Cardiovascular diseases are major causes of mortality globally. They often co-occur and are interrelated, leading to partial-order relationships among their onset times. However, these onset times are subject to informative censoring due to the occurrence of death, posing significant challenges for survival prediction. In this article, we propose a novel copula-based framework that learns dependence among multiple correlated marginal components through a pseudo-likelihood for estimation. We adopt nonparametric marginals, alleviating the reliance on marginal distribution assumptions typically required in conventional copula models, and estimate the association between the onsets of intermediate cardiovascular diseases and death by solving a concordance estimating equation. Under this framework, a renewable risk assessment method is developed for dynamic survival prediction, leveraging information on disease onset times and the maximum follow-up duration. Our proposed method yields estimators with well-established properties, and its flexibility and predictive effectiveness are demonstrated through extensive simulation studies. We apply the method to data from a heart disease study, demonstrating the benefits of incorporating the associations among various cardiovascular diseases and their synergistic effects on mortality for dynamic prediction of overall survival.

翻译：心血管疾病是导致全球死亡率的主要原因。这类疾病常伴随发生且相互关联，导致其发病时间存在偏序关系。然而，由于死亡事件的发生，这些发病时间会受信息性删失影响，给生存预测带来重大挑战。本文提出一种基于Copula的新型框架，通过伪似然估计方法学习多个相关边际成分间的依赖关系。我们采用非参数边际分布，突破了传统Copula模型对边际分布假设的依赖性，并通过求解一致性估计方程来评估中间心血管疾病发病与死亡之间的关联性。基于该框架，我们开发了一种用于动态生存预测的可更新风险评估方法，充分利用疾病发病时间与最长随访时长的信息。所提方法具有优良的估计量性质，并通过大量模拟研究验证了其灵活性与预测有效性。我们将该方法应用于一项心脏病研究数据，结果表明整合多种心血管疾病间的关联性及其对死亡的协同效应，能显著提升总体生存动态预测效果。