Estimation of the Proportional Mean Residual Life Model with Internal and Longitudinal Covariates

The proportional mean residual life model has been discussed by many authors and provides a useful alternative to the commonly used proportional hazards model for regression analysis of failure time data. In this paper, we discuss the estimation of the model when there exist internal and longitudinal covariates or variables in addition to the failure time variable of interest, for which it does not seem to exist an established estimation procedure. For the problem, a joint modeling approach is proposed and in the method, latent variables are used to describe the relationship between the failure time of interest and longitudinal variables. For estimation, a two-step estimation procedure is proposed and the simulation study shows that it works well in practical situations. The method is applied to a study on Alzheimer’s disease that motivated this investigation