Reference-Based Multiple Imputation—What is the Right Variance and How to Estimate It

Abstract

Reference-based multiple imputation methods have become popular for handling missing data in randomized clinical trials. Rubin’s variance estimator is well known to be biased compared to the reference-based imputation estimator’s true repeated sampling (frequentist) variance. Somewhat surprisingly given the increasing popularity of these methods, there has been relatively little debate in the literature as to whether Rubin’s variance estimator or alternative (smaller) variance estimators targeting the repeated sampling variance are more appropriate. We review the arguments made on both sides of this debate, and argue that the repeated sampling variance is more appropriate. We review different approaches for estimating the frequentist variance, and suggest a recent proposal for combining bootstrapping with multiple imputation as a widely applicable general solution. At the same time, in light of the consequences of reference-based assumptions for frequentist variance, we believe further scrutiny of these methods is warranted to determine whether the strength of their assumptions is generally justifiable.

KEYWORDS:

• Clinical trials
• Missing data
• Sensitivity analysis

Acknowledgments

The author’s institution has received consultancy fees for the author’s advice on statistical methodology from AstraZeneca, Bayer, Novartis, Roche. The author has received consultancy fees from Bayer. The author has received fees for provision of online courses from Roche.

Funding

The author(s) reported there is no funding associated with the work featured in this article.

Additional information

Funding

This work was supported by the UK Medical Research Council (Grant MR/T023953/1).