Abstract: We propose a novel additive mean residual life model to examine the effects of observable and latent risk factors on the mean residual life function of interest in the presence of right censoring. We use factor analysis to characterize the latent risk factors on the basis of multiple observed variables. We develop a borrow-strength estimation procedure that incorporates an asymptotically distribution-free generalized least square method and a corrected estimating equation approach. We establish the asymptotic properties of the proposed estimators. We develop a goodness-of-fit test for model checking. We report on simulations to evaluate the finite sample performance of the method. The application to a study on chronic kidney disease for type 2 diabetic patients reveals insights into the prevention of such common diabetic complications.

Key words and phrases: Borrow-strength estimation, corrected estimating equations, distribution-free factor analysis, latent variables, mean residual life function, model checking.