A General Estimation Framework for Multi-State Markov Processes with Flexible Specification of the Transition Intensities

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.