298 PART 5 Looking for Relationships with Correlation and Regression

the outcome, and the other will not. We can’t say for sure what values of covari-

ates will mean that you will for sure get the outcome. But that doesn’t mean you

can’t make causal inferences. Rothman conceptualized cause as an empty pie tin,

and when the pie tin is filled 100 percent with pieces of risk contributed by various

causes, then the individual will experience the outcome. The exposure and con-

founders in your regression model represent these pieces.

For example, cigarette smoking is a very strong cause of lung cancer, as is occu-

pational exposure to asbestos. There are other causes, but for each individual,

these other causes would fill up small pieces of the causal pie for lung cancer.

Some may have a higher genetic risk factor for cancer. However, if they do not

smoke and stay away from asbestos, they will not fill up much of their pie tin, and

may have necessary but insufficient cause for lung cancer. However, if they include

both asbestos exposure and smoking in their tin, they are risking filling it up and

getting the outcome.

Bradford Hill’s criteria of causality»

» ^{Sir Bradford Hill was a British epidemiologist who put forth criteria for}

causality that can be useful to consider when thinking of statistically signifi-

cant exposure–outcome relationships from final regression models. Although

there are more than the criteria we list here, we find the following criteria to

be the most useful when evaluating potential exposure–outcome causal

relationships in final models:»

» ^{First, consider if the data you are analyzing are from a clinical trial or cohort}

study. If they are, then you will have met the criterion of temporality, which

means the exposure or intervention preceded the outcome and is especially

strong evidence for causation.»

» ^{If the estimate for the exposure in your regression model is large, you can say}

you have a strong magnitude of association, and this is evidence of causation.

This is especially true if your estimate is larger than those of the confounders

in the model as well as similar estimates from the scientific literature.»

» ^{If your exposure shows a dose-response relationship with the outcome, it is}

evidence of causation. In other words, if your regression model shows that

the more individuals smoke, the higher their risk for lung cancer, this is

evidence of causation (see Chapter 18 for more on dose-response

relationships).»

» ^{If the estimate is consistent in size and direction with other analyses, including}

previous studies you’ve done and studies in the scientific literature, there is

more evidence for causation.