Combining dependent p-values by gamma distributions.

Combining correlated p-values from multiple hypothesis testing is a most frequently used method for integrating information in genetic and genomic data analysis. However, most existing methods for combining independent p-values from individual component problems into a single unified p-value are unsuitable for the correlational structure among p-values from multiple hypothesis testing. Although some existing p-value combination methods had been modified to overcome the potential limitations, there is no uniformly most powerful method for combining correlated p-values in genetic data analysis. Therefore, providing a p-value combination method that can robustly control type I errors and keep the good power rates is necessary. In this paper, we propose an empirical method based on the gamma distribution (EMGD) for combining dependent p-values from multiple hypothesis testing. The proposed test, EMGD, allows for flexible accommodating the highly correlated p-values from the multiple hypothesis testing into a unified p-value for examining the combined hypothesis that we are interested in. The EMGD retains the robustness character of the empirical Brown's method (EBM) for pooling the dependent p-values from multiple hypothesis testing. Moreover, the EMGD keeps the character of the method based on the gamma distribution that simultaneously retains the advantages of the z-transform test and the gamma-transform test for combining dependent p-values from multiple statistical tests. The two characters lead to the EMGD that can keep the robust power for combining dependent p-values from multiple hypothesis testing. The performance of the proposed method EMGD is illustrated with simulations and real data applications by comparing with the existing methods, such as Kost and McDermott's method, the EBM and the harmonic mean p-value method.