Bayesian Scalar on Image Regression With Nonignorable Nonresponse

Abstract

Medical imaging has become an increasingly important tool in screening, diagnosis, prognosis, and treatment of various diseases given its information visualization and quantitative assessment. The aim of this article is to develop a Bayesian scalar-on-image regression model to integrate high-dimensional imaging data and clinical data to predict cognitive, behavioral, or emotional outcomes, while allowing for nonignorable missing outcomes. Such a nonignorable nonresponse consideration is motivated by examining the association between baseline characteristics and cognitive abilities for 802 Alzheimer patients enrolled in the Alzheimer’s Disease Neuroimaging Initiative 1 (ADNI1), for which data are partially missing. Ignoring such missing data may distort the accuracy of statistical inference and provoke misleading results. To address this issue, we propose an imaging exponential tilting model to delineate the data missing mechanism and incorporate an instrumental variable to facilitate model identifiability followed by a Bayesian framework with Markov chain Monte Carlo algorithms to conduct statistical inference. This approach is validated in simulation studies where both the finite sample performance and asymptotic properties are evaluated and compared with the model with fully observed data and that with a misspecified ignorable missing mechanism. Our proposed methods are finally carried out on the ADNI1 dataset, which turns out to capture both of those clinical risk factors and imaging regions consistent with the existing literature that exhibits clinical significance.

Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

KEYWORDS:

• Bayesian approach
• Imaging data
• Instrumental variable
• Markov chain Monte Carlo
• Nonignorable nonresponse

Additional information

Funding

Dr. Feng’s work was partially supported by NSFC grants 71802166 and 71490722. Dr. Song’s work was partially supported by GRF grants 14303017 and 14301918 from the Research Grant Council of the Hong Kong Special Administration Region. Dr. Zhu’s work was partially supported by NIH grant MH086633, a grant from the Cancer Prevention Research Institute of Texas, and the endowed Bao-Shan Jing Professorship in Diagnostic Imaging. Dr. Li’s work was partially supported by NIH grant MH116527. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH or any other funding agency.