A Note on formulae for causal mediation analysis in an odds ratiocontext

Area of Science:

• Epidemiology
• Causal Inference
• Biostatistics

Background:

• Causal mediation analysis is crucial for understanding complex relationships.
• Previous methods by VanderWeele and Vansteelandt (VWV) relied on assumptions of normal mediator distribution and rare outcomes.
• These assumptions limit applicability in routine epidemiologic settings with skewed mediator distributions or non-rare diseases.

Purpose of the Study:

• To derive robust closed-form expressions for natural direct and indirect effects in causal mediation analysis.
• To relax restrictive assumptions of normality and rare outcomes in existing formulas.
• To provide alternative formulas applicable to a wider range of epidemiologic scenarios.

Main Methods:

• Building upon Judea Pearl's causal mediation framework.
• Deriving closed-form expressions for natural direct and indirect effects.
• Investigating the impact of relaxing mediator normality and rare outcome assumptions.
• Introducing the Bridge distribution for non-rare disease scenarios.

Main Results:

• VWV formulas for natural direct and indirect effects remain valid without mediator normality if no mediator-exposure interaction exists.
• When interaction is relaxed, VWV's indirect effect formula still applies without mediator normality.
• A new formula for the natural direct effect is derived when interaction is relaxed.
• Simple closed-form formulae are obtained for natural direct and indirect effects when mediators follow a Bridge distribution for non-rare diseases.

Conclusions:

• The study provides more flexible and widely applicable formulas for causal mediation analysis.
• These enhanced formulas accommodate non-normal mediator distributions and non-rare outcomes.
• The findings improve the utility of causal mediation analysis in diverse epidemiologic research.