  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.
