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

统计理论和方法在推进科学研究中发挥着关键作用。p值组合方法是元分析、数据整合和信号检测中重要数据驱动研究的基础统计方法。 尽管最近的理论和方法的进步，显着的差距仍然存在的文献。 许多假设，包括独立性，高斯性和大的组大小，是不现实的真实的数据应用程序。 此外，一些基于特别论点开发的方法缺乏对最优性的严格研究。 该项目旨在开发具有更强大和更强大性能的新方法。 该方法将被应用于肌萎缩侧索硬化症（ALS）研究的大外显子组测序数据的分析。 将大力鼓励代表性不足群体的学生参加这一项目。该项目的目标是开发强大而强大的p值组合测试，这些测试在广泛的信号模式下是最佳的和数据自适应的，并且容易适用于真实的数据分析。 将在小或中等组规模、非高斯分布、依赖性和基于线性模型的替代假设的现实假设下，开发p值和统计功效的分析计算以及渐近技术。 将研究两个统计系列，gGOF用于拟合优度类型检验，tFisher用于Fisher型p值组合。 除了研究功率和最优性之外，该项目还将开发综合测试，以适应未知的信号模式。 该项目将导致（1）一个新的统计框架，用于计算拟合优度型和Fisher型统计的一般族的分布，（2）给定信号模式的最佳统计以及模式未知时的数据自适应方法，以及（3）该奖项反映了NSF的法定使命，并被认为是值得支持的，使用基金会的知识价值和更广泛的影响审查标准进行评估。

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.