Robust sandwich covariance estimation for regression calibration estimator in Cox regression with measurement error

Prentice (1982) proposed a regression calibration estimator in Cox regression when covariate variables are measured with error. However, estimation of the covariance of this estimator has not yet been discussed in the literature. The regression calibration estimator is to replace an unobserved covariate variable by its conditional expectation given observed covariate variables. Therefore, a standard Cox (1972) regression program based on the partial-likelihood estimating equation (such as the coxreg function in S-plus) may be applied to the replacement data for parameter estimation. However, covariance estimation of the regression estimator based on a standard Cox regression program may lead to bias estimation. This paper provides a simple sandwich formula for the covariance estimation. The covariance estimator is valid under a possibly misspecified Cox proportional hazards model when repeated measurements are available for the covariate that is measured with error. This method is important in practice since it is easy to implement, and inference based on it is valid if the hazard ratio parameter for the mismeasured covariate is not large. Results from intensive simulation studies are given.