Get started
Work

Covariate powered cross-weighted multiple testing with false discovery rate control

Year: 2017
Type: preprint
Abstract: Consider a large-scale multiple testing setup where we observe pairs $((P_i, X_i))_{1\leq i \leq m}$ of p-values $P_i$ and covariates $X_i$, such that $P_i \perp X_i$ under the null hypothesis. Our goal is to use the information potentially available in the covariates about heterogeneities among hypotheses to increase power compared to conventional procedures that only use the $P_i$, while still controlling the false discovery rate (FDR). To this end, we recently introduced independent hypothesis weighting (IHW), a weighted variant of the Benjamini-Hochberg method, in which the weights are chosen in a data-driven manner as a function of the covariate $X_i$. We showed empirically that IHW leads to a large power increase, while asymptotically controlling the FDR. In this paper, we provide a rigorous statistical framework for understanding IHW: its asymptotic characteristics are viewed through the lens of the conditional two-groups model, while favorable finite-sample properties are achieved by cross-weighting, a novel data-splitting approach that enables learning the weight-covariate function without overfitting. We provide results on finite sample behavior of IHW and of IHW-Bonferroni, its adaptation to the family-wise error rate (FWER). These results are valid as long as the hypotheses can be partitioned into independent folds, with arbitrary within-fold dependence. Furthermore, under full independence, we prove finite sample FDR control for IHWc, a slightly modified variant of IHW. A key implication of IHW is that hypothesis rejection in heterogeneous multiple testing setups should not proceed according to the ranking implied by the p-values; the covariate-weighted p-values instead provide a more informative ranking.
Language: English
Open Access status: green
OpenAlex ID: W2582162679
Cites:
Cited by: 9
Related to: 10