Inference for the proportional hazards model with misclassified discrete-valued covariates

We consider the Cox proportional hazards model with discrete-valued covariates subject to misclassification. We present a simple estimator of the regression parameter vector for this model. The estimator is based on a weighted least squares analysis of weighted-averaged transformed Kaplan-Meier curves for the different possible configurations of the observed covariate vector. Optimal weighting of the transformed Kaplan-Meier curves is described. The method is designed for the case in which the misclassification rates are known or are estimated from an external validation study. A hybrid estimator for situations with an internal validation study is also described. When there is no misclassification, the regression coefficient vector is small in magnitude, and the censoring distribution does not depend on the covariates, our estimator has the same asymptotic covariance matrix as the Cox partial likelihood estimator. We present results of a finite-sample simulation study under Weibull survival in the setting of a single binary covariate with known misclassification rates. In this simulation study, our estimator performed as well as or, in a few cases, better than the full Weibull maximum likelihood estimator. We illustrate the method on data from a study of the relationship between trans-unsaturated dietary fat consumption and cardiovascular disease incidence.