Parametric dynamic survival models
A non-proportional hazards model is developed. The model can accommodate right censored, interval censored and double interval censored data sets. There is also an extension of the model to include multiplicative gamma frailties. The basic model is an extension of the dynamic Bayesian survival model developed by Gamerman (1987), but with some alterations and using a different method of model fitting. The model developed here, the Normal Dynamic Survival Model, models both the log-baseline hazard and covariate effects by a piecewise constant and correlated process, based on some division of the time axis. Neighbouring piecewise constant parameters are related by a simple evolution equation: normal with mean zero and unknown variance to be estimated. The method of estimation is to use Markov chain Monte Carlo simulations: Gibbs sampling with a Metropolis-Hastings step. For double interval censored data an iterative data augmentation procedure is considered: exploiting the comparative ease at which interval censored observations may be modelled. The model is applied within a range of well known, and illustrative data sets, with convincing results. In addition the impact of censoring is investigated by a simulation study.