296 PART 5 Looking for Relationships with Correlation and Regression

Computer software may include automated processes you can use for fitting mod-

els. We discourage you from using these in biostatistics because you want to have

a lot of control over how a model is being fitted to make it possible for you to

interpret the results. However, these processes can be used to create comparison

models  — or to simulate improved models  — which are perfectly reasonable

methods to explore ways to improve your model.

Understanding Interaction

(Effect Modification)

In Chapter 17, we touch on the topic of interaction (also known as effect modifica-

tion). This is where the relationship between an exposure and an outcome is

strongly dependent upon the status of another covariate. Imagine that you con-

ducted a study of laborers who had been exposed to asbestos at work, and you

found that being exposed to asbestos at work was associated with three times the

odds of getting lung cancer compared to not being exposed. In another study, you

found that individuals who smoked cigarettes had twice the odds of getting lung

cancer compared to those who did not smoke.

Knowing this, what would you predict are the odds of getting lung cancer for

asbestos-exposed workers who also smoke cigarettes, compared to workers who

aren’t exposed to asbestos and do not smoke cigarettes? Do you think it would be

additive — meaning three times for asbestos plus two times for smoking equals

five times the odds? Or do you think it would be multiplicative — meaning three

times two equals six times the odds?

Although this is just an example, it turns out that in real life, the effect of being

exposed to both asbestos and cigarette smoking represents a greater than multi-

plicative synergistic interaction (meaning much greater than six) in terms of the

odds for getting lung cancer. In other words, the risk of getting lung cancer for

cigarette smokers is dependent upon their asbestos-exposure status, and the risk

of lung cancer for asbestos workers is dependent upon their cigarette-smoking

status. Because the factors work together to increase the risk, this is a synergistic

interaction (with the opposite being an antagonistic interaction).

How and when do you model an interaction in regression? Typically, you first fit

your final model using a multivariate regression approach (see the earlier section

“Adjusting for confounders in regression” for more on this). Next, once the final

model is fit, you try to interact the exposure covariate or covariates with a con-

founder that you believe is the other part of the interaction. After that, you look at

the p value on the interaction term and decide whether or not to keep the

interaction.