Estimation and identification issues in the promotion time cure model when the same covariates influence long- and short-term survival.

The promotion time cure model is a survival model acknowledging that an unidentified proportion of subjects will never experience the event of interest whatever the duration of the follow-up. We focus our interest on the challenges raised by the strong posterior correlation between some of the regression parameters when the same covariates influence long- and short-term survival. Then, the regression parameters of shared covariates are strongly correlated with, in addition, identification issues when the maximum follow-up duration is insufficiently long to identify the cured fraction. We investigate how, despite this, plausible values for these parameters can be obtained in a computationally efficient way. The theoretical properties of our strategy will be investigated by simulation and illustrated on clinical data. Practical recommendations will also be made for the analysis of survival data known to include an unidentified cured fraction.