Post-selection Inference Following Aggregate Level Hypothesis Testing in Large Scale Genomic Data

In many genomic applications, hypotheses tests are performed by aggregating test-statistics across units within naturally defined classes for powerful identification of signals. Following class-level testing, it is naturally of interest to identify the lower level units which contain true signals. Testing the individual units within a class without taking into account the fact that the class was selected using an aggregate-level test-statistic, will produce biased inference. We develop a hypothesis testing framework that guarantees control for false positive rates conditional on the fact that the class was selected. Specifically, we develop procedures for calculating unit level p-values that allows rejection of null hypotheses controlling for two types of conditional error rates, one relating to family wise rate and the other relating to false discovery rate. We use simulation studies to illustrate validity and power of the proposed procedure in comparison to several possible alternatives. We illustrate the power of the method in a natural application involving whole-genome expression quantitative trait loci (eQTL) analysis across 17 tissue types using data from The Cancer Genome Atlas (TCGA) Project.