On p-value combination of independent and frequent signals: asymptotic efficiency and Fisher ensemble

TL;DR

This paper evaluates classical and recent p-value combination methods for meta-analysis, demonstrating Fisher and weighted Fisher methods' efficiency and proposing a Fisher ensemble approach that achieves optimality and robust performance in simulations and real data.

Contribution

It introduces a Fisher ensemble method combining top Fisher-based techniques, achieving asymptotic optimality and improved finite-sample performance in p-value combination.

Findings

Fisher and weighted Fisher methods outperform others in efficiency.

Fisher ensemble achieves asymptotic Bahadur optimality.

Application to transcriptomic data confirms method effectiveness.

Abstract

Combining p-values to integrate multiple effects is of long-standing interest in social science and biomedical research. In this paper, we focus on revisiting a classical scenario closely related to meta-analysis, which combines a relatively small (finite and fixed) number of p-values while the sample size for generating each p-value is large (asymptotically goes to infinity). We evaluate a list of traditional and recently developed modified Fisher's methods to investigate their asymptotic efficiencies and finite-sample numerical performance. The result concludes Fisher and adaptively weighted Fisher method to have top performance and complementary advantages across different proportions of true signals. Finally, we propose an ensemble method, namely Fisher ensemble, to combine the two top-performing Fisher-related methods using a robust truncated Cauchy ensemble approach. We show that Fisher ensemble achieves asymptotic Bahadur optimality and integrates the strengths of Fisher and adaptively weighted Fisher methods in simulations. We subsequently extend Fisher ensemble to a variant with emphasized power for concordant effect size directions. A transcriptomic meta-analysis application confirms the theoretical and simulation conclusions, generates intriguing biomarker and pathway findings and demonstrates strengths and strategy of using proposed Fisher ensemble methods.