On quadratic logistic regression models when predictor variables are subject to measurement error

Owing to its good properties and a simple model fitting procedure, logistic regression is one of the most commonly used methods applied to data consisting of binary outcomes and one or more predictor variables. However, if the predictor variables are measured with error and the functional relationship between the response and predictor variables is non-linear (e.g., quadratic) then consistent estimation of model parameters is more challenging to develop. To address the effects of measurement error in predictor variables when using quadratic logistic regression models, two novel approaches are developed: (1) an approximated refined regression calibration; and (2) a weighted corrected score method. Both proposed approaches offer several advantages over existing methods in that they are computationally efficient and are straightforward to implement. A simulation study was conducted to evaluate the estimators' finite sample performance. The proposed methods are also applied on real data from a medical study and an ecological application.