Making apples from oranges: Comparing noncollapsible effect estimators and their standard errors after adjustment for...

Area of Science:

• Biostatistics
• Epidemiology
• Causal Inference

Background:

• Effect measure collapsibility in regression models is often misunderstood.
• Conditional and marginal effect measures are frequently confused.

Purpose of the Study:

• To clarify the issue of (non)collapsibility of effect measures in regression models.
• To propose and evaluate methods for marginalizing conditional odds and hazard ratios.
• To provide an educational summary of collapsibility from a causal inference perspective.

Main Methods:

• Described an existing procedure for marginalizing conditional odds ratios.
• Proposed a new procedure for marginalizing conditional hazard ratios, accounting for right censoring.
• Evaluated the proposed methods through simulation studies and a reanalysis of existing trial data.

Main Results:

• Demonstrated the performance of the proposed marginalization procedures.
• Highlighted the importance of distinguishing between conditional and marginal effect measures.
• Showcased the practical application in analyzing primary biliary cirrhosis data.

Conclusions:

• The distinction between conditional (adjusted) and marginal (unadjusted) effect measures is crucial in regression analysis.
• The proposed methods offer practical solutions for obtaining marginal effect estimates.
• Improved understanding of collapsibility enhances causal inference from observational and experimental data.