A Simulation Study of Measurement Error Correction Methods in Logistic Regression

It is shown that the regression calibration method is a very good alternative to more mathematically sophisticated methods in this situation, and the naive estimator is the result of simply ignoring the fact that some of the explanatory variables are measured with error.

Abstract

Measurement error models in logistic regression have received considerable theoretical interest over the past 10-15 years. In this paper, we present the results of a simulation study that compares four estimation methods: the so-called regression calibration method, probit maximum likelihood as an approximation to the logistic maximum likelihood, the exact maximum likelihood method based on a logistic model, and the naive estimator, which is the result of simply ignoring the fact that some of the explanatory variables are measured with error. We have compared the behavior of these methods in a simple, additive measurement error model. We show that, in this situation, the regression calibration method is a very good alternative to more mathematically sophisticated methods.