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For missing data, imputing underlying continuous variables is better than binary. The substantive-model compatible fully conditional specification (SMC-FCS) method demonstrated superior performance in simulation studies for handling missing at random data.

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binary variablecompatibilityfully conditional specificationmultiple imputationmultivariate normal imputation

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Area of Science:

  • Statistics
  • Biostatistics
  • Data Science

Background:

  • Multiple imputation (MI) is a common technique for handling missing at random (MAR) data.
  • Continuous variables are frequently, yet often inappropriately, recoded into binary variables for analysis.
  • Imputation and analysis models should be compatible, ideally imputing variables in the form they are used in analysis.

Purpose of the Study:

  • To investigate optimal methods for imputing binary variables derived from underlying continuous variables.
  • To compare the performance of various imputation strategies under MAR conditions.
  • To evaluate the impact of recoding continuous variables on imputation accuracy.

Main Methods:

  • A simulation study was conducted using a continuous outcome and a binary covariate derived from an underlying continuous variable.
  • Data were simulated with varying sample sizes and MAR percentages (25%, 50%) for the covariate.
  • Five imputation methods were compared: binary logistic regression, continuous linear regression followed by categorization, standard fully conditional specification (FCS), multivariate normal imputation, and substantive-model compatible (SMC) FCS.

Main Results:

  • Imputing only the continuous variable resulted in substantial bias and large standard errors.
  • Standard FCS and multivariate normal imputation methods showed adequate performance but encountered mathematical difficulties.
  • The substantive-model compatible (SMC) FCS method exhibited the best performance across the simulated scenarios.

Conclusions:

  • Imputing the underlying continuous variable is generally more accurate than imputing the recoded binary variable.
  • The SMC-FCS method is recommended for imputing binary variables derived from continuous data due to its superior performance and stability.
  • Careful consideration of imputation model compatibility with the analysis model is crucial for valid results in missing data analysis.