A method of quantify confounding in regression analyses applied to data on diet and CHD incidence

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Linear regression analysis is widely used in scientific research.
• High correlation among independent variables (multicollinearity) can complicate interpretation of results.
• Existing methods may yield inconsistent findings, particularly stepwise regression.

Purpose of the Study:

• To present a novel method for visualizing and interpreting linear regression results with highly correlated independent variables.
• To decompose the sum of squares of regression (SSR) into orthogonal and shared components.
• To explain inconsistencies observed between forward and backward stepwise regression analyses.

Main Methods:

• The proposed method partitions the SSR for pairs of variables into orthogonal and shared components.
• A shared component quantifies the reduction in SSR when one variable is added to the regression equation containing another.
• The method was demonstrated by reanalyzing data on coronary heart disease (CHD) and diet.

Main Results:

• The analysis revealed how the SSR for a single variable is influenced by other variables in the regression model.
• Apparent contradictions between forward and backward stepwise regression were explained by this partitioning method.
• Dietary analysis indicated carbohydrate and alcohol intake are negatively associated with CHD due to caloric intake, while protein and fat intake are associated with both increased caloric intake and CHD risk factors.

Conclusions:

• The developed method provides a clearer understanding of variable contributions in multicollinear regression.
• This approach resolves inconsistencies in stepwise regression, enhancing analytical transparency.
• The reanalysis of CHD data highlights the complex interplay between diet, caloric intake, and cardiovascular risk.