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Combining p-values to integrate multiple effects is of long-standing interestin social science and biomedical research. In this paper, we focus onrevisiting a classical scenario closely related to meta-analysis, whichcombines a relatively small (finite and fixed) number of p-values while thesample size for generating each p-value is large (asymptotically goes toinfinity). We evaluate a list of traditional and recently developed modifiedFisher's methods to investigate their asymptotic efficiencies and finite-samplenumerical performance. The result concludes Fisher and adaptively weightedFisher method to have top performance and complementary advantages acrossdifferent proportions of true signals. Finally, we propose an ensemble method,namely Fisher ensemble, to combine the two top-performing Fisher-relatedmethods using a robust truncated Cauchy ensemble approach. We show that Fisherensemble achieves asymptotic Bahadur optimality and integrates the strengths ofFisher and adaptively weighted Fisher methods in simulations. We subsequentlyextend Fisher ensemble to a variant with emphasized power for concordant effectsize directions. A transcriptomic meta-analysis application confirms thetheoretical and simulation conclusions, generates intriguing biomarker andpathway findings and demonstrates strengths and strategy of using proposedFisher ensemble methods.

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