Conditional and marginal relative risk parameters for a class of recursive regression graph models

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Distortion of effects after marginalizing variables is a known issue in linear regression.
• While well-established for Gaussian variables, challenges remain for discrete variables, particularly in medical and social sciences.
• Existing generalizations beyond linear Gaussian models are limited for discrete data.

Purpose of the Study:

• To propose a multivariate regression framework for binary data.
• To derive a multivariate Relative Risk formula to define the relationship between marginal and conditional relative risks.
• To assess the effect of preoperative oral morphine on postoperative pain relief using the developed method.

Main Methods:

• Development of a multivariate regression framework for binary data.
• Regression coefficients are defined as the logarithm of relative risks.
• Derivation of a multivariate Relative Risk formula.

Main Results:

• A novel method for analyzing the relationship between marginal and conditional relative risks in binary data is presented.
• The proposed framework provides a way to address confounding and effect modification in discrete outcome settings.
• The analysis of morphine data demonstrated the practical application of the method.

Conclusions:

• The proposed multivariate regression framework offers a valuable tool for analyzing binary data in medical and social sciences.
• The derived multivariate Relative Risk formula clarifies the interplay between marginal and conditional risks.
• The method is effective for assessing treatment effects, such as oral morphine on pain relief.