (p-values) obtained from individual studies to test whether there is an overall effect is an important task in statistical data analysis. Many classical statistical tests, such as chi-square tests, can be viewed as being a p-value combination approach. It remains challenging to find powerful methods to combine p-values obtained from various sources. In this paper, we study a class of p-value combination methods based on gamma distribution. We show that this class of tests is optimal under certain conditions and several existing popular methods are equivalent to its special cases. An asymptotically and uniformly most powerful p-value combination test based on constrained likelihood ratio test is then studied. Numeric results from simulation study and real data examples demonstrate that the proposed tests are robust and powerful under many conditions. They have potential broad applications in statistical inference.