Improved methods for estimating fraction of missing information in multiple imputation

Area of Science:

• Statistics
• Biostatistics
• Data Science

Background:

• Multiple imputation (MI) is a widely adopted statistical technique for addressing missing data in research.
• The fraction of missing information (FMI) quantifies the impact of missing data, guiding analysis decisions.
• Current estimation of FMI (γm) relies on the number of imputations (m) but lacks rigorous justification.

Purpose of the Study:

• To evaluate the accuracy of the current sample-based FMI estimation method (γm).
• To demonstrate the inherent overestimation of the population FMI (γ0) by γm.
• To propose and validate improved methods for FMI estimation.

Main Methods:

• Quantitative analysis demonstrating the relationship between the number of imputations (m) and the expected value of γm (E(γm)).
• Theoretical evaluation showing E(γm) > γ0 for finite m.
• Empirical validation using data from the 2012 Physician Workflow Mail Survey (National Ambulatory Medical Care Survey, USA).

Main Results:

• The expected value of the sample FMI (E(γm)) decreases as the number of imputations (m) increases.
• Consequently, γm systematically overestimates the true population FMI (γ0) for any finite m.
• Three novel and improved FMI estimation methods were developed and tested.

Conclusions:

• The current method for estimating FMI using multiple imputation is biased and overestimates the true impact of missing data.
• Improved FMI estimation methods are necessary for accurate assessment of missing data in statistical analyses.
• Empirical evidence supports the proposed improvements, enhancing the reliability of missing data diagnostics.