Large-scale multiple testing via multivariate hidden Markov models

Abstract

Large-scale multiple testing with correlated tests and auxiliary statistics arises in a wide range of scientific fields. Conventional multiple testing procedures largely ignored auxiliary information, such as sparsity information, and the dependence structure among tests. This may result in loss of testing efficiency. In this paper, we propose a procedure, called multivariate local index of significance (mvLIS) procedure, for large-scale multiple testing. The mvLIS procedure can not only characterize local correlations among tests via a Markov chain but also incorporates auxiliary information via multivariate statistics. We present that the oracle mvLIS procedure is valid, namely, it controls false discovery rate (FDR) at the pre-specified level, and show that it yields the smallest false non-discovery rate (FNR) at the same FDR level. Then a data-driven mvLIS procedure is developed to mimic the oracle procedure. Comprehensive simulation studies and a real data analysis of schizophrenia (SCZ) data are performed to illustrate the superior performance of the mvLIS procedure. Moreover, as a byproduct that is of independent interest, we generalize the single-index modulated (SIM) multiple testing procedure, which embeds prior information via 2-dimensional p-values, to allow for d-dimensional ($d\ge 3$) statistics in multiple testing. The detailed extension is deferred to Discussion.

Keywords:

• False discovery rate
• Multivariate hidden Markov models
• Multiple testing

Acknowledgment

The authors are grateful to the editor, the associate editor, and the reviewer for their insightful comments that helped us greatly improve the quality of this article.

Data availability statement

The data that support the findings of this study are available from the Psychiatric Genetics Consortium (PGC). Restrictions apply to the availability of these data, which were used under license for this study. Data are available at https://www.med.unc.edu/pgc/download-results/scz/ with the permission of the PGC.

Additional information

Funding

P. F. Wang was partially supported by the Department of Education of Liaoning Province Grant (No. LN2020Q23) and Z. Q. Hou was partially supported by NSFC (No. 12101359).