Dynamic Survival Prediction Using Sparse Longitudinal Images via Multi-Dimensional Functional Principal Component Analysis

Abstract

Our work is motivated by predicting the progression of Alzheimer’s disease (AD) based on a series of longitudinally observed brain scan images. Existing works on dynamic prediction for AD focus primarily on extracting predictive information from multivariate longitudinal biomarker values or brain imaging data at the baseline; whereas in practice, the subject’s brain scan image represented by a multi-dimensional data matrix is collected at each follow-up visit. It is of great interest to predict the progression of AD directly from a series of longitudinally observed images. We propose a novel multi-dimensional functional principal component analysis based on alternating regression on tensor-product B-spline, which circumvents the computational difficulty of doing eigendecomposition, and offers the flexibility of accommodating sparsely and irregularly observed image series. We then use the functional principal component scores as features in the Cox proportional hazards model. We further develop a dynamic prediction framework to provide a personalized prediction that can be updated as new images are collected. Our method extracts visibly interpretable images of the functional principal components and offers an accurate prediction of the conversion to AD. We examine the effectiveness of our method via simulation studies and illustrate its application on the Alzheimer’s Disease Neuroimaging Initiative data. Supplementary materials for this article are available online.

KEYWORDS:

• Dynamic prediction
• Eigendecomposition
• Functional data analysis
• Functional principal component analysis
• Multi-dimensional process

Supplementary Materials

Supplementary Document:

The supplementary document includes the estimation details for the mean function and the additional results of simulation studies.

Acknowledgments

The authors thank the editor, the associate editor and two anonymous referees for many insightful comments. These comments are very helpful for us to improve our work.

Disclosure Statement

No potential competing interest was reported by the authors.

Additional information

Funding

Dr. Cao’s research is supported by the Discovery grant (RGPIN-2023-04057) from the Natural Sciences and Engineering Research Council of Canada (NSERC). Dr. Shi’s research is supported by the Discovery grant from NSERC (RGPIN-2021-02963).