Flexible control of the median of the false discovery proportion

TL;DR

This paper presents a new multiple testing procedure that controls the median of the false discovery proportion, offering greater flexibility and validity for finite samples without assuming independence, compared to traditional methods.

Contribution

The authors introduce a median FDP control method that is flexible post hoc and does not assume independence, extending the capabilities of existing procedures like Benjamini-Hochberg.

Findings

Controls median FDP effectively in simulations

Allows flexible alpha selection after data viewing

Operates with linear time complexity

Abstract

We introduce a multiple testing procedure that controls the median of the proportion of false discoveries (FDP) in a flexible way. The procedure only requires a vector of p-values as input and is comparable to the Benjamini-Hochberg method, which controls the mean of the FDP. Our method allows freely choosing one or several values of alpha after seeing the data -- unlike Benjamini-Hochberg, which can be very liberal when alpha is chosen post hoc. We prove these claims and illustrate them with simulations. Our procedure is inspired by a popular estimator of the total number of true hypotheses. We adapt this estimator to provide simultaneously median unbiased estimators of the FDP, valid for finite samples. This simultaneity allows for the claimed flexibility. Our approach does not assume independence. The time complexity of our method is linear in the number of hypotheses, after sorting the p-values.