Analytical p-value calculation for the higher criticism test in finite-d problems

Abstract

The higher criticism test is effective for testing a joint null hypothesis against a sparse alternative, e.g., for testing the effect of a gene or genetic pathway that consists of d genetic markers. Accurate p-value calculations for the higher criticism test based on the asymptotic distribution require a very large d, which is not the case for the number of genetic variants in a gene or a pathway. In this paper we propose an analytical method for accurately computing the p-value of the higher criticism test for finite-d problems. Unlike previous treatments, this method does not rely on asymptotics in d or on simulation, and is exact for arbitrary d when the test statistics are normally distributed. The method is particularly computationally advantageous when d is not large. We illustrate the proposed method with a case-control genome-wide association study of lung cancer and compare its power with competing methods through simulations.