Statistical Inferences for Complex Dependence of Multimodal Imaging Data

Abstract

Statistical analysis of multimodal imaging data is a challenging task, since the data involves high-dimensionality, strong spatial correlations and complex data structures. In this article, we propose rigorous statistical testing procedures for making inferences on the complex dependence of multimodal imaging data. Motivated by the analysis of multi-task fMRI data in the Human Connectome Project (HCP) study, we particularly address three hypothesis testing problems: (a) testing independence among imaging modalities over brain regions, (b) testing independence between brain regions within imaging modalities, and (c) testing independence between brain regions across different modalities. Considering a general form for all the three tests, we develop a global testing procedure and a multiple testing procedure controlling the false discovery rate. We study theoretical properties of the proposed tests and develop a computationally efficient distributed algorithm. The proposed methods and theory are general and relevant for many statistical problems of testing independence structure among the components of high-dimensional random vectors with arbitrary dependence structures. We also illustrate our proposed methods via extensive simulations and analysis of five task fMRI contrast maps in the HCP study. Supplementary materials for this article are available online.

KEYWORDS:

• FDR control
• High-dimensional inference
• Independence test
• Multimodal neuroimaging

Supplementary Materials

The supplementary material contains additional simulation results, additional details in analysis of HCP data and proofs of the main results in the article.

Acknowledgments

We are grateful to the editor, the associate editor and three referees for their constructive comments and suggestions.

Additional information

Funding

Chang, He and Wu were supported in part by the National Natural Science Foundation of China (grant nos. 71991472, 72125008, 11871401, and 11701466). Chang was also supported by the Center of Statistical Research at Southwestern University of Finance and Economics. Kang was supported in part by NIH R01DA048993, NIH R01MH105561, NIH R01GM124061, and NSF IIS2123777.