Classical joint modeling approaches often rely on competing risks or recurrent event formulations to describe complex processes involving evolving longitudinal biomarkers and discrete event occurrences, but these frameworks typically capture only limited aspects of the underlying event dynamics. We propose a general multi-state joint modeling framework that unifies longitudinal biomarker dynamics with multi-state time-to-event processes defined on arbitrary directed graphs. The proposed framework accommodates arbitrary directed transition graphs, nonlinear longitudinal submodels, and scalable inference via stochastic gradient descent. This formulation encompasses both Markovian and semi-Markovian transition structures, allowing recurrent cycles and terminal absorptions to be naturally represented. The longitudinal and event processes are linked through shared latent structures within nonlinear mixed-effects models, extending classical joint modeling formulations. We derive the complete likelihood, establish conditions for identifiability, and develop scalable inference procedures based on stochastic gradient descent to enable high-dimensional and large-scale applications. In addition, we formulate a dynamic prediction framework that provides individualized state-transition probabilities and personalized risk assessments along complex event trajectories. Through simulation and application to the PAQUID cohort, we demonstrate accurate parameter recovery and individualized prediction.

翻译：经典的联合建模方法通常依赖于竞争风险或复发事件框架来描述涉及动态纵向生物标志物和离散事件发生的复杂过程，但这些框架通常仅能捕捉潜在事件动态的有限方面。我们提出了一种通用的多状态联合建模框架，该框架将纵向生物标志物动态与定义在任意有向图上的多状态事件时间过程相统一。所提出的框架能够容纳任意有向转移图、非线性纵向子模型，以及通过随机梯度下降实现的可扩展推断。此公式同时包含马尔可夫和半马尔可夫转移结构，允许自然地表示复发循环和终端吸收状态。纵向过程与事件过程通过非线性混合效应模型内的共享潜在结构相连接，从而扩展了经典的联合建模公式。我们推导了完全似然函数，建立了可识别性条件，并开发了基于随机梯度下降的可扩展推断程序，以支持高维和大规模应用。此外，我们构建了一个动态预测框架，该框架能够沿着复杂的事件轨迹提供个体化的状态转移概率和个性化风险评估。通过模拟研究及在PAQUID队列中的应用，我们展示了准确的参数恢复能力和个体化预测性能。