Combining P-values Using Heavy Tailed Distributions and Their Asymptotic Results with Applications to Genomic Data
Junsik Kim, Junyong Park · Statistica Sinica · 2023
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 view point 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.