Efficient estimation via envelope chain in magnetic resonance imaging-based studies

Lan Liu, Wei Li, Zhihua Su, Dennis Cook, Luca Vizioli, Essa Yacoub

Research output: Contribution to journalArticlepeer-review


Magnetic resonance imaging (MRI) is a technique that scans the anatomical structure of the brain, whereas functional magnetic resonance imaging (fMRI) uses the same basic principles of atomic physics as MRI scans but image metabolic function. A major goal of MRI and fMRI study is to precisely delineate various types of tissues, anatomical structure, pathologies, and detect the brain regions that react to outer stimuli (e.g., viewing an image). As a key feature of these MRI-based neuroimaging data, voxels (cubic pixels of the brain volume) are highly correlated. However, the associations between voxels are often overlooked in the statistical analysis. We adapt a recently proposed dimension reduction method called the envelope method to analyze neuoimaging data taking into account correlation among voxels. We refer to the modified procedure the envelope chain procedure. Because the envelope chain procedure has not been employed before, we demonstrate in simulations the empirical performance of estimator, and examine its sensitivity when our assumptions are violated. We use the estimator to analyze the MRI data from ADHD-200 study. Data analyses demonstrate that leveraging the correlations among voxels can significantly increase the efficiency of the regression analysis, thus achieving higher detection power with small sample sizes.

Original languageEnglish (US)
JournalScandinavian Journal of Statistics
StateAccepted/In press - 2021

Bibliographical note

Funding Information:
We sincerely thank the editor, associate editor, and reviewers for their helpful and insightful comments. Professor Essa Yacoub is supported by NIH P41 EB015894. Lan Liu is supported by Grant‐in‐aid at the University of Minnesota at Twin Cities and NSF DMS 1916013. Wei Li is supported by the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China. The authors want to thank the audience at the Department of Biostatistics at the University of Pennsylvania, the Department of Statistics at Peking University for insightful comments and suggestions. The authors also express special thanks to Prof. Lexin Li and Prof. Joerg Polzehl for their tremendous help, patience and suggestions in the data processing procedure. The content is solely the responsibility of the authors.

Funding Information:
NIH, P41 EB015894; NSF, DMS 1916013; the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China Funding information

Publisher Copyright:
© 2021 Board of the Foundation of the Scandinavian Journal of Statistics.


  • efficiency gain
  • envelope method
  • neuroimaging
  • sufficient dimension reduction

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