Abstract

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.

摘要

本文考虑了一种联合建模框架，用于同时检查纵向和超高维图像的动态模式及其对兴趣生存的影响。考虑使用功能混合效应模型来描述纵向图像的轨迹。然后，采用高维函数主成分分析（HD-FPCA）提取主特征图像，以降低成像数据的超高维数。最后，使用Cox回归模型来检查纵向图像和其他风险因素对危险的影响。理论论证表明，即使纵向图像没有测量误差，单独分析联合模型每个部分的简单两阶段程序也会产生偏差估计。我们开发了一种贝叶斯联合估计方法，结合有效的马尔可夫链蒙特卡罗采样方案，对所提出的联合模型进行统计推断。提出了蒙特卡罗动态预测程序来预测给定历史纵向图像的受试者的未来生存概率。所提出的模型通过广泛的模拟研究和阿尔茨海默氏病神经影像计划的应用进行了评估，事实证明，与现有方法相比，该模型具有准确性的承诺，并且具有更高的生存结果预测能力。本文的补充材料可在线获取。提出了蒙特卡罗动态预测程序来预测给定历史纵向图像的受试者的未来生存概率。所提出的模型通过广泛的模拟研究和阿尔茨海默氏病神经影像计划的应用进行了评估，事实证明，与现有方法相比，该模型具有准确性的承诺，并且具有更高的生存结果预测能力。本文的补充材料可在线获取。提出了蒙特卡罗动态预测程序来预测给定历史纵向图像的受试者的未来生存概率。所提出的模型通过广泛的模拟研究和阿尔茨海默氏病神经影像计划的应用进行了评估，事实证明，与现有方法相比，该模型具有准确性的承诺，并且具有更高的生存结果预测能力。本文的补充材料可在线获取。