A Bias-Adjusted Approach for Logistic Modeling With Predicted Exposures

Bias-adjusted estimators are proposed for logistic regression parameters under a mixture measurement error model. In observational studies, collecting the true exposure for all units is often infeasible. This has led to the use of prediction models to estimate the true exposure. However, these estimates are error-prone, introducing measurement error. Measurement error in statistical analysis can result in biased parameter estimates and unreliable conclusions. The method developed in this work uses a mixture error model that accounts for both an error-prone predicted exposure and true exposure. The proposed bias-adjusted approach uses bootstrap estimators of the mixture error model parameters, a user-specified prediction model, and a linear regression calibration function. The approach applies to cohort designs under various exposure distributions when measurement error model parameters are unknown. A Wald confidence interval is constructed using the developed bias-adjusted estimators and their bootstrapped standard errors. The proposed method is evaluated in a simulation study and an observational study in which a logistic regression model relates hypertension incidence to glycohemoglobin exposure. Numerical results demonstrate accurate point estimates and coverage probabilities close to the nominal level. We further investigate the effects of selecting an incorrect prediction model on the proposed approach. The results indicate that using an oversimplified predictive model can lead to severe biases. Additionally, we show that even flexible machine learning models may offer lower accuracy and precision than correctly specified parametric models. Diagnostics for assessing model assumptions are provided in the Supporting Information and illustrated for the motivating example.