A simulation-free extrapolation method for misspecified models with errors-in-variables in epidemiological studies

Abstract: In epidemiology studies, it is often of interest to consider a misspecified model that categorizes continuous variables, such as calorie and nutrient intake, to analyze disease risk and achieve better model interpretation. When the original continuous variable is contaminated with measurement errors, ignoring this issue and performing regular statistical analysis leads to severely biased point estimators and invalid confidence intervals. Though errors-in-variables is a well-known critical issue in many areas, most existing methods addressing measurement errors either do not consider model misspecification or have strong parametric distributional assumptions. To this end, we propose a flexible simulation-free extrapolation method, which provides valid and robust statistical inference under various models and has no distributional assumptions on the observed data. Through extensive numerical studies, we demonstrate that the proposed method can provide unbiased point estimation and valid confidence intervals under various regression models. Through the analysis of the Food Frequency Questionnaire in UK Biobank data, we show that ignoring measurement errors underestimates the impact of high fat intake on BMI and obesity by at least 30% and 60%, respectively, compared to the results of correcting measurement errors by the proposed method.