A multiple imputation-based sensitivity analysis approach for data subject to missing not at random

Missingness mechanism is in theory unverifiable based only on observed data. If there is a suspicion of missing not at random, researchers often perform a sensitivity analysis to evaluate the impact of various missingness mechanisms. In general, sensitivity analysis approaches require a full specification of the relationship between missing values and missingness probabilities. Such relationship can be specified based on a selection model, a pattern-mixture model or a shared parameter model. Under the selection modeling framework, we propose a sensitivity analysis approach using a nonparametric multiple imputation strategy. The proposed approach only requires specifying the correlation coefficient between missing values and selection (response) probabilities under a selection model. The correlation coefficient is a standardized measure and can be used as a natural sensitivity analysis parameter. The sensitivity analysis involves multiple imputations of missing values, yet the sensitivity parameter is only used to select imputing/donor sets. Hence, the proposed approach might be more robust against misspecifications of the sensitivity parameter. For illustration, the proposed approach is applied to incomplete measurements of level of preoperative Hemoglobin A1c, for patients who had high-grade carotid artery stenosisa and were scheduled for surgery. A simulation study is conducted to evaluate the performance of the proposed approach.