Abstract
BackgroundMultiple 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.MethodsIn 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.ResultsOur 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.ConclusionsOverall, 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.Electronic supplementary materialThe online version of this article (doi:10.1186/s12874-015-0074-2) contains supplementary material, which is available to authorized users.
Highlights
Multiple imputation (MI) is a well-recognised statistical technique for handling missing data
In this paper we comprehensively evaluate the weighting approach for performing a sensitivity analysis after implementing the standard MI procedure under the Missing at random’ (MAR) assumption, and describe possible problems that might arise from applying this approach
Illustration using a single simulated dataset Complete case analysis and MI under MAR were used for handling missing data and the weighting approach was performed as a sensitivity analysis under Missing not at random’ (MNAR) following MI
Summary
Multiple imputation (MI) is a well-recognised statistical technique for handling missing data. 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. Multiple imputation (MI), which is widely available in standard software packages (e.g. R [9], SAS [10] and Stata [11]), is one of the most flexible approaches for handling missing data [12,13,14]. Each completed dataset is analysed separately using standard statistical methods, and the resulting point and interval estimates are combined using Rubin’s rules to obtain an overall MI inference for the parameter(s) of interest [7, 15, 16]
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