Alternative implementation of reference-based controlled imputation procedures

Reference-based controlled imputations have become a popular tool to assess the sensitivity of primary analysis inference to different post-dropout assumptions and to yield an alternative effectiveness estimand of treatment effect. As the imputation and analysis models are uncongenial in this setting, Rubin’s variance estimator overestimates the repeated sampling variability of the multiple imputation estimator of treatment effect. On the other hand, since reference-based methods borrow information across arms, the sampling variance of treatment effect estimator decreases as the proportion of missing data increases, rendering it inappropriate for use in sensitivity analysis. We propose to decouple the variance estimation from information borrowing by using a delta-adjusted pattern mixture model with delta-adjustments fixed at the maximum likelihood estimate. Reference-based pattern-mixture models can thus be embedded in the sensitivity analysis using delta-adjusted pattern-mixture models by identifying a scalar sensitivity parameter value to match the treatment effect estimate. We provide both theoretical and empirical justifications of the proposal approach and illustrate its use in the analysis of a clinical trial of major depressive disorders. Supplementary materials for this article are available online.