Bayesian proportional hazards model with latent variables

We consider a joint modeling approach that incorporates latent variables into a proportional hazards model to examine the observed and latent risk factors of the failure time of interest. An exploratory factor analysis model is used to characterize the latent risk factors through multiple observed variables. In commonly used confirmatory factor analysis, the number of latent variables and their observed indicators are specified prior to analysis. By contrast, the exploratory factor analysis model allows such information to be fully determined by the data. A Bayesian approach coupled with efficient sampling methods is developed to conduct statistical inference, and the performance of the proposed methodology is confirmed through simulations. The model is applied to a study on the risk factors of chronic kidney disease for patients with type 2 diabetes.