Multiple imputation of missing data under missing at random: compatible imputation models are not sufficient to avoid bias if they are mis-specified

Objectives: Epidemiological studies often have missing data, which are commonly handled by multiple imputation (MI). Standard (default) MI procedures use simple linear covariate functions in the imputation model. We examine the bias that may be caused by accep-tance of this default option and evaluate methods to identify problematic imputation models, providing practical guidance for researchers. Study Design and Setting: Using simulation and real data analysis, we investigated how imputation model mis-specification affected MI performance, comparing results with complete records analysis (CRA). We considered scenarios in which imputation model mis-specification occurred because (i) the analysis model was mis-specified or (ii) the relationship between exposure and confounder was mis-specified. Results: Mis-specification of the relationship between outcome and exposure, or between exposure and confounder, can cause biased CRA and MI estimates (in addition to any bias in the full-data estimate due to analysis model mis-specification). MI by predictive mean matching can mitigate model mis-specification. Methods for examining model mis-specification were effective in identifying mis-specified relationships. Conclusion: When using MI methods that assume data are MAR, compatibility between the analysis and imputation models is neces-sary, but not sufficient to avoid bias. We propose a step-by-step procedure for identifying and correcting mis-specification of imputation models. & COPY; 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).

Automated summary

Epidemiological studies often have missing data, which are commonly handled by multiple imputation (MI). This study examines the bias caused by the default option of using simple linear covariate functions in the imputation model and provides practical guidance for researchers. The results show that mis-specification of the relationship between outcome and exposure, or between exposure and confounder, can cause bias in MI estimates, and the method of predictive mean matching can mitigate model mis-specification.