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

In observational studies using routinely collected data, a variable with a high level of missingness or misclassification may determine whether an observation is included in the analysis. In settings where inclusion criteria are assessed after imputation, the popular multiple-imputation variance estimator proposed by Rubin ("Rubin's rules" (RR)) is biased due to incompatibility between imputation and analysis models. While alternative approaches exist, most analysts are not familiar with them. Using partially validated data from a human immunodeficiency virus cohort, we illustrate the calculation of an imputation variance estimator proposed by Robins and Wang (RW) in a scenario where the study exclusion criteria are based on a variable that must be imputed. In this motivating example, the corresponding imputation variance estimate for the log odds was 29% smaller using the RW estimator than using the RR estimator. We further compared these 2 variance estimators with a simulation study which showed that coverage probabilities of 95% confidence intervals based on the RR estimator were too high and became worse as more observations were imputed and more subjects were excluded from the analysis. The RW imputation variance estimator performed much better and should be employed when there is incompatibility between imputation and analysis models. We provide analysis code to aid future analysts in implementing this method.