Nonparametric Misclassification Simulation and Extrapolation Method and Its Application

The misclassification simulation extrapolation (MC-SIMEX) method proposed by Küchenho et al. is a general method of handling categorical data with measurement error. It consists of two steps, the simulation and extrapolation steps. In the simulation step, it simulates observations with varying degrees of measurement error. Then parameter estimators for varying degrees of measurement error are obtained based on these observations. In the extrapolation step, it uses a parametric extrapolation function to obtain the parameter estimators for data with no measurement error. However, as shown in many studies, the parameter estimators are still biased as a result of the parametric extrapolation function used in the MC-SIMEX method. Therefore, we propose a nonparametric MC-SIMEX method in which we use a nonparametric extrapolation function. It uses the fractional polynomial method with cross-validation to choose the appropriate fractional polynomial terms. An example is provided based on data from the National Health and Nutrition Examination Survey.