Abstract: Combining individual p-values to handle large scale inferences or to aggregate results of different studies is one of major interest in meta-analysis which has been traditionally based on independent p-values. In contrast to combining methods that are constructed when p-values are independent, recently proposed combinations of p-values transformed into heavy-tailed distribution are known to be robust to the dependence structure of p-values. In this paper, we investigate theoretical properties of combining p-value methods for different heaviness of transformation under a wider class of correlation structures compared to existing studies from the viewpoint of controlling Type I error and obtaining powers. We also investigate relationships between harmonic mean type combination methods and combining methods that use transformation of p-values into stable distribution including Cauchy and Lévy combination methods. We provide extensive numerical studies supporting theoretical results. We also apply these p-value combining methods to real example of Crohn's disease data and present some idea on how to validate these methods.

Key words and phrases: Cauchy transformation, combining p-values, GWAS, Lévy transformation, meta-analysis.