Of MICE and MNAR : A Simulation Study of Imputation Methods and Sensitivity Analysis

Sammanfattning

Missing data are common in empirical research and may lead to biased conclusions if the missingness mechanism is not appropriately addressed. This thesis evaluates the performance of multiple imputation methods under a Missing Not At Random (MNAR) mechanism through a controlled simulation study. Complete data were generated under two data-generating mechanisms: one linear and one nonlinear. For each setting, 100 Monte Carlo replications with a sample size of 500 were simulated, after which 20% missingness was introduced under both Missing Completely At Random (MCAR) and MNAR mechanisms. The imputation methods considered were mean/mode imputation, predictive mean matching (PMM), classification and regression trees (CART), random forest (RF), and eXtreme Gradient Boost (XGB) within a Multiple Imputation by Chained Equations (MICE) framework. To address the MNAR mechanism, delta adjustment was applied as a sensitivity analysis. Performance was evaluated using both inferential and distributional measures. Inferential performance was assessed by estimating the mean of the outcome variable using bias, relative bias, relative standard error, and relative root mean squared error. Distributional quality was evaluated using energy distance. The results show that PMM performed best under the linear data-generating mechanism, while CART generally achieved the strongest performance in the highly nonlinear setting. However, the choice of delta adjustment had a greater impact on performance than the choice of imputation method. Mean/mode imputation occasionally produced low bias but performed poorly in terms of distributional quality, highlighting the importance of evaluating imputation methods beyond point estimation. XGB performed competitively in some settings but did not consistently outperform simpler tree-based methods. Overall, the study highlights the importance of sensitivity analysis when handling MNAR data and supports the use of both inferential and distributional metrics when evaluating imputation methods.