Flexible estimation in cure survival models using Bayesian P-splines

Abstract

In the analysis of survival data, it is usually assumed that any unit will experience the event of interest if it is observed for a sufficiently long time. However, it can be explicitly assumed that an unknown proportion of the population under study will never experience the monitored event. The promotion time model, which has a biological motivation, is one of the survival models taking this feature into account. The promotion time model assumes that the failure time of each subject is generated by the minimum of N independent latent event times with a common distribution independent of N. An extension which allows the covariates to influence simultaneously the probability of being cured and the latent distribution is presented. The latent distribution is estimated using a flexible Cox proportional hazard model where the logarithm of the baseline hazard function is specified using Bayesian P-splines. Introducing covariates in the latent distribution implies that the population hazard function might not have a proportional hazard structure. However, the use of P-splines provides a smooth estimation of the population hazard ratio over time. The identification issues of the model are discussed and a restricted use of the model when the follow-up of the study is not sufficiently long is proposed. The accuracy of our methodology is evaluated through a simulation study and the model is illustrated on data from a Melanoma clinical trial.