  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 sufficient long time.
However, one can explicitly assume 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 latent event times which
are independent with a common distribution independent of N. We propose an
extension which allows the covariates to influence simultaneously the
probability of being cured and the latent distribution. We estimate the latent
distribution 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 the P-splines provides a smooth estimation of the population hazard
ratio over time. We propose a restricted use of the model when the follow up of
the study is not sufficiently long. A simulation study evaluating the accuracy
of our methodology is presented. The proposed model is illustrated on data from
the phase III Melanoma e1684 clinical trial.
