A Bayesian approach to efficient estimation with censored survival data
By making use of recent advances in Bayesian nonparametrics, we treat two problems of current interest in survival analysis.
A long-standing problem in survival analysis is efficient estimation of the multivariate survival function when the observations are subject to censoring. The difficulty is caused by singly censored observations. We propose to resolve this problem by using a Bayesian approach involving the Dirichlet process prior. The index measure of the prior is a smoothed version of an estimator proposed by Prentice and Cai. It puts mass in some neighborhood of observations and redistribute mass in a self-consistent way to the half-lines with singly censored observations as the left endpoints. An algorithm is provided to carry out the simulation-based Bayesian procedure. Simulation results show that the Bayesian estimator has better performance than the Prentice-Cai estimator, which is known to be the best to date. It is also demonstrated that the estimator has asymptotically efficient frequentist properties.
The second problem is the estimation of multivariate density function based on censored data. A Bayesian procedure is proposed to estimate the density function. We use the kernel method and provide a Polya urn algorithm to implement the estimation. The prior parameter is well chosen so that the computation is simple. Simulation studies show that the Bayesian estimator works well and has better practical performance than an estimator proposed by Wells and Yeo.