Appropriate inclusion of interactions was needed to avoid bias in multiple imputation

Objective

Missing data are a pervasive problem, often leading to bias in complete records analysis (CRA). Multiple imputation (MI) via chained equations is one solution, but its use in the presence of interactions is not straightforward .

Study Design and Setting

We simulated data with outcome Y dependent on binary explanatory variables X and Z and their interaction XZ. Six scenarios were simulated (Y continuous and binary, each with no interaction, a weak and a strong interaction), under 5 missing data mechanisms. We use DAGs to identify when CRA and MI would each be unbiased. We evaluate the performance of CRA, MI without interactions, MI including all interactions, and stratified imputation. We also illustrated these methods using a simple example from the National Child Development Study (NCDS).

Results

MI excluding interactions is invalid, and resulted in biased estimates and low coverage. When XZ was zero, MI excluding interactions gave unbiased estimates but over-coverage. MI including interactions and stratified MI gave equivalent, valid inference in all cases. In the NCDS example, MI excluding interactions incorrectly concluded there was no evidence for an important interaction.

Conclusions

Epidemiologists carrying out MI should ensure that their imputation model(s) are compatible with their analysis model.