Rejoinder to the letter: "Standard and reference-based conditional mean imputation: Regulators and trial statisticians be aware!"

Abstract

We appreciate Cro et al.'s efforts to bring wider attention to the debate surrounding variance estimation for reference-based imputation methods. However, we believe that the way this debate is presented as "multiple imputation" versus "conditional mean imputation" can be misleading. Both of these imputation methods rely on identical assumptions and provide essentially identical treatment effect estimates. While conditional mean imputation naturally focuses on the frequentist repeated sampling variance, we show here that it can be easily adapted to target a variance with similar properties to Rubin's variance. Therefore, conditional mean imputation combined with jackknife resampling remains a valid and effective deterministic method for handling missing data under missing-at-random or reference-based assumptions regardless of the user's preference for variance estimation. We also reappraise the frequentist variance by arguing that it correctly reflects the strong assumptions of reference-based imputation. In contrast, we are not aware of any frequentist or Bayesian framework under which Rubin's variance provides correct inference.