In medical studies, time-to-event outcomes such as time to death or relapse of a disease are routinely recorded along with longitudinal data that are observed intermittently during the follow-up period. For various reasons, marginal approaches to model the event time, corresponding to separate approaches for survival data/longitudinal data, tend to induce bias and lose efficiency. Instead, a joint modeling approach that brings the two types of data together can reduce or eliminate the bias and yield a more efficient estimation procedure. A well-established avenue for joint modeling is the joint likelihood approach that often produces semiparametric efficient estimators for the finite-dimensional parameter vectors in both models. Through a transformation survival model with an unspecified baseline hazard function, this review introduces joint modeling that accommodates both baseline covariates and time-varying covariates. The focus is on the major challenges faced by joint modeling and how they can be overcome. A review of available software implementations and a brief discussion of future directions of the field are also included.

中文翻译：

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纵向和存活数据的联合建模


在医学研究中，事件发生时间结果（例如死亡时间或疾病复发时间）与随访期间间歇性观察到的纵向数据一起定期记录。由于各种原因，模拟事件时间的边际方法，对应于生存数据/纵向数据的单独方法，往往会引起偏差并失去效率。相反，将两种数据类型结合在一起的联合建模方法可以减少或消除偏差，并产生更有效的估计程序。联合建模的一种行之有效的途径是联合似然法，它通常为两个模型中的有限维参数向量生成半参数有效估计量。通过具有未指定基线风险函数的转换生存模型，本文介绍了同时容纳基线协变量和时变协变量的联合建模。重点是联合建模面临的主要挑战以及如何克服这些挑战。还包括对可用软件实现的回顾和对该领域未来方向的简要讨论。