Cure-rate estimation under Case-1 interval censoring

We consider nonparametric estimation of cure-rate based on mixture model under Case-1 interval censoring. We show that the nonparametric maximum-likelihood estimator (NPMLE) of cure-rate is non-unique as well as inconsistent, and propose two estimators based on the NPMLE of the distribution function under this censoring model. We present a cross-validation method for choosing a `cut-off' point needed for the estimators. The limiting distributions of the latter are obtained using extreme-value theory. Graphical illustration of the procedures based on simulated data are provided.