Multiple-Imputation Variance Estimation in Studies With Missing or Misclassified Inclusion Criteria

Area of Science:

• Biostatistics
• Epidemiology
• Data Science

Background:

• Routinely collected data in observational studies often contain missing or misclassified variables that influence analysis inclusion.
• Multiple imputation is common, but standard variance estimators like Rubin's rules (RR) can be biased when imputation and analysis models are incompatible, particularly with post-imputation exclusion criteria.

Purpose of the Study:

• To illustrate and evaluate the Robins-Wang (RW) imputation variance estimator as an alternative to Rubin's rules (RR) when study exclusion criteria rely on imputed variables.
• To compare the performance of RW and RR estimators using a human immunodeficiency virus (HIV) cohort dataset and a simulation study.

Main Methods:

• Applied the Robins-Wang (RW) imputation variance estimator to a partially validated HIV cohort dataset where exclusion criteria were based on an imputed variable.
• Conducted a simulation study to compare the bias and coverage probabilities of 95% confidence intervals generated by the RW and RR estimators under varying degrees of imputation and subject exclusion.

Main Results:

• The RW estimator yielded a 29% smaller imputation variance estimate for the log odds compared to the RR estimator in the HIV cohort example.
• Simulation results indicated that RR-based confidence intervals exhibited inflated coverage probabilities, which worsened with increased imputation and exclusion rates.
• The RW estimator demonstrated superior performance in maintaining accurate coverage probabilities.

Conclusions:

• The Robins-Wang (RW) imputation variance estimator should be preferred over Rubin's rules (RR) when imputation and analysis models are incompatible, especially when exclusion criteria depend on imputed data.
• The RW method provides a more reliable approach for variance estimation in complex observational studies using routinely collected data.
• Analysis code is provided to facilitate the adoption of the RW estimator by researchers.