  We investigate the performance of model based bootstrap methods for
constructing point-wise confidence intervals around the survival function with
interval censored data. We show that bootstrapping from the nonparametric
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.
