Nonparametric bayes estimation of the survival function from a record of failures and follow-ups

In some observational studies, we have random censoring model. However, the data available may be partially observable censored data consisting of the observed failure times and only those nonfailure times which are subject to follow-up. Suzuki (1985) discussed the problem of nonparametric estimation of the survival function from such partially observable censored data. In this article, we derive a nonparametric Bayes estimator of the survival function for such data of failures and follow-ups under a Dirichlet process prior and squared error loss. The limiting properties such as the mean square consistency, weak convergence and strong consistency of the Bayes estimator are studied. Finally, the procedures developed are illustrated by means of an example.