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Multiple imputation provides us with efficient estimators in model-basedmethods for handling missing data under the true model. It is alsowell-understood that design-based estimators are robust methods that do notrequire accurately modeling the missing data; however, they can be inefficient.In any applied setting, it is difficult to know whether a missing data modelmay be good enough to win the bias-efficiency trade-off. Raking of weights isone approach that relies on constructing an auxiliary variable from dataobserved on the full cohort, which is then used to adjust the weights for theusual Horvitz-Thompson estimator. Computing the optimally efficient rakingestimator requires evaluating the expectation of the efficient score given thefull cohort data, which is generally infeasible. We demonstrate multipleimputation (MI) as a practical method to compute a raking estimator that willbe optimal. We compare this estimator to common parametric and semi-parametricestimators, including standard multiple imputation. We show that whileestimators, such as the semi-parametric maximum likelihood and MI estimator,obtain optimal performance under the true model, the proposed raking estimatorutilizing MI maintains a better robustness-efficiency trade-off even under mildmodel misspecification. We also show that the standard raking estimator,without MI, is often competitive with the optimal raking estimator. Wedemonstrate these properties through several numerical examples and provide atheoretical discussion of conditions for asymptotically superior relativeefficiency of the proposed raking estimator.

Combining multiple imputation with raking of weights: An efficient and robust approach in the setting of nearly-true models