Causal Diagram for Confounding
Cis a common cause ofEandD
C
E
D
NoncausalE–Dassociation
C confoundstheE–Drelationship
The pathE–C–Dis abackdoor path
fromEtoD
C 2
C 1
C 3
D
E
E–C 1 – C 2 – C 3 – Dis a backdoor path
Can control for eitherC 1 orC 2 orC 3
Lung cancer a common effect
Smoking
Lung Cancer
Genetic factor (GF)In general population:
No association between GF and
smoke
Among lung cancer patients:
Smokers may get lung
cancer because they smoke
Smoking is not a reason that
a nonsmoker gets lung
cancer (omitting secondhand
smoke as a reason)
So nonsmokers more likely to
have genetic factor than
smokers (smoking associated
with GF among lung cancer
patients)Confoundingof the exposure–disease associa-
tion is rooted in a common cause (C) of the
exposure (E) and disease (D), leading to a spu-
riousE–Dassociation.The diagram on the left illustrates thatEdoes
not causeD, yet there is a noncausal pathway
betweenEandDthroughC. Such a noncausal
pathway between two variables of interest is
called a “backdoor path”. The noncausal path
fromEtoDgoes throughCand is denoted as
E–C–D.The next diagram (on the left) is somewhat
more complicated.C 2 is a common cause ofE
(throughC 1 ) andD(throughC 3 ). A noncausal
backdoor path E–C 1 – C 2 – C 3 – Dwill lead to a
spurious association betweenEandDif not
adjusted. AlthoughC 2 is the common cause,
you can control for (condition on) eitherC 1 or
C 2 orC 3. A confounder need not be the com-
mon cause; it just needs to be on the path to or
from the common cause.The next type of causal structure we examine is
one that contains a common effect from two or
more causes. Consider two independent risk
factors for lung cancer: smoking and some
genetic factor (GF). As shown on the left, lung
cancer is a common effect of these risk factors.Suppose there is no association between
smoking and the genetic factor in the general
population. Nevertheless, among lung cancer
patients, there likely is an association between
smoking and the genetic factor. Nonsmokers
who get lung cancer get lung cancer for some
reason. Since smoking is not the reason they
got lung cancer, nonsmokers may be more
likely to have the genetic factor as the reason
compared to smokers who get lung cancer.Presentation: V. Causal Diagrams 177