A Nonparametric Multiple Imputation Approach For MNAR Mechanism Using the Sample Selection Model Framework

Abstract

Missing data is an unavoidable issue when performing data analysis. If the missing probability is related to unobserved variables, missingness is considered as missing not at random (MNAR). It is challenging to analyze data subject to MNAR. There are two ways to induce MNAR mechanism: sample selection model and pattern mixture model. Under the sample se-lection model framework, we develop a nonparametric multiple imputation (NNMI) method to estimate the marginal mean of an outcome subject to MNAR mechanism, where the sample se-lection model is only used as a working model to define the imputing set for each missing indi-vidual. We perform simulation studies to compare the performance of the proposed approach with a parametric multiple imputation approach, which directly uses the sample selection model to impute missing individuals. The results show that our method performs well for data subject to MNAR mechanism. Due to the limitations of current estimation method, we have not found solid proof to demonstrate the proposed method has better performance than parametric multi-ple imputation to handle MNAR when the sample selection model is misspecified. We also ap-ply the proposed approach to a real dataset to estimate the marginal mean of HbA1c level for carotid patients, whose HbA1c is subject to missingness.