A method for combining p-values in meta-analysis by gamma distributions

Combining p-values from statistical tests across different studies is the most commonly used approach in meta-analysis for evolutionary biology. The most commonly used p-value combination methods mainly incorporate the z-transform tests (e.g., the un-weighted z-test and the weighted z-test) and the gamma-transform tests (e.g., the CZ method [Z. Chen, W. Yang, Q. Liu, J.Y. Yang, J. Li, and M.Q. Yang, A new statistical approach to combining p-values using gamma distribution and its application to genomewide association study, Bioinformatics 15 (2014), p. S3]). However, among these existing p-value combination methods, no method is uniformly most powerful in all situations [Chen et al. 2014]. In this paper, we propose a meta-analysis method based on the gamma distribution, MAGD, by pooling the p-values from independent studies. The newly proposed test, MAGD, allows for flexible accommodating of the different levels of heterogeneity of effect sizes across individual studies. The MAGD simultaneously retains all the characters of the z-transform tests and the gamma-transform tests. We also propose an easy-to-implement resampling approach for estimating the empirical p-values of MAGD for the finite sample size. Simulation studies and two data applications show that the proposed method MAGD is essentially as powerful as the z-transform tests (the gamma-transform tests) under the circumstance with the homogeneous (heterogeneous) effect sizes across studies.