Time-varying coefficient additive hazards model with latent variables

This study considers a time-varying coefficient additive hazards model with latent variables to examine potential observed and latent risk factors for survival of interest. The model consists of two parts: confirmatory factor analysis to measure each latent factor through multiple observable variables and a varying coefficient additive hazards model to examine the time-varying effects of the observed and latent risk factors on the hazard function. A hybrid estimation procedure that combines the expectation-maximum algorithm and corrected estimating equation method is developed to estimate the unknown parameters and nonparametric cumulative hazard functions. The consistency and asymptotic normality of the proposed estimators are established, and the pointwise confidence intervals and general confidence bands of the nonparametric functions are constructed accordingly. A satisfactory performance of the proposed method is demonstrated through simulation studies. An application to a study of chronic kidney disease for Chinese type 2 diabetes patients is presented.