Random weighted bootstrap method for recurrent events with informative censoring

Using the data from the AIDS Link to Intravenous Experiences cohort study as an example, an informative censoring model was used to characterize the repeated hospitalization process of a group of patients. Under the informative censoring assumption, the estimators of the baseline rate function and the regression parameters were shown to be related to a latent variable. Hence, it becomes impractical to directly estimate the unknown quantities in the moments of the estimators for the bandwidth selection of a smoothing estimator and the construction of confidence intervals, which are respectively based on the asymptotic mean squared errors and the asymptotic distributions of the estimators. To overcome these difficulties, we develop a random weighted bootstrap procedure to select appropriate bandwidths and to construct approximated confidence intervals. One can see that our method is simple and faster to implement from a practical point of view, and is at least as accurate as other bootstrap methods. In this article, it is shown that the proposed method is useful through the performance of a Monte Carlo simulation. An application of our procedure is also illustrated by a recurrent event sample of intravenous drug users for inpatient cares over time.