Joint Modeling of Longitudinal Imaging and Survival Data

This 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.本文构建了一种联合建模框架，用于同时分析纵向超高维影像的动态变化模式，及其对目标生存结局的影响。本文采用功能混合效应模型（functional mixed effects model）刻画纵向影像的变化轨迹。随后，采用高维功能主成分分析（high-dimensional functional principal component analysis, HD-FPCA）提取主特征影像，以降低影像数据的超高维度。最后，构建Cox回归模型，分析纵向影像与其他风险因素对风险率的影响。理论推导表明，即便纵向影像不存在测量误差，仅对联合模型各部分单独分析的简单两阶段方法仍会产生有偏估计。为此，本文提出一种贝叶斯联合估计方法，结合高效的马尔可夫链蒙特卡罗（Markov chain Monte Carlo, MCMC）抽样策略，对所提出的联合模型开展统计推断。本文还提出一种蒙特卡洛动态预测方法，基于受试者的历史纵向影像预测其未来生存概率。通过大量模拟实验与阿尔茨海默病神经影像倡议（Alzheimer’s Disease Neuroimaging Initiative, ADNI）的真实数据应用，对所提模型进行了评估。结果表明，相较于现有方法，该模型具备更高的预测准确性与生存结局预测能力。本文的补充材料可在线获取。