Generalized Structural Equation Model with Survival Outcomes and Time-Varying Coefficients

The conventional Cox proportional hazards (PH) model typically assumes fully observed predictors and constant regression coefficients. However, some predictors are latent variables, each of which must be characterized by multiple observed indicators from various perspectives. Moreover, the predictor effects may vary with time in practice. Accommodating such latent variables and identifying temporal covariate effects are frequently of primary interest. This study proposes a generalized structural equation model to investigate the temporal effects of observed and latent risk factors on the hazards of interest. The proposed model comprises a confirmatory factor analysis model as the measurement equation and a varying-coefficient PH model with observed and latent predictors as the structural equation. A hybrid procedure that combines the expectation-maximization (EM) algorithm and the corrected estimating equation approach is developed to estimate unknown parameters and coefficient functions. Simulation studies demonstrate the satisfactory performance of the proposed method. An application to a health survey study reveals insights into risk factors for elders' life expectancy.