A comparison of multiple imputation methods for bivariate hierarchical outcomes

TL;DR

This study compares various multiple imputation methods for handling missing data in bivariate hierarchical outcomes in cluster randomized trials, highlighting the importance of method choice on bias and coverage.

Contribution

It provides a comprehensive simulation-based evaluation of multiple imputation approaches, emphasizing the effectiveness of multilevel imputation in clustered data scenarios.

Findings

Complete case analysis yields biased estimates when treatment is linked to missingness.

Multilevel multiple imputation achieves approximately 95% coverage across scenarios.

Fixed-effects multiple imputation often results in over-coverage, exceeding 99%.

Abstract

Missing observations are common in cluster randomised trials. Approaches taken to handling such missing data include: complete case analysis, single-level multiple imputation that ignores the clustering, multiple imputation with a fixed effect for each cluster and multilevel multiple imputation. We conducted a simulation study to assess the performance of these approaches, in terms of confidence interval coverage and empirical bias in the estimated treatment effects. Missing-at-random clustered data scenarios were simulated following a full-factorial design. An Analysis of Variance was carried out to study the influence of the simulation factors on each performance measure. When the randomised treatment arm was associated with missingness, complete case analysis resulted in biased treatment effect estimates. Across all the missing data mechanisms considered, the multiple imputation methods provided estimators with negligible bias. Confidence interval coverage was generally in excess of nominal levels (up to 99.8%) following fixed-effects multiple imputation, and too low following single-level multiple imputation. Multilevel multiple imputation led to coverage levels of approximately 95% throughout. The approach to handling missing data was the most influential factor on the bias and coverage. Within each method, the most important factors were the number and size of clusters, and the intraclass correlation coefficient.