On Bayesian estimation of a survival curve: comparative study and examples

A nonparametric Bayesian approach is applied to estimate a survival curve by means of a functional of the subsurvival functions associated with censored and non-censored events. In order to actually compute the Bayesian estimator, a numerical algorithm based on the Runge-Kutta fourth-order method is introduced. It provides good accuracy and is simple to program. Using a simulated data set, the performance of the Bayesian estimator is compared to the Product-Limit. A descriptive analysis of the results from the simulations is presented. The conclusions are given in terms of the proportion of the censored data and sample size. Also, the predictive value of the estimations is investigated using a cross-validation measure, namely the mean square predictive value. The numerical methodology is illustrated considering the original Kaplan-Meier data. Finally, the Bayesian analysis is applied to a real case of cervix uterine cancer, where the elicitation of the prior distribution considers the high proportion of censoring in the sample.