# Interaction

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## Biostatistics and epidemiology

#### Epidemiology

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A randomized controlled trial is conducted to study the effects of baseline BMI on the incidence of gestational hypertension in pregnant women. Initial analysis shows an attributable risk (AR) of 12% in individuals with a BMI of >30 kg/m^{2} at baseline. Multiparity is considered an important covariable, so a stratified analysis is conducted. Among multiparas with BMI <30 kg/m^{2}, the AR is 6%. Finally, the attributable risk for multiparous women with BMI >30 kg/m^{2} is 72%. Considering the absolute risk of gestational hypertension to be 3% in nulliparous women with BMI <30 kg/m^{2}, which of the following is the most likely cause of the observed findings?

### Interaction exam links

#### Content Reviewers:

Rishi Desai, MD, MPH#### Contributors:

Justin Ling, MD, MS, Evan Debevec-McKenneyThe word “interaction” can refer to biological interaction - which is where two exposures like radon gas and toxins in cigarettes work together to influence an outcome - like lung cancer.

But the word “interaction” can also refer to statistical interaction, also called effect modification, which is the statistical methodology used to find out if there’s a biological interaction.

Most diseases are caused by multiple exposures that work together, like our example of radon gas and smoking cigarettes leading to lung cancer.

Radon is a radioactive gas that gets released from the decay of elements like uranium and radium in rocks and soil.

It can be found in dust particles in the air, so most people breathe in a low level of radon every day.

Unfortunately, radon causes mutations in DNA and people who breathe in high levels of radon have an increased risk of lung cancer.

Similarly, people who smoke cigarettes have a higher risk of lung cancer because of tobacco contains various toxins that also mutate the DNA.

In addition, cigarette smoke harms the cilia in the lungs. Those are the little hairlike structures that normally clear out things like mucus, dust particles, and chemicals.

Damaged cilia is a big problem for people who are exposed to high levels of radon, because the lungs can’t get rid of radon-containing dust.

This is an example of biological interaction, because even though radon and smoking can both separately cause lung cancer, they also work together to amplify the risk.

Statistical interaction can help us figure out how much the risk increases for people who are exposed to both factors compared to people who are exposed to one factor or the other.

Statistical interaction can be assessed by comparing the effect of one exposure on the outcome in each strata or level of the other exposure.

For example, you could figure out how smoking affects the risk of lung cancer among people exposed to high levels of radon, and how it affects the risk of lung cancer among people exposed to low levels of radon.

To do this, you might start by looking at the crude or unstratified effect, so you’d recruit 100 people who smoke and 100 people who don’t smoke, and compare the proportion of people in each group who develop lung cancer in the next ten years.

Let’s say you find an overall relative risk, or crude effect, of 7.5 - so people that smoke have 7.5 times the risk of developing lung cancer, compared to people that don’t smoke.

After you find the crude effect, you want to see if the risk of lung cancer changes for each level of radon exposure.

So, let’s say that overall, there are 140 people in the study that were exposed to low levels of radon and 60 people in the study that were exposed to high levels of radon.

Now, of the 140 people in the low radon group, 60 people smoked and 80 people didn’t smoke. Of the 60 smokers, 40 of them - 67% - developed lung cancer, and of the 80 non-smokers, 35 of them - 44% - developed lung cancer. This gives us a relative risk of 1.5 in the low radon group, which is lower than the crude relative risk of 7.5.

On the flip side, of the 60 people in the high radon group, 40 people smoked and 20 didn’t smoke. Of the 40 smokers, 35 of them - 88% - developed lung cancer, and of the 20 non-smokers, 5 of them - 25% - developed lung cancer. This gives us a relative risk of 3.5 in high radon group, which is lower than the crude relative risk, but higher than the relative risk in the low radon group.

We’d call this result a heterogeneity of effects - because each strata has a different risk.

One common mistake is distinguishing between confounding and interaction.

In confounding, a third variable is associated with both the outcome and the exposure, whereas in interaction a third variable is associated with the outcome but not the exposure.

For example, let’s say that smoking is the exposure, lung cancer is the outcome, and radon exposure is the third variable.

Here, there’s an association between radon and an increased risk of lung cancer, but people exposed to high levels of radon aren’t more likely to be smokers - so it’s not associated with the exposure.

In contrast, exposure to coal dust would be a confounder, because just like radon it’s associated with an increased risk of lung cancer.

Additionally, exposure to coal dust is also associated with smoking, because coal miners tend to smoke more cigarettes than people in other professions.

Statistical interaction can be used to figure out if the joint or combined effect of the two exposures is different from what we expect them to be, based on their independent effects.

In other words, if we add or multiply the effect of one exposure with the effect of the other exposure, will the joint effect match what we think it should?

We can figure out the expected joint effect of two exposures in two ways.

Interaction can refer to biological interaction - which is where two exposures like radon gas and toxins in cigarettes work together to influence an outcome - like lung cancer. It can also refer to statistical interaction, also called effect modification, which is the statistical methodology used to find out if there's a biological interaction.