  Continuous-time multi-state survival models can be used to describe
health-related processes over time. In the presence of interval-censored times
for transitions between the living states, the likelihood is constructed using
transition probabilities. Models can be specified using parametric or
semi-parametric shapes for the hazards. Semi-parametric hazards can be fitted
using $P$-splines and penalised maximum likelihood estimation. This paper
presents a method to estimate flexible multi-state models which allows for
parametric and semi-parametric hazard specifications. The estimation is based
on a scoring algorithm. The method is illustrated with data from the English
Longitudinal Study of Ageing.
