When there is evidence of long term survivors, cure rate models have been used by researchers to model the tail behavior of the survival curve. Mixture models were traditionally used, and different parameter estimation approaches for parametric and semi-parametric models have been suggested. A common aspect of the traditional cure rate models is that they implicitly assume there is no additional information about the status of cure, thus the indicator of cure has been modeled as latent variable. This assumption is not entirely valid in many cases, when some diagnostic procedure can provide information about the status of cure. This dissertation proposes a novel extension to incorporate the additional information about status of cure in the cure rate models. It also shows that, with this additional information, more efficient estimator can be obtained. The efficiency gain increases with better sensitivity and specificity of the diagnostic procedure. The efficiency gain is larger when the censoring rate is high.

This extension can be applied when the latency part is modeled parametrically, semi-parametrically, or non-parametrically. Both proportional hazards (PH) cure rate models and accelerated failure time (AFT) cure rate models can use this model extension. Simulation study and a case study results are presented.