A common objective in longitudinal studies is to characterize the relationship between a failure time process and time-independent and time-dependent covariates. Time-dependent covariates are generally available as longitudinal data collected periodically during the course of the study. We assume that these data follow a linear mixed effects model with normal measurement error and that the hazard of failure depends both on the underlying random effects describing the covariate process and other time-independent covariates through a proportional hazards relationship. A routine, convenient assumption is that the random effects are normally distributed; however, this need not hold in practice. Within this framework, we develop a method for estimating the proportional hazards model parameters that requires no assumptions on the distribution of the random effects by exploiting the conditional score approach of Stefanski and Carroll (1987, Biometrika 74:703-706). Large sample properties are discussed, and finite sample performance is assessed and compared to competing methods via simulation.
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