A scaled sample space cube used to illustrate attributable fractions.

Area of Science:

• Epidemiology
• Statistical Graphics
• Data Visualization

Background:

• Understanding the association between multiple explanatory variables and categorical responses is crucial in epidemiology.
• Existing methods for visualizing complex relationships and attributable fractions can be challenging to interpret.
• Communicating epidemiological risk factors and their impact requires accessible graphical tools.

Purpose of the Study:

• To propose a novel three-dimensional (3D) graphic method for displaying associations between multiple explanatory variables and a categorical response.
• To illustrate the concept of attributable fractions in epidemiology, specifically disease risk reduction.
• To extend the method for visualizing the impact of modifying exposure distributions or removing exposures on disease risk.

Main Methods:

• Combines techniques from mosaic displays and scaled Venn diagrams into a 3D representation.
• Utilizes a scaled sample space cube to depict relationships and attributable fractions.
• Applies the method to theoretical models and real-world data, including the Hordaland study on obstructive lung disease.

Main Results:

• The 3D graphic method effectively displays the association structure between multiple variables and a categorical response.
• The method successfully illustrates disease risk reduction and the impact of exposure modifications.
• Demonstrations show the utility in understanding attributable fractions related to smoking and occupational exposures.

Conclusions:

• The proposed 3D graphic method offers an intuitive way to visualize complex epidemiological data and attributable fractions.
• This approach enhances communication of disease risk concepts to statisticians, medical professionals, and the public.
• The underlying principle of adding a third dimension to graphical displays has broader applications in statistical analysis, such as residual analysis.