Package: DPComb 1.0

DPComb: Discrete p-Value Combination Tests

Provides tools for performing p-value combination tests with discrete input p-values. These tests combine significance evidence derived from independent discrete statistics to test a global null hypothesis, which is defined by the specified null distribution(s) of these discrete statistics. The testing procedure involves two main steps: (1) Wasserstein Adjustment: Each component of the combination statistic is replaced by an adjusted Z statistic. This adjustment, based on the minimum Wasserstein distance, preserves the discrete nature of the original statistics while better aligning them with their counterparts under continuity. (2) Calculation of the Significance of the Combination Statistic: A continuous distribution that optimally matches the discrete distribution of the combination statistic is obtained, and the testing p-value for the global null hypothesis is computed. The first step is analogous to Lancaster's approach but is generalized based on Wasserstein optimization. The second step allows for asymptotic control of Type I error with higher statistical power. The package implements several p-value combination methods, including Fisher’s, Pearson’s, George’s, Stouffer’s, and Edgington’s methods. The individual tests to be combined can be right-sided, left-sided, or two-sided, and can be based on binomial, Poisson, hypergeometric, noncentral hypergeometric, negative binomial, or geometric distributions, or a mixture of them. The underlying methodology and its foundations are described in the following references: Contador, Gonzalo and Wu, Zheyang (2025). A minimum Wasserstein distance approach to Fisher's combination of independent, discrete p-values. Scandinavian Journal of Statistics, 52(3), 1281-1300. <doi:10.1111/sjos.12787> Contador, Gonzalo and Wu, Zheyang (2026). Optimal Adjustment and Combination of Independent Discrete p-Values. Under revision at the Journal of Computational and Graphical Statistics. <doi:10.48550/arXiv.2508.02647> Lancaster, HO (1949). The combination of probabilities arising from data in discrete distributions. Biometrika, 36(3/4), 370-382. <doi:10.1093/biomet/36.3-4.370>.

Authors:Gonzalo Contador [aut, cre], Shuaichuan Feng [aut], Zheyang Wu [aut]