When interest lies in the progression of a disease rather than on a single outcome, non-homogeneous multi-state Markov models constitute a natural and powerful modelling approach. Constant monitoring of a phenomenon of interest is often unfeasible, hence leading to an intermittent observation scheme. This setting is challenging and existing models and their implementations do not yet allow for flexible enough specifications that can fully exploit the information contained in the data. To widen significantly the scope of multi-state Markov models, we propose a closed-form expression for the local curvature information of a key quantity, the transition probability matrix. Such development allows one to model any type of multi-state Markov process, where the transition intensities are flexibly specified as functions of additive predictors. Parameter estimation is carried out through a carefully structured, stable penalised likelihood approach. The methodology is exemplified via two case studies that aim at modelling the onset of cardiac allograft vasculopathy, and cognitive decline. To support applicability and reproducibility, all developed tools are implemented in the R package flexmsm.

翻译：当研究关注疾病的进展而非单一结局时，非齐次多状态马尔可夫模型构成了一种自然且有力的建模方法。由于对感兴趣现象的持续监测往往不可行，因此产生了间歇性观测方案。这一场景具有挑战性，现有模型及其实现尚无法提供足够灵活的设定以充分挖掘数据中的信息。为显著拓宽多状态马尔可夫模型的应用范围，我们提出了关键量——转移概率矩阵——的局部曲率信息的闭式表达式。这一进展使得任何类型的多状态马尔可夫过程均可建模，其中转移强度被灵活设定为加性预测变量的函数。参数估计通过精心构建的稳定惩罚似然方法完成。该方法的有效性通过两个案例研究加以验证，分别针对心脏移植血管病变的发病与认知功能衰退的建模。为支持方法的实用性与可复现性，所有开发工具均已集成至R包flexmsm中。