New results for adaptive false discovery rate control with p-value weighting

The prior information regarding the truth or falsehood of a hypothesis is expressed with random p-value weights. We find that the weighted Benjamini-Hochberg procedure is conservative in controlling the false discovery rate (FDR). Also, the power of the procedure can be improved by plugging in a suitable estimate of the product of the proportion of true null hypotheses and the mean weight of the true null hypotheses to the thresholds. We propose two such estimates and theoretically prove that the resulting adaptive multiple testing procedures control the FDR. However, for two other model-based estimates, the control over false discovery rate of the adaptive procedures is verified through simulation experiments. We also incorporate random p-value weights to an adaptive one-stage step-up procedure, and prove its control over the FDR. The p-value weighted multiple testing procedures lead to the improvement of power of the unweighted procedures when the assignment of weights is positively associated with the falsehood of the hypotheses. Extensive simulation studies are performed to evaluate the performances of the proposed multiple testing procedures. Finally, the proposed procedures are illustrated using a real life data set.