A multiple imputation-based sensitivity analysis approach for regression analysis with an missing not at random covariate

Missing covariate problems are common in biomedical and electrical medical record data studies while evaluating the relationship between a biomarker and certain clinical outcome, when biomarker data are not collected for all subjects. However, missingness mechanism is unverifiable based on observed data. If there is a suspicion of missing not at random (MNAR), researchers often perform sensitivity analysis to evaluate the impact of various missingness mechanisms. Under the selection modeling framework, we propose a sensitivity analysis approach with a standardized sensitivity parameter using a nonparametric multiple imputation strategy. The proposed approach requires fitting two working models to derive two predictive scores: one for predicting missing covariate values and the other for predicting missingness probabilities. For each missing covariate observation, the two predictive scores along with the pre-specified sensitivity parameter are used to define an imputing set. The proposed approach is expected to be robust against mis-specifications of the selection model and the sensitivity parameter since the selection model and the sensitivity parameter are not directly used to impute missing covariate values. A simulation study is conducted to study the performance of the proposed approach when MNAR is induced by Heckman's selection model. Simulation results show the proposed approach can produce plausible regression coefficient estimates. The proposed sensitivity analysis approach is also applied to evaluate the impact of MNAR on the relationship between post-operative outcomes and incomplete pre-operative Hemoglobin A1c level for patients who underwent carotid intervetion for advanced atherosclerotic disease.