Inference for multi-state models from interval-censored data

Clinical statuses of subjects are often observed at a finite number of visits. This leads to interval-censored observations of times of transition from one state to another. The likelihood can still easily be written in terms of both transition probabilities and transition intensities. In homogeneous Markov models, transition probabilities can be expressed simply in terms of transition intensities, but this is not the case in more general multi-state models. In addition, inference in homogeneous Markov models is easy because these are parametric models. Non-parametric approaches to non-homogeneous Markov models may follow two paths: one is the completely non-parametric approach and can be seen as a generalisation of the Turnbull approach; the other implies a restriction to smooth intensities models. In particular, the penalized likelihood method has been applied to this problem. This paper gives a review of these topics.