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.

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