Cox Models with Smooth Functional Effect of Covariates Measured with Error

Abstract

We propose, develop and implement a fully Bayesian inferential approach for the Cox model when the log hazard function contains unknown smooth functions of the variables measured with error. Our approach is to model nonparametrically both the log-baseline hazard and the smooth components of the log-hazard functions using low-rank penalized splines. The likelihood of the Cox model is coupled with the likelihood of the measurement error process. Careful implementation of the Bayesian inferential machinery is shown to produce remarkably better results than the naive approach. Our methodology was motivated by and applied to the study of progression time to chronic kidney disease (CKD) as a function of baseline kidney function and applied to the Atherosclerosis Risk in Communities (ARIC) study, a large epidemiological cohort study.