  In decision modelling with time to event data, parametric models are often
used to extrapolate the survivor function. One such model is the piecewise
exponential model whereby the hazard function is partitioned into segments,
with the hazard constant within the segment and independent between segments
and the boundaries of these segments are known as change-points. We present an
approach for determining the location and number of change-points in piecewise
exponential models. Inference is performed in a Bayesian framework using Markov
Chain Monte Carlo (MCMC) where the model parameters can be integrated out of
the model and the number of change-points can be sampled as part of the MCMC
scheme. We can estimate both the uncertainty in the change-point locations and
hazards for a given change-point model and obtain a probabilistic
interpretation for the number of change-points. We evaluate model performance
to determine changepoint numbers and locations in a simulation study and show
the utility of the method using two data sets for time to event data. In a
dataset of Glioblastoma patients we use the piecewise exponential model to
describe the general trends in the hazard function. In a data set of heart
transplant patients, we show the piecewise exponential model produces the best
statistical fit and extrapolation amongst other standard parametric models.
Piecewise exponential models may be useful for survival extrapolation if a
long-term constant hazard trend is clinically plausible. A key advantage of
this method is that the number and change-point locations are automatically
estimated rather than specified by the analyst.
