Abstract: Combining p-values to integrate multiple effects is of long-standing interest in social science and biomedical research. In this study, we revisit a classical scenario closely related to a meta-analysis with unknown heterogeneity that combines a finite and fixed number of p-values, while allowing the sample size for generating each p-value to go to infinity. Although many modified Fisher"s methods have been developed for this purpose, their asymptotic properties and finite-sample numerical performance have not been examined, and so is the motivation for our study. Our results show that Fisher and adaptive rank truncated product methods have top performance and complementary advantages across different proportions of true signals. Consequently, we propose an ensemble method, called the Fisher ensemble, that combines the two top-performing Fisher-related methods using a robust harmonic mean ensemble approach. We show that the Fisher ensemble achieves asymptotic Bahadur optimality and integrates advantages of the two methods in simulations. We subsequently extend the Fisher ensemble to a variation that is particularly powerful for concordant effect size directions. A transcriptomic meta-analysis application confirms the theoretical and simulation conclusions, generates intriguing biomarker and pathway findings, and demonstrates the strengths and strategy of using the proposed Fisher ensemble methods.

Key words and phrases: Ensemble method, global hypothesis testing, p-value combination, omnibus test.