Analytic P-value Calculation for the Higher Criticism Test in Finite Problems

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