Bayesian variable selection in the accelerated failure time model with an application to the surveillance, epidemiology, and end results breast cancer data

Abstract

Accelerated failure time model is a popular model to analyze censored time-to-event data. Analysis of this model without assuming any parametric distribution for the model error is challenging, and the model complexity is enhanced in the presence of large number of covariates. We developed a nonparametric Bayesian method for regularized estimation of the regression parameters in a flexible accelerated failure time model. The novelties of our method lie in modeling the error distribution of the accelerated failure time nonparametrically, modeling the variance as a function of the mean, and adopting a variable selection technique in modeling the mean. The proposed method allowed for identifying a set of important regression parameters, estimating survival probabilities, and constructing credible intervals of the survival probabilities. We evaluated operating characteristics of the proposed method via simulation studies. Finally, we apply our new comprehensive method to analyze the motivating breast cancer data from the Surveillance, Epidemiology, and End Results Program, and estimate the five-year survival probabilities for women included in the Surveillance, Epidemiology, and End Results database who were diagnosed with breast cancer between 1990 and 2000.