In a logistic regression model when covariates are subject to measurement error the naive estimator, obtained by regressing on the observed covariates, is asymptotically biased. We introduce a bias-adjusted estimator and two estimators appropriate for normally distributed measurement errors -a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency. The four proposals are studied asymptotically under conditions which are appropriate when the measurement error is small. A small Monte Carlo study illustrates the superiority of the measurement-error estimators in certain situations.
"Covariate Measurement Error in Logistic Regression." Ann. Statist. 13 (4) 1335 - 1351, December, 1985. https://doi.org/10.1214/aos/1176349741