Comparison of imputation variance estimators

Rachael A. Hughes*, J. A C Sterne, K. Tilling

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

23 Citations (Scopus)


Appropriate imputation inference requires both an unbiased imputation estimator and an unbiased variance estimator. The commonly used variance estimator, proposed by Rubin, can be biased when the imputation and analysis models are misspecified and/or incompatible. Robins and Wang proposed an alternative approach, which allows for such misspecification and incompatibility, but it is considerably more complex. It is unknown whether in practice Robins and Wang's multiple imputation procedure is an improvement over Rubin's multiple imputation. We conducted a critical review of these two multiple imputation approaches, a re-sampling method called full mechanism bootstrapping and our modified Rubin's multiple imputation procedure via simulations and an application to data. We explored four common scenarios of misspecification and incompatibility. In general, for a moderate sample size (n = 1000), Robins and Wang's multiple imputation produced the narrowest confidence intervals, with acceptable coverage. For a small sample size (n = 100) Rubin's multiple imputation, overall, outperformed the other methods. Full mechanism bootstrapping was inefficient relative to the other methods and required modelling of the missing data mechanism under the missing at random assumption. Our proposed modification showed an improvement over Rubin's multiple imputation in the presence of misspecification. Overall, Rubin's multiple imputation variance estimator can fail in the presence of incompatibility and/or misspecification. For unavoidable incompatibility and/or misspecification, Robins and Wang's multiple imputation could provide more robust inferences.

Original languageEnglish
Pages (from-to)2541-2557
Number of pages17
JournalStatistical Methods in Medical Research
Issue number6
Early online date28 Mar 2014
Publication statusPublished - 1 Dec 2016


  • bootstrap confidence intervals
  • imputation inference
  • missing data
  • multiple imputation
  • variance estimator


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