Approximation methods for global hypothesis testing with discrete and non independent p-values

Music City Center 

Mathematically sound and straightforward and computationally inexpensive methods for combining continuous and independent p-values are the building block of global hypothesis testing, with the seminal work of Tukey, Fisher, Pearson, among others, still being widely applied by practitioners almost a century after their initial proposal. Discrete and/or dependent p-values, on the other hand, present a wide arrange of mathematical issues that make their mathematical modelling less straightforward, with contemporary proposals like the Cauchy Combination Statistic, the Gfisher statistic and the Wasserstein projection method having adressed either of these issues separately. This presentation proposes a bridge between the Cauchy Combination Statistic and the closest-to-continuous Wasserstein projection that allows for combining discrete and exchangeable p-values with accurately asymptotic type I error control. Statistical power and further mathematical properties are demonstrated via extensive simulation studies, with particular focus on contingency table data spanning from highly unbalanced case-control studies.

Global hypotesis testing

Approximation Theory

Cauchy Combination Statistic

Discrete and dependent p-values

Wasserstein Metric

Case-control studies 

IMS