Joint Modeling of Longitudinal Imaging and Survival Data

AbstractThis article considers a joint modeling framework for simultaneously examining the dynamic pattern of longitudinal and ultrahigh-dimensional images and their effects on the survival of interest. A functional mixed effects model is considered to describe the trajectories of longitudinal images. Then, a high-dimensional functional principal component analysis (HD-FPCA) is adopted to extract the principal eigenimages to reduce the ultrahigh dimensionality of imaging data. Finally, a Cox regression model is used to examine the effects of the longitudinal images and other risk factors on the hazard. A theoretical justification shows that a naive two-stage procedure that separately analyzes each part of the joint model produces biased estimation even if the longitudinal images have no measurement error. We develop a Bayesian joint estimation method coupled with efficient Markov chain Monte Carlo sampling schemes to perform statistical inference for the proposed joint model. A Monte Carlo dynamic prediction procedure is proposed to predict the future survival probabilities of subjects given their historical longitudinal images. The proposed model is assessed through extensive simulation studies and an application to Alzheimer's Disease Neuroimaging Initiative, which turns out to hold the promise of accuracy and possess higher predictive capacity for survival outcome compared with existing methods. Supplementary materials for this article are available online.Keywords: HD-FPCAImaging dataLongitudinal responseMCMC methodsTime-to-event outcome Supplementary MaterialsIn the supplementary material, Appendix 1 describes the preprocessing of MRI data. Appendix 2 provides the likelihood function in (10). Appendix 3 provides the proof of Theorem 1 in Section 3. Appendices 4 and 5 provides additional numerical results in the simulation and ADNI study, respectively.AcknowledgmentsThe authors are thankful to the editor, the associate editor, and two anonymous reviewers for their valuable comments and suggestions, which have helped improve the article substantially.Additional informationFundingThis research was supported by GRF grants (14301918, 14302220) from the Research Grant Council of the Hong Kong Special Administration Region.