Increasing the power of meta-analysis of genome-wide association studies to detect heterogeneous effects

Motivation: Meta-analysis is essential to combine the results of genome-wide association studies (GWASs). Recent large-scale meta-analyses have combined studies of different ethnicities, environments and even studies of different related phenotypes. These differences between studies can manifest as effect size heterogeneity. We previously developed a modified random effects model (RE2) that can achieve higher power to detect heterogeneous effects than the commonly used fixed effects model (FE). However, RE2 cannot perform meta-analysis of correlated statistics, which are found in recent research designs, and the identified variants often overlap with those found by FE. Results: Here, we propose RE2C, which increases the power of RE2 in two ways. First, we generalized the likelihood model to account for correlations of statistics to achieve optimal power, using an optimization technique based on spectral decomposition for efficient parameter estimation. Second, we designed a novel statistic to focus on the heterogeneous effects that FE cannot detect, thereby, increasing the power to identify new associations. We developed an efficient and accurate p-value approximation procedure using analytical decomposition of the statistic. In simulations, RE2C achieved a dramatic increase in power compared with the decoupling approach (71% vs. 21%) when the statistics were correlated. Even when the statistics are uncorrelated, RE2C achieves a modest increase in power. Applications to real genetic data supported the utility of RE2C. RE2C is highly efficient and can meta-analyze one hundred GWASs in one day.