Coconut: covariate-assisted composite null hypothesis testing with applications to replicability analysis of high-throughput experimental data.

Background: Multiple testing of composite null hypotheses is critical for identifying simultaneous signals across studies. While it is common to incorporate external information in simple null hypotheses, exploiting such auxiliary covariates to provide prior structural relationships among composite null hypotheses and boost the statistical power remains challenging.

Results: We propose a robust and powerful covariate-assisted composite null hypothesis testing (CoCoNuT) procedure based on a Bayesian framework to identify replicable signals in two studies while asymptotically controlling the false discovery rate. CoCoNuT innovatively adopts a three-dimensional mixture model to consider two primary studies and an integrative auxiliary covariate jointly. While accounting for heterogeneity across studies, the local false discovery rate optimally captures cross-study and cross-feature information, providing improved rankings of feature importance.

Conclusions: Theoretical and empirical evaluations confirm the validity and efficiency of CoCoNuT. Extensive simulations demonstrate that CoCoNuT outperforms conventional methods that do not exploit auxiliary covariates while controlling the FDR. We apply CoCoNuT to schizophrenia genome-wide association studies, illustrating its higher power in identifying replicable genetic variants with the assistance of relevant auxiliary studies.