Defective 3-parameter Gompertz model with frailty term for estimating cure fraction in survival data

In several survival data, a proportion of units is not susceptible to the event of interest, even if, accompanied by a sufficiently large time, which is so-called immune or cured. In this paper, the defective Gamma 3-parameter Gompertz model with a frailty term is proposed for estimating the cure fraction. This model does not require adding extra parameters for modeling the cure rate, and it accommodates unimodal hazard shapes as well as monotone hazards. A simulation study has been carried out to assess the performance of the maximum likelihood estimators. The model was applied to two real data sets.