2025/08/04 by Gonzalo Contador, Zheyang Wu, Contador, Gonzalo +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #Advanced Causal Inference Techniques #FOS: Computer and information sciences #FOS: Mathematics #Genetic Associations and Epidemiology #Methodology (stat.ME) #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2508.02647
openalex publication_date 2025/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Combining p-values from multiple independent tests is a fundamental task in statistical inference, but presents unique challenges when the p-values are discrete. We extend a recent optimal transport-based framework for combining discrete p-values, which constructs a continuous surrogate distribution by minimizing the Wasserstein distance between the transformed discrete null and its continuous analogue. We provide a unified approach for several classical combination methods, including Fisher's, Pearson's, George's, Stouffer's, and Edgington's statistics. Our theoretical analysis and extensive simulations show that accurate Type I error control is achieved when the variance of the adjusted discrete statistic closely matches that of the continuous case. We further demonstrate that, when the likelihood ratio test is a monotonic function of a combination statistic, the proposed approximation achieves power comparable to the uniformly most powerful (UMP) test. The methodology is illustrated with a genetic association study of rare variants using case-control data, and is implemented in the R package DPComb.