Corrected Score Estimation in the Cox Regression Model with Misclassified Discrete Covariates

Abstract

We consider Cox proportional hazards regression when the covariate vector includes error-prone discrete covariates along with error-free covariates that may be discrete or continuous. The misclassification in the discrete error-prone covariates is allowed to be of arbitrary form. Building on work of Nakamura and his colleagues, we develop a corrected score method for this setting. The method can handle all three major study designs (internal validation design, external validation design, and replicate measures design), both functional and structural error models, and time-dependent covariates satisfying a certain "localized error" condition. This chapter presents the method, briefly describes its asymptotic properties, and illustrates it on data from a study of the relationship between dietary calcium intake and distal colon cancer. Zucker and Spiegelman (2007, 2008) present further details on the asymptotic theory and a simulation study under Weibull survival with a single binary covariate having known misclassification rates. In these simulations, the method presented here performed similarly to related methods we have examined in previous work. Specifically, our new estimator performed as well as or, in a few cases, better than the full Weibull maximum likelihood estimator. In further simulations for the case where the misclassification probabilities are estimated from an external replicate measures study our method generally performed well. The new estimator has a broader range of applicability than many other estimators proposed in the literature, including those described in our own earlier work, in that it can handle time-dependent covariates with an arbitrary misclassification structure.