BACKGROUND: Multiple imputation (MI) is a well-recognised statistical technique for handling missing data. As usually implemented in standard statistical software, MI assumes that data are 'Missing at random' (MAR); an assumption that in many settings is implausible. It is not possible to distinguish whether data are MAR or 'Missing not at random' (MNAR) using the observed data, so it is desirable to discover the impact of departures from the MAR assumption on the MI results by conducting sensitivity analyses. A weighting approach based on a selection model has been proposed for performing MNAR analyses to assess the robustness of results obtained under standard MI to departures from MAR. METHODS: In this article, we use simulation to evaluate the weighting approach as a method for exploring possible departures from MAR, with missingness in a single variable, where the parameters of interest are the marginal mean (and probability) of a partially observed outcome variable and a measure of association between the outcome and a fully observed exposure. The simulation studies compare the weighting-based MNAR estimates for various numbers of imputations in small and large samples, for moderate to large magnitudes of departure from MAR, where the degree of departure from MAR was assumed known. Further, we evaluated a proposed graphical method, which uses the dataset with missing data, for obtaining a plausible range of values for the parameter that quantifies the magnitude of departure from MAR. RESULTS: Our simulation studies confirm that the weighting approach outperformed the MAR approach, but it still suffered from bias. In particular, our findings demonstrate that the weighting approach provides biased parameter estimates, even when a large number of imputations is performed. In the examples presented, the graphical approach for selecting a range of values for the possible departures from MAR did not capture the true parameter value of departure used in generating the data. CONCLUSIONS: Overall, the weighting approach is not recommended for sensitivity analyses following MI, and further research is required to develop more appropriate methods to perform such sensitivity analyses.