Hierarchical correction of p-values via an ultrametric tree running Ornstein-Uhlenbeck process

TL;DR

This paper introduces a hierarchical p-value correction method using an Ornstein-Uhlenbeck process on a tree structure, improving detection of associations in dependent tests, demonstrated through simulations and a metagenomic dataset.

Contribution

It presents a novel hierarchical p-value correction technique based on an Ornstein-Uhlenbeck process, incorporating dependence structure for improved multiple testing correction.

Findings

Enhanced ability to discover new associations in dependent tests

Effective smoothing of p-values using the Ornstein-Uhlenbeck process

Validated performance through simulations and real data analysis

Abstract

Statistical testing is classically used as an exploratory tool to search for association between a phenotype and many possible explanatory variables. This approach often leads to multiple testing under dependence. We assume a hierarchical structure between tests via an Ornstein-Uhlenbeck process on a tree. The process correlation structure is used for smoothing the p-values. We design a penalized estimation of the mean of the Ornstein-Uhlenbeck process for p-value computation. The performances of the algorithm are assessed via simulations. Its ability to discover new associations is demonstrated on a metagenomic dataset. The corresponding R package is available from https://github.com/abichat/zazou.