Multiple imputation of missing data under missing at random: including a collider as an auxiliary variable in the...

Area of Science:

• Epidemiology
• Biostatistics
• Statistical Modeling

Background:

• Missing data are prevalent in epidemiological studies.
• Multiple imputation (MI) is a common method for handling missing data.
• Auxiliary variables can improve MI but lack clear selection guidelines.

Purpose of the Study:

• To examine the impact of poorly chosen auxiliary variables in MI.
• To identify the consequences of using 'collider' variables in imputation models.
• To quantify bias and standard error changes due to auxiliary variable selection.

Main Methods:

• Algebraic derivations to model bias and standard error.
• Simulation studies to assess performance under various missingness scenarios.
• Analysis of bias and standard error when exposure or outcome is incomplete.

Main Results:

• Inclusion of collider auxiliary variables can induce bias and increase standard error in MI.
• Bias can be substantial when the outcome is partially observed.
• Bias is smaller when the exposure is partially observed, unless the outcome influences missingness in the exposure.

Conclusions:

• Careful selection of auxiliary variables in MI is crucial.
• Potential auxiliary variables should be evaluated for their relationship with the outcome and missingness mechanism.
• Understanding causal diagrams and missingness mechanisms is vital to avoid using colliders in MI.