Optimal and Adaptive p-Value Combination Methods with Application to ALS Exome Sequencing Study

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Statistical theory and methodology play a key role in advancing scientific research. The p-value combination approach is a foundational statistical method for important data-driven research in meta-analysis, data integration, and signal detection. Despite recent theoretical and methodological advances, significant gaps still exist in the literature. Many of the assumptions including independence, Gaussianity, and large group size, are not realistic for real data applications. Further, some methods developed based on ad hoc arguments lack a rigorous study of optimality. This project seeks to develop new methods that exhibit more powerful and robust performance. The methods will be applied to the analysis of large exome sequencing data from a study of amyotrophic lateral sclerosis (ALS). Students from underrepresented groups will be strongly encouraged to participate in this project. The objective of this project is to develop powerful and robust p-value combination tests that are optimal and data-adaptive under a wide spectrum of signal patterns and readily applicable to real data analysis. Analytical calculations for p-value and statistical power, and asymptotic techniques, under realistic assumptions of small or moderate group size, non-Gaussian distribution, dependence, and linear-model-based alternative hypotheses, will be developed. Two statistics families, gGOF for goodness-of-fit type tests, and tFisher for Fisher type p-value combination, will be investigated. In addition to a study of power and optimality, the project will also develop omnibus tests for adapting to unknown signal patterns. The project will lead to (1) a new statistical framework for calculating the distributions of generic families of goodness-of-fit type and Fisher type statistics, (2) optimal statistics for given signal patterns as well as data-adaptive methods when patterns are unknown, and (3) genetic association test strategies for detecting genetic effects.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.