Improved methods for estimating fraction of missing information in multiple imputation

Multiple imputation (MI) has become the most popular approach in handling missing data. Closely associated with MI, the fraction of missing information (FMI) is an important parameter for diagnosing the impact of missing data. Currently γ(m), the sample value of FMI estimated from MI of a limited m, is used as the estimate of γ(0), the population value of FMI, where m is the number of imputations of the MI. This FMI estimation method, however, has never been adequately justified and evaluated. In this paper, we quantitatively demonstrated that E(γ(m)) decreases with the increase of m so that E(γ(m)) > γ(0) for any finite m. As a result γ(m) would inevitably overestimate γ(0). Three improved FMI estimation methods were proposed. The major conclusions were substantiated by the results of the MI trials using the data of the 2012 Physician Workflow Mail Survey of the National Ambulatory Medical Care Survey, USA.