Covariate measurement errors and parameter estimation in a failure time regression model

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SUMMARY Estimation in Cox's failure time regression model is considered when the regression vector is subject to measurement error. A hazard function model is induced for the failure rate given the measured covariate and a partial likelihood function is derived for the relative risk parameters. This partial likelihood function may involve the baseline hazard function as well as the regression parameter, but useful inference techniques arise for testing whether the regression parameter equals zero and for more general inferences in important special cases. Explicit consideration is given to testing equality of survival curves when group membership is subject to misclassification and to relative risk estimation with normally distributed covariates. Approaches to regression estimation using the overall likelihood function, and a marginal likelihood function based on failure time ranks, are also indicated. Illustration of the possible effect of covariate errors on relative risk estimation is provided.