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STAT Seminar Series: A Bayesian Nonparametric Regression Model for Survival Data

Speaker Name: 
Valerie Poynor
Speaker Title: 
Assistant Professor
Speaker Organization: 
CSU Fullerton
Start Time: 
Monday, April 29, 2019 - 4:00pm
End Time: 
Monday, April 29, 2019 - 5:00pm


Title: A Bayesian Nonparametric Regression Model for Survival Data

Abstract: In survival analysis, obtaining inference for the hazard rate and mean residual life functions are of key interest.  The mean residual life function, in particular,has received limited attention in terms of inference methods under a probabilistic modeling framework. Under the regression setting, existing models have primarily been constructed under the proportional mean residual life assumption, which can often be unrealistic. Moreover, the mean residual life function at a given covariate is typically limited to have monotonic or unimodal behavior. We seek to provide general modeling approach to achieve flexible inference for the mean residual life regression while also offering desirable inferential properties for the hazard rate regression. In particular, we employ Dirichlet process mixture modeling for the joint stochastic mechanism of the random covariates and survival responses. This approach implies a model structure for both the mean residual life and hazard rate of the conditional response distribution, allowing general shapes for the function of covariates given a specific time point, as well as a function of time given particular values of the covariate vector. To expand the scope of the modeling framework, we extend the mixture model to incorporate dependence across fixed groups. This extension is built from a dependent Dirichlet process prior for the group-specific mixing distributions, with common locations and weights that vary across groups through latent bivariate Beta distributed random variables.  We illustrate the different components of the model through simulated data examples as well as real data examples.