PLACE: 319 Snedecor

SPEAKER:
Dr. Wesley Johnson, Division of Statistics, University of California - Davis

TITLE:
Bayesian Semi-parametric Analysis of Survival Data via Mixtures of Polya Trees

ABSTRACT:

The ubiquitous proportional hazards model often fails to fit real data.  A classic alternative to the PH model is the parametric accelerated failure time model, for example, a log normal regression is a special case.  While a number of semi-parametric methods have been developed, to date we are not aware of any whose practical implementation for routine use seems feasible.  Moreover, most of the methods that have been developed require large sample theory as a justification and several of them seem to have some peculiar properties. Here, we model the error distribution in the semi-parametric version of the AFT model as a mixture of Polya trees constrained to have median zero.  By considering a mixture, we smooth out the partitioning effects of a simple Polya tree, considered by Walker and Mallick.  The predictive error density has a derivative everywhere, except zero, and moreover, the predictive density (which can be considered to be a density function estimate for a particular individual with given risk factors) is differentiable everywhere and is thus smooth. The error distribution is centered around a standard parametric family of distributions and may therefore be viewed as a generalization of standard models (such as a log normal for example) in which important, data-driven features, such as skewness and multimodality, are allowed.  By marginalizing the Polya tree (integration over the space of all baseline error distributions), exact inference is possible up to MCMC error.  Emphasis will be on the implementation of the procedure, which will be illustrated using constructed data, and data on time to abortion in dairy cattle. (Joint work with Tim Hanson from the University of New Mexico and former student at UCD).
 

COFFEE: 3:45 p.m., 104 Snedecor Hall