Additive Interaction

Lead Author(s): Jeff Martin, MD

Definition of Additive Interaction

When there is interaction in terms of the difference measure of association or the risk difference. When there is interaction in terms of the ratio measure of association or the risk ratio,

Example of Additive Interaction

Risk difference or RD is the absolute difference between exposed and unexposed. When there is interaction in terms of the ratio measure of association (in this case, the risk ratio), we call this multiplicative interaction.


This is called additive interaction because there is a difference in risk between the caffeine users and the non-caffeine users. (Some texts call this attributable risk.)

Assessment of Whether Interaction Is Present

Assessment of whether interaction is present depends upon the measure of association:

(1) Ratio measures (multiplicative interaction)

(2) Difference measures additive interaction.

So, when talking about interaction, we have to be precise about whether we are talking about interaction of ratio measures (i.e., multiplicative interaction) or interaction of differences measures (i.e., additive interaction) or both. That’s why some like to call this effect-measure modification, because whether or not interaction is occurring depends upon the measure of association in question.

Absence of Multiplicative Interacton- Presence of Additive Interaction

Absence of multiplicative interaction typically implies presence of additive interaction as seen in graph below.

As you can see here, although there is no interaction for the ratio of risks, 0413_12add_nomulti.JPG

When the third variable is present, the risk difference is 0.1, but when the third variable is absent the risk difference is 0.3.

Presence of Additive Interaction May Have Multiplicative Interaction

The presence of additive interaction may or may not be accompanied by multiplicative interaction. 0413_13a_add_multi.JPG

Presence of Qualtiative Multiplicative Interaction = Qualitiative Additive Interaction

Presence of qualitative multiplicative interaction is always accompanied by qualitative additive interaction.

Choosing Additive Measures

Which do you want to use: additive versus multiplicative measures?

Additive measures (e.g., risk difference): e.g. 1/risk difference = number needed to treat to prevent (or avert) one case of disease or

Minor vs Major Public Health Importance

Causally related but minor public health importance: Consider the figure below.

A simple way to infer this is if you took 100000 exposed persons and then took away their exposure, you would end up 5 cases of disease (the background) and 5 cases of disease averted.

Causally related and major public health importance: Consider the figure below.


Reporting: Additive Interaction or Risk Ratio?

Let's look at the figure below from a hypothetical example of a cohort study. In the figure below we see that there is not multiplicative interaction, the risk ratios are the same in both strata (RR 2.0). 0414_3smoking.JPG

Goal: Etiology/Risk Factor - If your goal was simply to assess whether smoking was a risk factor, you would probably go with the risk ratio of 2 and not bother to report the additive interaction to your readers. After all, it is much easier to report just one number instead of two particularly when your study may have many different risk factors.

Goal: Defining Sub-groups to Target - But say you already had a pretty good sense that smoking was a risk factor and now your goal is to see where you can have the most impact in terms of getting persons to stop smoking. So, if your goal is to identify subgroups of persons to target with an intervention (say a smoking cessation intervention), then you have actually found something interesting. The impact of an intervention would differ depending upon the third variable, family history. Hence, it is well worth it to report the presence of interaction based upon family history. This is the mathematical basis of choosing high risk groups when searching for the targets for such interventions.