Bias and efficiency of multiple imputation compared with complete-case analysis for missing covariate values
Article first published online: 13 SEP 2010
Copyright © 2010 John Wiley & Sons, Ltd.
Statistics in Medicine
Volume 29, Issue 28, pages 2920–2931, 10 December 2010
How to Cite
White, I. R. and Carlin, J. B. (2010), Bias and efficiency of multiple imputation compared with complete-case analysis for missing covariate values. Statist. Med., 29: 2920–2931. doi: 10.1002/sim.3944
- Issue published online: 22 NOV 2010
- Article first published online: 13 SEP 2010
- Manuscript Accepted: 19 MAR 2010
- Manuscript Received: 3 NOV 2008
- missing data;
- multiple imputation;
- complete-case analysis;
- missing covariates
When missing data occur in one or more covariates in a regression model, multiple imputation (MI) is widely advocated as an improvement over complete-case analysis (CC). We use theoretical arguments and simulation studies to compare these methods with MI implemented under a missing at random assumption.
When data are missing completely at random, both methods have negligible bias, and MI is more efficient than CC across a wide range of scenarios. For other missing data mechanisms, bias arises in one or both methods. In our simulation setting, CC is biased towards the null when data are missing at random. However, when missingness is independent of the outcome given the covariates, CC has negligible bias and MI is biased away from the null. With more general missing data mechanisms, bias tends to be smaller for MI than for CC.
Since MI is not always better than CC for missing covariate problems, the choice of method should take into account what is known about the missing data mechanism in a particular substantive application. Importantly, the choice of method should not be based on comparison of standard errors. We propose new ways to understand empirical differences between MI and CC, which may provide insights into the appropriateness of the assumptions underlying each method, and we propose a new index for assessing the likely gain in precision from MI: the fraction of incomplete cases among the observed values of a covariate (FICO). Copyright © 2010 John Wiley & Sons, Ltd.