Combining Partial True Discovery Guarantee Procedures

Closed testing has recently been shown to be optimal for simultaneous true discovery proportion control. It is, however, challenging to construct true discovery guarantee procedures in such a way that it focuses power on some feature sets chosen by users based on their specific interest or expertise. We propose a procedure that allows users to target power on prespecified feature sets, that is, "focus sets." Still, the method also allows inference for feature sets chosen post hoc, that is, "nonfocus sets," for which we deduce a true discovery lower confidence bound by interpolation. Our procedure is built from partial true discovery guarantee procedures combined with Holm's procedure and is a conservative shortcut to the closed testing procedure. A simulation study confirms that the statistical power of our method is relatively high for focus sets, at the cost of power for nonfocus sets, as desired. In addition, we investigate its power property for sets with specific structures, for example, trees and directed acyclic graphs. We also compare our method with AdaFilter in the context of replicability analysis. The application of our method is illustrated with a gene ontology analysis in gene expression data.