Conventional joint modeling approaches generally characterize the relationship between longitudinal biomarkers and discrete event occurrences within terminal, recurring or competing risk settings, thereby offering a limited representation of complex, multi-state trajectories. 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 also accomodates 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, model selection criteria, 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：传统的联合建模方法通常在终点事件、复发事件或竞争风险事件背景下刻画纵向生物标志物与离散事件发生之间的关系，从而对复杂多状态轨迹的表征能力有限。我们提出了一种通用的多状态联合建模框架，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。该框架支持非线性纵向子模型，并能通过随机梯度下降实现可扩展的推断。该公式同时包含马尔可夫与半马尔可夫转移结构，可自然表征复发循环和终点吸收状态。纵向过程与事件过程通过非线性混合效应模型中的共享潜结构相连接，从而扩展了经典的联合建模形式。我们推导了完全似然函数与模型选择准则，并开发了基于随机梯度下降的可扩展推断流程，以支持高维与大规模应用。此外，我们构建了一个动态预测框架，能够沿复杂事件轨迹提供个体化的状态转移概率与个性化风险评估。通过模拟研究及在PAQUID队列数据中的应用，我们验证了模型参数恢复的准确性与个体化预测的有效性。