Graphical Approach to Interaction

Lead Author(s): Jeff Martin, MD

Many texts use a graphical approach to depict interaction.

To determine interactions we graphically look at the presence or absence of a third variable .

No Interaction

If you look at the graph below, you will see: 0413_1nointer.JPG

Presence of the third variable: In other words in the presence of a third variable, the risk of disease in the unexposed group is 0.05 and it goes up three fold to 0.15 in the exposed group.

Absence of the third variable: In other words in the presence of a third variable, the risk of disease in the unexposed is 0.15 and it goes up three fold to 0.45 in the exposed group.

No interaction: The lines are parallel. This means that there is not interaction in terms of the risk ratio.

Interaction

If you look at the graph below, you will see: 0413_2inter.JPG

Presence of the third variable: In other words in the presence of a third variable, the risk of disease in the unexposed group is 0.05 and it goes up three fold to 0.15 in the exposed group.

Absence of the third variable: In other words in the presence of a third variable, the risk of disease in the unexposed is 0.08 and it goes up 11.2 times to 0.9 in the exposed group.

Interaction: Non-parallel lines equal interaction. This means that there is an interaction in terms of the risk ratio.

Qualitative Interaction

If you look at the graph below, you will see: 0413_3qualinter.JPG

Presence of the third variable: In other words in the presence of a third variable, the risk of disease in the unexposed group is 0.18 and it goes down to 0.13 in the exposed group. Exposed persons appear to be protected relative to exposed.

Absence of the third variable: In other words in the presence of a third variable, the risk of disease in the unexposed is 0.08 and it goes up two fold two fold to 0.19 in the exposed group. We see this in the Stanton example of smoking, caffeince use, and delayed conception.

Interaction: This is what we call qualitative interaction. The interaction is huge!