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A stacked approach for chained equations multiple imputation incorporating the substantive model.

Lauren J Beesley1, Jeremy M G Taylor1

  • 1University of Michigan, Department of Biostatistics, Ann Arbor, Michigan.

Biometrics
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PubMed
Summary

This study introduces imputation stacking to handle missing data, ensuring analysis models are compatible with imputation. This novel method, using weighted analysis on stacked data, offers a flexible approach for complex missing data scenarios.

Keywords:
chained equationsmultiple imputationstacked imputationsubstantive model compatible imputation

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Area of Science:

  • Statistics
  • Data Science
  • Biostatistics

Background:

  • Multiple Imputation by Chained Equations (MICE) is widely used for missing data.
  • Incorporating outcome information into MICE covariate imputation models is challenging, especially for complex outcomes.
  • Ensuring congeniality between imputation and analysis models is crucial for valid results.

Purpose of the Study:

  • To propose a novel strategy for handling missing data by directly incorporating the analysis model into the imputation process.
  • To develop a method that ensures the imputation model is congruent with the intended analysis model.
  • To provide a flexible and widely applicable approach for analyzing stacked multiple imputations.

Main Methods:

  • Multiple imputations of missing covariates are generated without using outcome information.
  • Imputation stacking is employed, creating a large dataset by stacking imputations.
  • The analysis model is incorporated using weights, fitting a weighted version of the model on the stacked data.
  • A novel estimator for standard errors is proposed, based on the observed data information principle.

Main Results:

  • The proposed method directly incorporates the analysis model into missing data handling.
  • Parameter estimates are obtained by fitting a weighted analysis model on the stacked data, bypassing Rubin's combining rules.
  • A new estimator for standard errors in stacked and weighted analyses is introduced.
  • The approach is applicable to a broad range of standard analysis models and missing data settings.

Conclusions:

  • The imputation stacking method offers a novel and effective way to handle missing data, particularly when complex outcomes are involved.
  • This approach ensures congeniality between imputation and analysis models, leading to more reliable results.
  • The R package StackImpute facilitates the application of this method across various statistical analyses and missing data situations.