Nonparametric Bayesian estimation from interval-censored data using Monte Carlo methods

We study the estimation of the survival function based on interval-censored data from a nonparametric Bayesian point of view. Interval censoring arises when the time variable of interest cannot be directly observed and it is only known to have occurred during a randominterval of time. Susarla and Van Ryzin (1976) derived the nonparametric Bayesian estimator of the survival function for right-censored data, based on the class of Dirichlet processes introduced by Ferguson (1973). The extension of this theory to more complex censoring schemes is in general not straightforward because the corresponding nonparametric Bayesian estimators are not obtainable in explicit form. In this work, we propose a methodology that accommodates Susarla and Van Ryzin estimator to an interval-censoring scheme by using Markov Chain Monte Carlo methods. The methodology is illustrated with the analysis of the data corresponding to an AIDS clinical trial. The proposed Bayesian estimator can be interpreted as a way of ‘shrinking’ Turnbull’s nonparametric estimator to a smooth parametric family. A simulation study has been conducted to illustrate the gain in smoothing as long as the degree of ‘shrinkage’ is bounded as the sample size grows