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

ABSTRACT

In many genomic applications, hypotheses tests are performed for powerful identification of signals by aggregating test-statistics across units within naturally defined classes. 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. Supplementary materials for this article are available online.

KEYWORDS:

• Conditional p-value
• False discovery rate
• Multiple testing
• Selective inference

Supplementary Material

In the supplementary materials, we provide additional theoretical results under dependence, as well as for overall error control. We also present additional simulation results and details about the cross-tissue eQTL analysis.

Acknowledgment

This work was initiated while Ruth Heller was a visiting scholar at the National Cancer Institute. The authors gratefully acknowledge Yoav Benjmaini, Marina Bogomolov, the editor, associate editor, and the anonymous reviewers, for their constructive comments that helped us improve the article substantially.

Additional information

Funding

Study supported by the National Cancer Institute Intramural Research Program. Ruth Heller acknowledges support by Israel Science Foundation grant no. 1049/16.