Choosing methods of approximating and combining discrete p-values: an optimal transport approach

Oregon Convention Center 

Combining p-values in meta-analysis is a popular method when test data are unavailable or challenging to merge into a global significance. A variety of methods with different statistical properties exist in the continuous case (when the null distribution of the p-value is uniform). Heard and Delanchy (2018) reframed each method as a likelihood ratio test, guiding the selection of a most powerful combiner for a specific alternative. Discrete p-values present additional challenges, as their null distribution varies significantly, making the distribution of each combiner intractable. We first present a testing framework based on a Wasserstein-closest modification of a p-value towards a target distribution, show that under very mild conditions it produces asymptotically consistent tests. We present the closed form approximation statistics for common methods (Fisher, Pearson, Edgington, Stouffer, George) and presenting the optimal choice of a most powerful discrete combiner in many alternative hypothesis settings, presenting some applications in public health, weak and sparse signal detection, and genetic and genomic association tests.

p-value combination

Meta-Analysis

Stouffer's Method

Edgington’s method

Fisher’s method

George’s method 

Section on Statistical Computing