Empirically adjusted fixed-effects meta-analysis methods in genomic studies

In recent years, meta-analyzing summary results from multiple studies has become a common practice in genomic research, leading to a significant improvement in the power of statistical detection compared to an individual genomic study. Meta analysis methods that combine statistical estimates across studies are known to be statistically more powerful than those combining statistical significance measures. An approach combining effect size estimates based on a fixed-effects model, called METAL, has gained extreme popularity to perform the former type of meta-analysis. In this article, we discuss the limitations of METAL due to its dependence on the theoretical null distribution, leading to incorrect significance testing results. Through various simulation studies and real genomic data application, we show how modifying the z-scores in METAL, using an empirical null distribution, can significantly improve the results, especially in presence of hidden confounders. For the estimation of the null distribution, we consider two different approaches, and we highlight the scenarios when one null estimation approach outperforms the other. This article will allow researchers to gain an insight into the importance of using an empirical null distribution in the fixed-effects meta-analysis as well as in choosing the appropriate empirical null distribution estimation approach.