  Multistate models can be used to describe transitions over time across
states. In the presence of interval-censored times for transitions, the
likelihood is constructed using transition probabilities. Models are specified
using proportional hazards model for the transitions. Time-dependency is
usually defined by parametric models, which can be too restrictive.
Nonparametric hazards specification with splines allow for flexible modelling
of time-dependency without making strong model assumptions. Penalised maximum
likelihood is used to estimate the models. Selecting the optimal amount of
smoothing is challenging as the problem involves multiple penalties. We propose
an automatic and efficient method to estimate multistate models with splines in
the presence of interval-censoring. The method is illustrated with a data
analysis and a simulation study.
