A flexible semi-Markov model for interval-censored data and goodness-of-fit testing

Multi-state approaches are becoming increasingly popular to analyse the complex evolution of patients with chronic diseases. For example, the evolution of kidney transplant recipients can be broken down into several clinical states. With this application in mind, we present a flexible semi-Markov model. The distribution functions are fitted to the durations in states and the relevance of the generalised Weibull distribution is shown. The corresponding likelihood function allows for interval censoring, i.e. the times of transitions and the sequences of states are not available during the elapsed times between two visits. The explanatory variables are introduced through the Markov chain and through the probability density functions of durations. A goodness-of-fit test is also defined to examine the stationarity of the semi-Markov model.