Modelling survival data with a cured fraction using frailty models

Cure models have historically been utilized to analyse time-to-event data with a cured fraction. We consider the use of frailty models as an alternative approach to modelling such data. An attractive feature of the models is the allowance for heterogeneity in risk among those individuals experiencing the event of interest in addition to the incorporation of a cured component. Utilizing maximum likelihood techniques, we fit models to data concerning the recurrence of leukaemia among patients receiving autologous transplantation treatment. The analysis suggests that the gamma frailty mixture model and the compound Poisson improve on the fit of the leukaemia data as compared to the standard cure model.