Robust variance estimation for multiple imputation using predictive mean matching or parametric imputation models
Multiple imputation (MI) is widely used for handling missing data in medical research, with variance commonly estimated using Rubin's rules (RR). RR is simple to apply, but under uncongeniality between the imputation and analysis procedures, its variance estimate can be either too small or too large, leading to miscalibrated confidence intervals. Robins and Wang (RW) developed an estimating-equation variance estimator that does not require congeniality under the conditions of their parametric imputation framework. Practical use of RW, however, has been limited by the lack of accessible software and by the additional variance calculations required for modern imputation workflows. We develop an R package, rw, construct RW variance components for normal and logistic conditional imputation models fitted through mice, and propose an approximate RW variance procedure for predictive mean matching (PMM). The PMM procedure preserves the original imputations and selected donors. For the variance calculation, we define differentiable donor probabilities and use expected analysis scores to approximate the cross-moment between analysis and imputation scores. Analysis scores are summed by recorded donor to account for donor reuse. We evaluate the proposed methods in benchmark simulations based on the original RW setting and in validation-study simulations motivated by electronic health record data. RR coverage was up to approximately 23 percentage points below the nominal 95% level in some settings and above nominal in others. The proposed RW estimators generally produced coverage closer to the nominal level in larger samples under both parametric and PMM imputation, while retaining the same completed-data point estimates as RR.