  The mixture cure model for analyzing survival data is characterized by the
assumption that the population under study is divided into a group of subjects
who will experience the event of interest over some finite time horizon and
another group of cured subjects who will never experience the event
irrespective of the duration of follow-up. When using the Bayesian paradigm for
inference in survival models with a cure fraction, it is common practice to
rely on Markov chain Monte Carlo (MCMC) methods to sample from posterior
distributions. Although computationally feasible, the iterative nature of MCMC
often implies long sampling times to explore the target space with chains that
may suffer from slow convergence and poor mixing. Furthermore, extra efforts
have to be invested in diagnostic checks to monitor the reliability of the
generated posterior samples. An alternative strategy for fast and flexible
sampling-free Bayesian inference in the mixture cure model is suggested in this
paper by combining Laplace approximations and penalized B-splines. A logistic
regression model is assumed for the cure proportion and a Cox proportional
hazards model with a P-spline approximated baseline hazard is used to specify
the conditional survival function of susceptible subjects. Laplace
approximations to the conditional latent vector are based on analytical
formulas for the gradient and Hessian of the log-likelihood, resulting in a
substantial speed-up in approximating posterior distributions. Results show
that LPSMC is an appealing alternative to classic MCMC for approximate Bayesian
inference in standard mixture cure models.
