Abstract:
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A usual strategy for multiple testing involves thresholding p-values. Ordered hypothesis testing procedures are multiple testing procedures which exploit a pre-specified ordering of the null hypotheses, from most to least promising. We propose a class of ordered testing procedures, called Adaptive P-values Thresholding (AdaPT), which takes the prior domain knowledge into account. We prove the exact false discovery rate (FDR) control of AdaPT based on martingale theory and analyze and compare the power of AdaPT as well as several recent proposals using the asymptotic framework of Li & Barber (2015). Then we discuss a special case, called adaptive SeqStep, as a generalization of selective SeqStep, proposed by Barber & Candes (2015). Our theoretical results show that accumulation tests including ForwardStop can be quite powerful when the ordering is very informative, they are asymptotically powerless when the ordering is weaker. On contrast, adaptive SeqStep is much more robust to the quality of the ordering and is always more powerful than selective SeqStep. We apply the procedure to GEOquery data (Davis & Meltzer, 2007) and obtain significantly more rejections than other methods.
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