Functional Joint Models for Longitudinal and Time-to-Event Data

Kan Li, The University of Texas School of Public Health


In the study of Alzheimer's disease (AD), researchers often collect repeated measurements of clinical variables, neurocognitive assessments (scalar outcomes), neuroimaging (functional outcome), genetic information, and event history to better understand the diseases. Given the lack of disease-modifying treatments for AD, an accurate prediction of the time to AD conversion based on this multimodal information is particularly helpful for physicians to monitor patients' disease progression and to plan timely interventions. We propose a series of novel functional joint models (FJM) to incorporate both scalar outcomes and functional outcomes in the framework of joint modeling of longitudinal and survival data. In the first part of this work, we propose a functional joint model that accounts for time-invariant functional outcomes as predictors in both longitudinal and survival submodels in the joint modeling framework. We develop a Bayesian approach for statistical inference and a personalized dynamic prediction framework that provides an accurate prediction of target patients' future scalar health outcome and risk of AD conversion. In the second part of this work, we extend the model to account for time-variant functional outcome in a Bayesian multivariate joint modeling framework. The proposed functional joint model consists of a longitudinal function-on-scalar submodel, a regular longitudinal submodel, and a survival submodel which allows time-variant functional and scalar predictors. A dynamic prediction approach for predicting the patient's future scalar and functional outcomes, as well as the risk of AD conversion, is also developed. We conduct extensive simulation studies to assess the performance of our proposed methods. The models are applied to the motivating Alzheimer's Disease Neuroimaging Initiative (ADNI) study, suggesting that incorporating the imaging markers as functional predictors into the model could improve the predictive ability. In the third part, we propose a novel framework for the use of multiple longitudinal scalar outcomes and longitudinal high-dimensional functional outcome (e.g., neuroimaging) to further improve the prediction of AD progression. We introduce various functional principal components (FPC) based approaches for dimension reduction and feature extraction on multiple longitudinal outcomes. We use these features as predictors in a Cox proportional hazards model to conduct predictions over time. Such framework is also feasible for a dynamic prediction purpose. Compare to conventional joint modeling approach, the method is computational attractive when there are a large number of longitudinal outcomes and high-dimensional data. Simulation studies and application on ADNI dataset demonstrate the robust performance of the proposed method for prediction under various scenarios.

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Recommended Citation

Li, Kan, "Functional Joint Models for Longitudinal and Time-to-Event Data" (2018). Texas Medical Center Dissertations (via ProQuest). AAI10748657.