Reference-Based Multiple Imputation for Longitudinal Binary Data

In clinical trials, a treatment policy strategy is often used to handle treatment nonadherence. However, estimation in this context is complicated when data are missing after treatment deviation. Reference-based multiple imputation has been developed for the analysis of a longitudinal continuous outcome in this setting. It has been shown that Rubin's variance estimator ensures that the proportional loss of information due to missing data is approximately the same as that seen in analysis under the missing-at-random assumption for a broad range of commonly used reference-based alternatives; that is it is information anchored. However, the best way to implement reference-based multiple imputation for longitudinal binary data is unclear.

We formulate and describe two algorithms for implementing reference-based multiple imputation for longitudinal binary outcome data using: (i) joint modeling with the multivariate normal distribution and an adaptive rounding algorithm and (ii) joint modeling with a latent multivariate normal model. A simulation study was performed to compare the properties of the two methods.

Across the broad range of scenarios evaluated, the latent normal approach typically gave slightly less bias; both methods provided approximately information anchored inference. The advantage of the latent normal approach was more marked with a rarer outcome. However, both approaches may not perform satisfactorily if the outcome prevalence is very rare, that is, $$ .

Reference-based multiple imputation provides a practical information anchored tool for inferences about the treatment effect for a treatment policy estimand with a longitudinal binary outcome. The latent multivariate normal model is the preferred implementation.