- Definition of Multiplicative Interaction
- Assessment of Whether Interaction Is Present
- Presence of Multiplicative Interaction - Absence of Additive Interaction
- Presence of Multiplicative Interaction - May Have Additive Interaction
- Presence of Qualitative Multiplicative Interaction = Qualitative Additive Interaction
- Choosing Multiplicative Measures

When there is interaction in terms of the difference measure of association or the risk difference, we call it an **additive interaction**.

In the Stanton example with smoking, caffeine use, and delayed conception below

- we call this
**multiplicative interaction**because there is interaction in terms of the measure of association or the risk ratio.

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 **additive interaction** (when an effect is truly present)

- implies presence of
**multiplicative interaction**as seen in the graph below.

Here, the risk difference is 0.1 in both strata of the third variable.

The risk ratio differs between strata (1.7 and 3.0) -- **multiplicative interaction** is present.

- In the graph below, we see that despite the presence of
**multiplicative interaction**, (RR 2.0 and RR 3.0) - the risk difference is 0.1 in both strata of the third variable - ie no additive interaction.

In the graph below, there is again

- but risk difference in one stratum is 0.1 and 0.4 in another -
- i.e., additive interaction is present.

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

An example can be found in Stanton's Study of caffeine use, smoking, and delayed concenception.

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

**Multiplicative measures** (e.g., risk ratio)

- Favored measure when looking for causal association (etiologic research)
- Not dependent upon background incidence of disease

Topic revision: r15 - 05 Jun 2009 - 16:21:06 - MaryB?

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