Comparison of imputation variance estimators.

Area of Science:

• Statistics
• Biostatistics
• Data Science

Background:

• Accurate statistical inference relies on unbiased imputation and variance estimators.
• Rubin's commonly used variance estimator may be biased if imputation and analysis models are misspecified or incompatible.
• Robins and Wang proposed a more complex alternative for such scenarios.

Purpose of the Study:

• To critically review and compare Rubin's and Robins and Wang's multiple imputation (MI) approaches.
• To evaluate a re-sampling method (full mechanism bootstrapping) and a modified Rubin's MI procedure.
• To assess performance under various misspecification and incompatibility scenarios.

Main Methods:

• Comparative analysis of multiple imputation techniques.
• Simulations were conducted under four common misspecification/incompatibility scenarios.
• An application to real-world data was performed.

Main Results:

• Robins and Wang's MI yielded narrowest confidence intervals with acceptable coverage for moderate sample sizes (n=1000).
• Rubin's MI generally outperformed other methods for small sample sizes (n=100).
• Full mechanism bootstrapping was inefficient and required strong assumptions; the modified Rubin's MI improved upon the original in misspecification cases.

Conclusions:

• Rubin's variance estimator can fail when models are incompatible or misspecified.
• Robins and Wang's MI provides more robust inferences when incompatibility/misspecification is unavoidable.
• The choice of MI method depends on sample size and the degree of model misspecification.