Model Based Bootstrap Methods for Interval Censored Data

We investigate the performance of model based bootstrap methods for con-structing point-wise confidence intervals around the survival function with interval censored data. We show that bootstrapping from the nonparamet-ric maximum likelihood estimator of the survival function is inconsistent for both the current status and case 2 interval censoring models. A model based smoothed bootstrap procedure is proposed and shown to be consistent. In addition, simulation studies are conducted to illustrate the (in)-consistency of the bootstrap methods. Our conclusions in the interval censoring model would extend more generally to estimators in regression models that exhibit non-standard rates of convergence.