Abstract: In this paper we investigate semiparametric estimation methods in logistic regression models with measurement error in the continuous covariates. The measurement error models under consideration have in general two data sets: the validation and nonvalidation data sets. Some covariates are missing in the nonvalidation data set, but a surrogate variable may be available in both data sets. When a covariate variable is missing at random, we consider two kernel assisted estimation methods which extend the pseudo conditional likelihood (PCL) estimate of Breslow and Cain (1988) and the mean-score method of Reilly and Pepe (1995) to continuous covariates and surrogates. The asymptotic results of the two estimators for prospective logistic regression are given. Furthermore, we discuss the asymptotic theory of the PCL estimate in a two-stage case-control (retrospective sampling) study when the covariates and the surrogate are continuous. A simulation study is also given to demonstrate and compare their finite sample properties.
Key words and phrases: Case-control study, errors in variable, kernel smoother, logistic regression, mean-score method, pseudo conditional likelihood.