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When interest lies in the progression of a disease rather than on a singleoutcome, non-homogeneous multi-state Markov models constitute a natural andpowerful modelling approach. Constant monitoring of a phenomenon of interest isoften unfeasible, hence leading to an intermittent observation scheme. Thissetting is challenging and existing models and their implementations do not yetallow for flexible enough specifications that can fully exploit the informationcontained in the data. To widen significantly the scope of multi-state Markovmodels, we propose a closed-form expression for the local curvature informationof a key quantity, the transition probability matrix. Such development allowsone to model any type of multi-state Markov process, where the transitionintensities are flexibly specified as functions of additive predictors.Parameter estimation is carried out through a carefully structured, stablepenalised likelihood approach. The methodology is exemplified via two casestudies that aim at modelling the onset of cardiac allograft vasculopathy, andcognitive decline. To support applicability and reproducibility, all developedtools are implemented in the R package flexmsm.

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