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Biometrika 2001 88(2):447-458; doi:10.1093/biomet/88.2.447
© 2001 by Biometrika Trust
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A semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error

Anastasios A.Tsiatis1 and Marie Davidian1

1 Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695-8203, U.S.Atsiatis{at}stat.ncsu.edudavidian{at}stat.ncsu.edu

A common objective in longitudinal studies is to characterise 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 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.

Key Words: Conditional score; Measurement error; Mixed effects model; Regression calibration; Semiparametric; Survival analysis

Received November 1999. Revised November 2000


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