MMCTest - A Safe Algorithm for Implementing Multiple Monte Carlo Tests

TL;DR

MMCTest is a sequential algorithm that safely implements multiple hypothesis tests using simulation, providing high-probability correctness and efficiency, applicable to procedures like FDR and Bonferroni.

Contribution

Introduces MMCTest, a novel sequential method for multiple testing with simulation, ensuring high-probability correctness and computational efficiency.

Findings

Effective in biological data scenarios

Computationally more efficient than existing methods

Provides reliable decision sets at any interruption point

Abstract

Consider testing multiple hypotheses using tests that can only be evaluated by simulation, such as permutation tests or bootstrap tests. This article introduces MMCTest, a sequential algorithm which gives, with arbitrarily high probability, the same classification as a specific multiple testing procedure applied to ideal p-values. The method can be used with a class of multiple testing procedures which includes the Benjamini & Hochberg False Discovery Rate (FDR) procedure and the Bonferroni correction controlling the Familywise Error Rate. One of the key features of the algorithm is that it stops sampling for all the hypotheses which can already be decided as being rejected or non-rejected. MMCTest can be interrupted at any stage and then returns three sets of hypotheses: the rejected, the non-rejected and the undecided hypotheses. A simulation study motivated by actual biological data shows that MMCTest is usable in practice and that, despite the additional guarantee, it can be computationally more efficient than other methods.