We introduce a numerically tractable formulation of Bayesian joint models for longitudinal and survival data. The longitudinal process is modeled using generalized linear mixed models, while the survival process is modeled using a parametric general hazard structure. The two processes are linked by sharing fixed and random effects, separating the effects that play a role at the time scale from those that affect the hazard scale. This strategy allows for the inclusion of nonlinear and time-dependent effects while avoiding the need for numerical integration, which facilitates the implementation of the proposed joint model. We explore the use of flexible parametric distributions for modeling the baseline hazard function which can capture the basic shapes of interest in practice. We discuss prior elicitation based on the interpretation of the parameters. We present an extensive simulation study, where we analyze the inferential properties of the proposed models, and illustrate the trade-off between flexibility, sample size, and censoring. We also apply our proposal to two real data applications in order to demonstrate the adaptability of our formulation both in univariate time-to-event data and in a competing risks framework. The methodology is implemented in rstan.

中文翻译：

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用于纵向和生存数据的易处理贝叶斯联合模型

我们为纵向和生存数据引入了贝叶斯联合模型的数值易处理公式。纵向过程使用广义线性混合模型建模，而生存过程使用参数化一般风险结构建模。这两个过程通过共享固定效应和随机效应相互联系，将在时间尺度上起作用的效应与影响危害尺度的效应分开。该策略允许包含非线性和时间相关效应，同时避免对数值积分的需要，这有助于实施所提出的联合模型。我们探索使用灵活的参数分布对基线危险函数进行建模，该函数可以在实践中捕获感兴趣的基本形状。我们根据对参数的解释讨论先验启发。我们进行了广泛的模拟研究，分析了所提出模型的推理特性，并说明了灵活性、样本量和审查之间的权衡。我们还将我们的建议应用于两个真实的数据应用程序，以证明我们的公式在单变量事件时间数据和竞争风险框架中的适应性。该方法是在 我们还将我们的建议应用于两个真实的数据应用程序，以证明我们的公式在单变量事件时间数据和竞争风险框架中的适应性。该方法是在 我们还将我们的建议应用于两个真实的数据应用程序，以证明我们的公式在单变量事件时间数据和竞争风险框架中的适应性。该方法是在斯坦。