  Health policy decisions are often informed by estimates of long-term survival
based primarily on short-term data. A range of methods are available to include
longer-term information, but there has previously been no comprehensive and
accessible tool for implementing these. This paper introduces a novel model and
software package for parametric survival modelling of individual-level,
right-censored data, optionally combined with summary survival data on one or
more time periods. It could be used to estimate long-term survival based on
short-term data from a clinical trial, combined with longer-term disease
registry or population data, or elicited judgements. All data sources are
represented jointly in a Bayesian model. The hazard is modelled as an M-spline
function, which can represent potential changes in the hazard trajectory at any
time. Through Bayesian estimation, the model automatically adapts to fit the
available data, and acknowledges uncertainty where the data are weak. Therefore
long-term estimates are only confident if there are strong long-term data, and
inferences do not rely on extrapolating parametric functions learned from
short-term data. The effects of treatment or other explanatory variables can be
estimated through proportional hazards or with a flexible non-proportional
hazards model. Some commonly-used mechanisms for survival can also be assumed:
cure models, additive hazards models with known background mortality, and
models where the effect of a treatment wanes over time. All of these features
are provided for the first time in an R package, $\texttt{survextrap}$, in
which models can be fitted using standard R survival modelling syntax. This
paper explains the model, and demonstrates the use of the package to fit a
range of models to common forms of survival data used in health technology
assessments.
