A semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error

SUMMARY A common objective in longitudinal studies is to characterise the relationship between a failure time process and time-independent and time-dependent covariates. Timedependent 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 assumption is that the random effects are normally distributed; however, this need not hold in practice. Within this framework, we develop a simple method for estimating the proportional hazards model parameters that requires no assumption on the distribution of the random effects. Large-sample properties are discussed, and finite-sample performance is assessed and compared to competing methods via simulation.

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