Summary: Analysing data from large-scale, multiexperiment studies requires scientists to both analyse each experiment and to assess the results as a whole. In this article, we develop double empirical Bayes testing (DEBT), an empirical Bayes method for analysing multiexperiment studies when many covariates are gathered per experiment. DEBT is a two-stage method: in the first stage, it reports which experiments yielded significant outcomes and in the second stage, it hypothesises which covariates drive the experimental significance. In both of its stages, DEBT builds on the work of Efron, who laid out an elegant empirical Bayes approach to testing. DEBT enhances this framework by learning a series of black box predictive models to boost power and control the false discovery rate. In Stage 1, it uses a deep neural network prior to report which experiments yielded significant outcomes. In Stage 2, it uses an empirical Bayes version of the knockoff filter to select covariates that have significant predictive power of Stage 1 significance. In both simulated and real data, DEBT increases the proportion of discovered significant outcomes and selects more features when signals are weak. In a real study of cancer cell lines, DEBT selects a robust set of biologically plausible genomic drivers of drug sensitivity and resistance in cancer.
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