Logistic Regression: A Self-learning Text, Third Edition (Statistics in the Health Sciences)

Lung cancer

Above causal diagram

Bias if we condition on X-ray status

Smoking

Abnormal

chest X-ray

⇐

Explanation:
Among smokers with abnormal
chest X-ray
 High odds of lung cancer
Among nonsmokers with abnormal
X-ray
 High odds of lung cancer

Among those with abnormal chest
X-ray
 Odds ratio (smoking vs. non-
smoking) closer to null than in
general population (a bias)

Depending on the underlying causal
structure, adjustment may:

 Remove bias

 Lead to bias

 Neither of the above

Causal diagrams may help under-
standing of:

 Causation

 Association

 Bias

The causal diagram at the left describes the

likely causal pathway that involves the three

variables smoking, lung cancer, and abnormal

chest X-ray.

We can use this diagram to explain why any

association between smoking and lung cancer

is weakened (and therefore biased) if we con-

trol for X-ray status. In particular, a conse-

quence of the causal effect of smoking on

lung cancer is to increase the likelihood of an

abnormal X-ray.

Explaining the reason for this bias, we would

expect a large proportion of smokers who have

an abnormal chest X-ray to have lung cancer

simply because an abnormal X-ray is a strong

indicator of lung cancer. However, we would

also expect a large proportion of nonsmokers

who have an abnormal chest X-ray to have lung

cancer. So among those who have an abnormal

chest X-ray, the odds of lung cancer would not

substantially differ comparing smokers to non-

smokers, even though the odds would differ

greatly in the general population.

The point of the above example is that even

though the adjusted odds ratio may be much

different than the unadjusted odds ratio, adjust-

ment may cause bias rather than remove bias.

Whether adjustment causes bias or removes

bias (or neither), depends on the underlying

causal structure of the variables of interest.

Causal diagrams provide a graphical perspec-

tive for understanding epidemiologic concepts

involving causation, association, and bias. In

this section, we highlight the key concepts.

A more detailed description of causal diagrams

can be found elsewhere (Rothman et al., 2008).

176 6. Modeling Strategy Guidelines