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Heckman imputation models for binary or continuous MNAR outcomes and MAR predictors.

Jacques-Emmanuel Galimard1,2, Sylvie Chevret3,4,5, Emmanuel Curis6,7

  • 1INSERM U1153, Epidemiology and Biostatistics Sorbonne Paris Cité Research Center (CRESS), ECSTRA team, Service de Biostatistique et Information Médicale, Hôpital Saint-Louis, AP-HP, 1 avenue Claude Vellefaux, Paris, F-75010, France. jacques-emmanuel.galimard@inserm.fr.

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Summary

This study introduces a new imputation method for handling missing data, particularly when outcomes are missing not at random (MNAR). The approach, based on Heckman

Keywords:
Heckman’s modelMissing dataMissing not at random (MNAR)Multiple imputation by chained equation (MICE)Sample selection method

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Area of Science:

  • Statistics
  • Biostatistics
  • Data Science

Background:

  • Multiple Imputation by Chained Equations (MICE) typically assumes data are missing at random (MAR).
  • Missing Not At Random (MNAR) data require specialized joint models for accurate statistical inference.
  • Heckman's model offers a framework for addressing MNAR mechanisms.

Purpose of the Study:

  • To develop and evaluate an imputation model for MNAR binary and continuous outcomes within a MICE framework.
  • To improve upon existing methods for MNAR data by incorporating Heckman's model.
  • To handle both MNAR outcomes and MAR predictors simultaneously.

Main Methods:

  • Derived a one-step maximum likelihood imputation model for MNAR binary data using Heckman's model.
  • Extended this approach to MNAR continuous outcomes, improving a two-step estimator method.
  • Simulated 1000 datasets with varying MAR and MNAR mechanisms for outcomes and MAR for predictors.

Main Results:

  • Methods employing Heckman's model demonstrated unbiasedness for MNAR outcomes.
  • The developed imputation approach significantly outperformed complete case and classical Heckman's model estimates when MAR predictors were present.
  • The proposed method effectively handled both MNAR outcomes and MAR predictors within the MICE procedure.

Conclusions:

  • A novel imputation approach effectively addresses MNAR binary or continuous outcomes under a Heckman assumption within MICE.
  • This method is particularly advantageous when MAR predictors are also present.
  • The study provides a practical solution for complex missing data scenarios in statistical analysis.