Bayesian Survival Analysis Using Log-Linear Median Regression Models

Abstract

For the analysis of survival data from clinical trials, the popular semiparametric models such as Cox’s (1972) proportional hazards model and linear transformation models (Cheng et al. 1995) usually focus on modeling effects of covariates on the hazard ratio or the survival response. Often, there is substantial information available in the data to make inferences about the median/quantiles. Models based on the median/quantiles (Ying et al. 1995) survival have been shown to be useful in for describing covariate effects. In this paper, we present two novel survival models with log-linear median regression functions. These two wide classes of semiparametric models have many desirable properties including model identifiability, closed form expressions for all quantile functions, and nonmonotone hazards. Our models also have many important practical advantages, including the ease of determination of priors, a simple interpretation of the regression parameters via the ratio of median survival times, and the ability to address heteroscedasticity of survival response. We illustrate the advantages of proposed methods through extensive simulation studies investigating small sample performance and robustness properties compared to competing methods for median regression, which provide further guidance regarding appropriate modeling in clinical trial.