Nonparametric Bayesian Inference for Mean Residual Life Functions in Survival Analysis

• Activity Number: 345
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Valerie Poynor*+
• Keywords: Bayesian nonparametrics ; Dirichlet process mixture models ; Mean residual life ; Right censoring ; Survival function

Abstract

In survival analysis interest lies in modeling data that describe the time to an event. Informative functions can be obtained from the model's distribution function. We focus on the mean residual life (mrl) function which provides the expected remaining life given survival up to a particular time. This function is of direct interest in reliability, medical, and actuarial fields. In addition to its practical interpretation, the mrl function characterizes the survival distribution. We review key properties of the mrl function and investigate its form for some common distributions. We develop general Bayesian nonparametric inference for mrl functions built from a Dirichlet process mixture model for the associated survival distribution. We discuss the importance of careful kernel selection to ensure desirable properties for the function. We advocate for a mixture model with a gamma kernel and dependent baseline distribution for the Dirichlet process prior. We study the empirical performance of our modeling technique in two simulation examples, a data set of two experimental groups, and a data set involving right censoring. We compare our results with an exponentiated Weibull model.