Fast Bayesian inference using Laplace approximations in a flexible promotion time cure model based on P-splines

Bayesian methods for flexible time-to-event models usually rely on the theory of Markov chain Monte Carlo (MCMC) to sample from posterior distributions and perform statistical inference. These techniques are often plagued by several potential issues such as high posterior correlation between parameters, slow chain convergence and foremost a strong computational cost. A novel methodology is proposed to overcome the inconvenient facets intrinsic to MCMC sampling with the major advantage that posterior distributions of latent variables can rapidly be approximated with a high level of accuracy. This can be achieved by exploiting the synergy between Laplace's method for posterior approximations and P-splines, a flexible tool for nonparametric modeling. The methodology is developed in the class of cure survival models, a useful extension of standard time-to-event models where it is assumed that an unknown proportion of unidentified (cured) units will never experience the monitored event. An attractive feature of this new approach is that point estimators and credible intervals can be straightforwardly constructed even for complex functionals of latent model variables. The properties of the proposed methodology are evaluated using simulations and illustrated on two real datasets. The fast computational speed and accurate results suggest that the combination of P-splines and Laplace approximations can be considered as a serious competitor of MCMC to make inference in semi-parametric models, as illustrated on survival models with a cure fraction.