Abstract:
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Combining p-values to aggregate multiple small effects is a long-standing statistical topic. In recent years, advances in big data analysis promoted methods to aggregate correlated, sparse, and weak signals. Under such context, we investigate a family of p-value combination methods, formulated as the sum of transformed p-values with the transformations by a broad family of heavy-tailed distributions, namely regularly varying distributions. We explore the conditions for a method of the family to possess robustness to dependency for type I error control and optimal power in terms of detection boundary for detecting weak and sparse signals. We show that only an equivalent class of the Cauchy and harmonic mean tests has sufficient robustness to dependency in a practical sense. We also propose an improved truncated Cauchy method, which belongs to the equivalent class with fast computation, to address the issue caused by the large negative penalty in the Cauchy method. Finally, We present comprehensive simulations and a neuroticism GWAS application to verify our theoretical findings, provide a recommendation to real practice, and demonstrate the advantages of the truncated Cauchy method.
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