Bayesian Inference for Mean Residual Life Functions in Survival Analysis

• Activity Number: 424
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Valerie Poynor*+
• Companies: University of California at Santa Cruz
• Keywords: bayesian nonparametrics ; survival analysis ; Dirichlet Process ; mean residual life ; right censoring

Abstract

In survival analysis interest lies in modeling data that describe the time to a particular event. Informative functions, namely the hazard function and mean residual life function (MRL) , can be obtained from the model's distribution function. The MRL function provides the expected remaining life given survival up to a particular time. This function is of interest in reliability, medical, and actuarial fields. The MRL function not only has a simple and practical interpretation, it characterizes the distribution through the Inversion Formula. Thus the MRL function can be used in fitting a model to the data. We review the key properties of the MRL function and investigate its form for some common distributions. We also study Bayesian nonparametric inference for MRL functions obtained from a flexible mixture model for the corresponding survival distribution. In particular, we develop Markov Chain Monte Carlo posterior simulation methods to fit a nonparametric lognormal Dirichlet process mixture model to two experimental groups. We perform a model comparison with a parametric exponentiated Weibull model. Finally, we fit a nonparametric mixture model to a right censored dataset.