UCSC-SOE-13-04: Nonparametric Bayesian Inference for Mean Residual Life Functions in Survival Analysis

Valerie Poynor and Athanasios Kottas
03/26/2013 03:24 PM
Applied Mathematics & Statistics
Modeling and inference for survival analysis problems typically revolves around different functions related to the survival distribution. Here, we focus on the mean residual life function which provides the expected remaining lifetime given that a subject has survived (i.e., is event-free) up to a particular time. This function is of direct interest in reliability, medical, and actuarial fields. In addition to its practical interpretation, the mean residual life function characterizes the survival distribution. We review key properties of the mean residual life function and investigate its form for some common distributions. We then develop general Bayesian nonparametric inference for mean residual life functions built from a Dirichlet process mixture model for the associated survival distribution. Particular emphasis is placed on kernel selection to ensure desirable properties for the mean residual life function arising from the mixture
distribution. We advocate for a mixture model with a gamma kernel and dependent
baseline distribution for the Dirichlet process prior. The empirical performance of our modeling technique is studied with two simulation examples, a data set of two experimental groups, and a data set involving right censoring. Moreover, to illustrate the practical utility of the nonparametric mixture model, we compare it in the context of one of the data examples with an exponentiated Weibull model, a parametric survival distribution that allows various shapes for the mean residual life function.

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