Parameter Estimation for the Logistic Regression Model With Errors in Covariate

In a logistic regression model, when the covariate is measured with error, the estimators of the regression coefficient parameters can be biased. We propose a method for estimating parameters of a logistic regression with case-control data, when the covariate is subject to measurement error. The density of the covariate is estimated by using the deconvolution kernel density estimation. The parameters of the regression are estimated by the integrated squared distance based on the log ratio of the estimated density. We show the consistency and the asymptotic normality of the proposed estimators. Simulation study shows the superiority of the proposed method in different sample sizes and measurement error magnitudes scenario. The methodology is applied to estimating the relationship of systolic blood pressure and the presence of coronary heart disease