We consider measurement error problem in the Cox model, where the underlying association between the true exposure and its surrogate is unknown, but can be estimated from a validation study. Under this framework, one can accommodate general distributional structures for the error-prone covariates, not restricted to a linear additive measurement error model or Gaussian measurement error. The proposed copula-based approach enables us to fit flexible measurement error models, and to be applicable with an internal or external validation study. Large sample properties are derived and finite sample properties are investigated through extensive simulation studies. The methods are applied to a study of physical activity in relation to breast cancer mortality in the Nurses' Health Study.
Keywords: Bias correction; Copula; Error-prone covariate; Measurement error; Semiparametric; Survival analysis.