HEAVY-TAILED DISTRIBUTION FOR COMBINING DEPENDENT p-VALUES WITH ASYMPTOTIC ROBUSTNESS

In statistics, researchers sometimes combine individual p-values to aggregate multiple small effects. Recent advances in big data analysis have led to methods that aggregate correlated, sparse, and weak signals. In this context, we investigate a wide range of p-value combination methods, formulated as the sum of p-values that are transformed using a broad family of heavy-tailed distributions, namely, regularly varying distributions. Here, we also include the Cauchy and harmonic mean tests. We explore the conditions under which a method of the family is robust to dependency for type-I error control and possesses optimal power in terms of the boundary used to detect weak and sparse signals. We show that only an equivalent class of Cauchy and harmonic mean tests has sufficient robustness to dependency, in a practical sense. We also propose an improved truncated Cauchy method that belongs to the equivalent class with fast computation to address the problem caused by the large negative penalty in the Cauchy method. We use comprehensive simulations to verify our theoretical insights and provide practical recommendations. Finally, we apply the truncated Cauchy method to data from a neuroticism genome-wide association study to illustrate our theoretical findings in the regularly varying distribution family and the advantages of the method.