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Continuous-time multi-state survival models can be used to describehealth-related processes over time. In the presence of interval-censored timesfor transitions between the living states, the likelihood is constructed usingtransition probabilities. Models can be specified using parametric orsemi-parametric shapes for the hazards. Semi-parametric hazards can be fittedusing $P$-splines and penalised maximum likelihood estimation. This paperpresents a method to estimate flexible multi-state models which allows forparametric and semi-parametric hazard specifications. The estimation is basedon a scoring algorithm. The method is illustrated with data from the EnglishLongitudinal Study of Ageing.

Flexible multi-state models for interval-censored data: specification, estimation, and an application to ageing research