Definition and identification of causal ratio effects

Area of Science:

• Statistics
• Causal Inference
• Epidemiology

Background:

• Ratio effect measures like risk and odds ratios are commonly used in generalized linear models.
• Concerns exist regarding the causal interpretation of these ratio measures due to issues like noncollapsibility.

Purpose of the Study:

• To provide a comprehensive derivation and definition of ratio effect measures within causal inference frameworks.
• To examine the identifiability of simple ratios and odds ratios under various causality conditions.
• To propose an alternative, identifiable computation for ratio effects.

Main Methods:

• Defining simple ratios and odds ratios based on the stochastic theory of causal effects.
• Analyzing the identifiability of expected ratio effects under four specified causality conditions.
• Developing an alternative ratio effect computation as a ratio of causally unbiased expectations.

Main Results:

• Demonstrates how simple and odds ratios can be formally defined using causal effect stochastic theory.
• Identifies conditions under which expectations of these ratio measures are identifiable.
• Presents an alternative ratio effect computation that is identifiable under all considered causality conditions.

Conclusions:

• Ratio effect measures can be rigorously defined and analyzed within causal inference.
• The proposed alternative computation offers a robust method for estimating ratio effects, consistent with difference effects.
• This work addresses a gap in the literature regarding the causal identification of ratio effect measures.