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Title: Optimal and adaptive P-value combination methods Authors:  Zheyang Wu - Worcester Polytechnic Institute (United States) [presenting]
Abstract: P-value combination is an important statistical approach for information-aggregated decision making. It is foundational to a lot of applications such as meta-analysis, data integration, signal detection, and others. We propose two generic statistic families for combining p-values: gGOF, a general family of goodness-of-fit type statistics, and tFisher, a family of Fisher type p-value combination with a general weighting-and-truncation scheme. The two families unify many optimal statistics over a wide spectrum of signal patterns, including both sparse and dense signals. We provide efficient solutions for analytical calculations of p-value and statistical power, as well as studies of asymptotic efficiencies, while emphasizing the conditions of realistic data analysis: small or moderate group size, Gaussian and non-Gaussian distributions, correlated data, generalized linear model based alternative hypotheses, etc. Based on these two families of statistics, omnibus tests are also designed for adapting the family-retained advantages to unknown signal patterns. Applications of these methods are illustrated in analyses of large-scale omics data.