Multiple testing in genome-wide association studies via hierarchical hidden Markov models

Abstract

Problems of large-scale multiple testing are often encountered in modern scientific research. Conventional multiple testing procedures usually suffer considerable loss of testing efficiency when correlations among tests are ignored. In fact, appropriate use of correlation information not only enhances the efficacy of the testing procedure, but also improves the interpretability of the results. Since the disease- or trait-related single nucleotide polymorphisms (SNPs) tend to be clustered and exhibit serial correlations, hidden Markov model (HMM) based multiple testing procedures have been successfully applied in genome-wide association studies (GWAS). However, modeling the entire chromosome using a single HMM is somewhat rough. To overcome this issue, this paper employs the hierarchical hidden Markov model (HHMM) to describe local correlations among tests, and develops a multiple testing procedure that can automatically divide different class of chromosome regions, while taking into account local correlations among tests. We first propose an oracle procedure that is shown theoretically to be valid, and in fact optimal in some sense. We then develop a date-driven procedure to mimic the oracle version. Extensive simulations and a real data example show that the novel multiple testing procedure outperforms its competitors.