Joint modelling rationale for chained equations.

Area of Science:

• Statistics
• Medical Research Methodology

Background:

• Chained equations imputation is a flexible method for handling diverse variable types in medical research.
• It relies on conditional models, offering advantages over joint modeling but may not align with a joint distribution if models are incompatible.
• Previous work suggests equivalence between chained equations and joint modeling imputation in finite samples.

Purpose of the Study:

• To establish sufficient conditions for chained equations and joint modeling to produce imputations from the same predictive distribution in finite samples.
• To investigate the consequences of violated conditions, particularly when conditional models are compatible but other assumptions are not met.

Main Methods:

• Developed a theoretical proof for sufficient conditions linking chained equations and joint modeling imputation.
• Applied the proof to four specific scenarios.
• Conducted a simulation study to assess the impact of incompatible conditions, focusing on order effects.

Main Results:

• Introduced a "non-informative margins" condition, which, alongside model compatibility, ensures equivalence.
• Demonstrated that this condition is often unmet, even with compatible conditional models (e.g., two continuous and one binary variable).
• Simulation results revealed order effects (variable ordering influencing imputation) when the non-informative margins condition is violated, though these effects were generally small, especially with weak variable associations.

Conclusions:

• Order effects in chained equations imputation are likely common in medical research datasets with mixed variable types.
• Despite their prevalence, these order effects may be small enough to be considered negligible in many practical applications.