Change-point Detection for Piecewise Exponential Models

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.