Bayesian analysis of semi-parametric Cox models with latent variables

Respiratory cancer is one of the most commonly diagnosed cancers as well as the leading cause of cancer death. Numerous efforts have been devoted to reducing the death rate of respiratory cancer. In this article, we propose a semi-parametric Cox model with latent variables to assess the effects of observed and latent risk factors on survival time of respiratory cancer. The characteristics of latent risk factors are characterized via multiple observed indicators by a confirmatory factor analysis model. We develop a Bayesian estimation procedure to obtain the estimates of parameters. Simulation shows that the performance of the proposed methodology is satisfactory. The proposed method is applied to analyze the Surveillance, Epidemiology, and End Results Program data set.