Title: Further Results on Controlling the False Discovery Rate Under Some Complex Grouping Structure of Hypotheses

Abstract: Modern studies from large datasets often produce massive amounts of hypotheses that exhibit complex group structures. We consider three different classification settings of the hypotheses into groups – (a) hierarchical classification, (b) simultaneous multi-way classification, and a combination of (a) and (b). The aim of this research is to introduce false discovery rate (FDR) controlling methods for testing multiple hypotheses under such different classification settings. The methods are developed in their oracle forms as special cases of a weighted version of the Benjamini-Hochberg (BH, 1995) method, with the weights encoding the underlying structural information about the hypotheses. Each of them controls the FDR when the p-values involved are Positively Regression Dependent on the Subset (PRDS) of null p-values, and are more powerful than the BH procedure. Data-adaptive versions of these methods are also proposed by appropriately estimating the weights under the different types of classification. The proposed data-adaptive methods control the FDR at the desired level when the p-values are independent and, as simulations show, they can be more powerful FDR controlling methods, even under certain dependencies, than some existing comparable multiple testing methods. We apply the data-adaptive method under the above-mentioned combined classification setting to analyze a publicly available neuro-imaging dataset. Such data typically have complex classification structures that were not addressed in previously available multiple testing methods, as far as we know.