Bias-corrected imputation method for missing not at random nonresponse under arbitrary response probability model

Numerous methods have been studied for appropriately handling nonresponse, and recent attention has focused on missing not at random (MNAR) nonresponse, where the response probability depends on the variable of interest.Lee and Shin (2022) and Lee and Shin (2024) proposed imputation methods to appropriately handle such non-ignorable nonresponse.In both studies, bias derived from known response probability models was estimated and removed from the imputation estimators, thereby improving the accuracy of the estimation.However, the application of known response probability models is often limited in practice.This study proposes a biascorrected imputation method that estimates theoretical bias under an arbitrary response probability model and an arbitrary outcome model, and applies this correction to the imputation estimator.Furthermore, the validity of the proposed method is verified through simulation studies.