Simultaneous Covariance Inference for Multimodal Integrative Analysis

Abstract

Multimodal integrative analysis fuses different types of data collected on the same set of experimental subjects. It is becoming a norm in many branches of scientific research, such as multi-omics and multimodal neuroimaging analysis. In this article, we address the problem of simultaneous covariance inference of associations between multiple modalities, which is of a vital interest in multimodal integrative analysis. Recognizing that there are few readily available solutions in the literature for this type of problem, we develop a new simultaneous testing procedure. It provides an explicit quantification of statistical significance, a much improved detection power, as well as a rigid false discovery control. Our proposal makes novel and useful contributions from both the scientific perspective and the statistical methodological perspective. We demonstrate the efficacy of the new method through both simulations and a multimodal positron emission tomography study of associations between two hallmark pathological proteins of Alzheimer’s disease.

Key Words:

• Extreme value distribution
• False discovery control
• Minimax rate optimality
• Multimodal integrative analysis
• Multiple testing
• Positron emission tomography

Supplementary Materials

In the supplementary materials, we present additional simulation results, a collection of technical lemmas, and the proofs of the theorems in the article.

Acknowledgment

The authors thank the Editor, theAssociate Editor, and two referees for their constructive comments.

Additional information

Funding

Xia’s research was partially supported by NSFC grants 11771094, 11690013 and The Recruitment Program of Global Experts Youth Project. Li’s research was partially supported by NSF grant DMS-1613137 and NIH grants R01AG034570 and R01AG061303. Lockhart’s research was partially supported by NIH grant P30AG049638. Jagust’s research was partially supported by NIH grants R01AG034570 and R01AG061303.