Robust Methods to combine p-values from independent experiments

Abstract

Meta-analyses increase statistical power by combining statistics from multiple studies. Meta-analysis methods have mostly been evaluated under the condition that all the data in each study have a nonzero effect. However, specific experimental conditions or genetic heterogeneity can lead to random statistic in each study. Here, we show that power of most conventional meta-analysis methods rapidly decreases as increasing numbers of random statistics are included. The classical Fisher’s method, however, exhibits relatively high power that is robust to addition of random statistics. We demonstrate that degrees of freedom used for each study have a large effect on the robustness of methods and propose the use of a novel weighted Fisher’s method that is superior to original Fisher’s method, both with or without random statistics. We also propose another robust method based on joint distribution of ordered p-values. Simulation analyses for t-test and genome-wide association study (GWAS) demonstrated that our proposed methods, when a small number of studies have nonzero effects, outperformed existing p-value combining methods and also compared favorably with state-of-the-art methods for GWAS. Finally, our methods were applied to common variants in T2D-GENES consortium data and detected a novel locus (rs37411300; BUD13) associated with triglyceride levels. The metapro R package that implements the proposed methods is available from both CRAN and GitHub (http://github.com/unistbig/metapro).