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Determining the number of imputations for multiple imputation is crucial. More imputations are needed for stable standard error estimates, increasing quadratically with missing data, not linearly.

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Area of Science:

  • Statistics
  • Data Science
  • Biostatistics

Background:

  • Multiple imputation is a common technique for handling missing data in statistical analyses.
  • Existing recommendations for the number of imputations (2-10) primarily focus on the efficiency of point estimates, not the stability of standard error estimates.

Purpose of the Study:

  • To determine the number of imputations required for stable standard error (SE) estimates in multiple imputation.
  • To propose a method for calculating the necessary number of imputations for replicable SE estimates.

Main Methods:

  • Investigated the relationship between the fraction of missing information and the number of imputations needed for SE replicability.
  • Developed and implemented a two-stage procedure using a SAS macro (%mi_combine) and a Stata command (how_many_imputations) to guide imputation number selection.

Main Results:

  • The number of imputations required for stable SE estimates increases quadratically with the fraction of missing information.
  • Previous linear assumptions for SE stability are insufficient; more imputations are needed than commonly recommended.

Conclusions:

  • A pilot analysis followed by calculation using the proposed two-stage procedure ensures adequate imputations for replicable SE estimates.
  • The new SAS macro and Stata command facilitate the practical application of this evidence-based approach to multiple imputation.