A joint model for survival and longitudinal data measured with error.

TL;DR: This work argues that the Cox proportional hazards regression model method is superior to naive methods where one maximizes the partial likelihood of the Cox model using the observed covariate values and improves on two-stage methods where empirical Bayes estimates of the covariate process are computed and then used as time-dependent covariates.

Abstract: The relationship between a longitudinal covariate and a failure time process can be assessed using the Cox proportional hazards regression model We consider the problem of estimating the parameters in the Cox model when the longitudinal covariate is measured infrequently and with measurement error We assume a repeated measures random effects model for the covariate process Estimates of the parameters are obtained by maximizing the joint likelihood for the covariate process and the failure time process This approach uses the available information optimally because we use both the covariate and survival data simultaneously Parameters are estimated using the expectation-maximization algorithm We argue that such a method is superior to naive methods where one maximizes the partial likelihood of the Cox model using the observed covariate values It also improves on two-stage methods where, in the first stage, empirical Bayes estimates of the covariate process are computed and then used as time-dependent covariates in a second stage to find the parameters in the Cox model that maximize the partial likelihood