AdaPT: an interactive procedure for multiple testing with side information

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2018 · Volume 80 · Issue 4

Abstract

We consider the problem of multiple-hypothesis testing with generic side information: for each hypothesiswe observe both ap-valuepiand some predictorxiencoding contextual information about the hypothesis. For large-scale problems, adaptively focusing power on the more promising hypotheses (those more likely to yield discoveries) can lead to much more powerful multiple-testing procedures. We propose a general iterative framework for this problem, the adaptivep-value thresholding procedure which we call AdaPT, which adaptively estimates a Bayes optimalp-value rejection threshold and controls the false discovery rate in finite samples. At each iteration of the procedure, the analyst proposes a rejection threshold and observes partially censoredp-values, estimates the false discovery proportion below the threshold and proposes another threshold, until the estimated false discovery proportion is belowα. Our procedure is adaptive in an unusually strong sense, permitting the analyst to use any statistical or machine learning method she chooses to estimate the optimal threshold, and to switch between different models at each iteration as information accrues. We demonstrate the favourable performance of AdaPT by comparing it with state of the art methods in five real applications and two simulation studies.

Keywords

Adaptive inference, False discovery rate, Martingales, Multiple testing, p-value weighting, Selective inference

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