Bootstrap Bandwidth for Estimation in the Missing Censoring Indicator Model

In cancer survival studies, death certificate information can be missing, or incidental and fatal occurrences may be indistinguishable for some subjects, leading to missing censoring indicators (MCIs). For the framework of right censored data with MCIs, sub-density function kernel estimators play a significant role for estimating a survival function. Data-driven bandwidths for computing these kernel estimators are proposed. The bandwidths are obtained as minimizers of certain estimates of the mean integrated squared error (MISE). It is shown that the smoothed bootstrap offers a motivation for choosing the proposed MISE estimates for minimization. The efficacy of the proposed procedures is investigated through several simulation studies. Three illustrations are provided, using a mice data set, a data set extracted from the SEER database, and the well-known Primary Biliary Cirrhosis data.