F is a common effect ofEandD:
E
D
F
Conditioning on F creates a spur-
ious association betweenEandD
E
D
F
E
D
F
Backdoor pathE–F–Dis blocked by
common effect. No spurious asso-
ciation unless we condition on F.
Berkson’s bias:
Selecting only hospital patients
could lead to bias of A–B
association.
A
B
Hospital
Selecting volunteers could lead to
bias of X–Y association.
X
Y
Volunteers
Conditioning on a common cause can
Remove bias
Conditioning on a common effect can
Induce bias
This spurious association produced by condi-
tioning on a common effect can be expressed
with causal diagrams. Let F be a common
effect of the exposure (E) and disease (D) with
exposure unrelated to disease.
The second causal diagram, with the box
around F (the common effect), indicates con-
ditioning, or adjusting, on F. The dotted lines
betweenEandDwithout a causal arrow indi-
cate that a spurious association betweenEand
Dwas produced because of the conditioning on
F (i.e., within strata of F).
If we do not condition on a common effect
we may still wonder if there is a spurious asso-
ciation betweenEandDbecause of the back-
door path E–F–D. However, a backdoor path
through a common effect willnotcreate a spu-
rious association, unless we condition on that
common effect.
Joseph Berkson illustrated this bias in studies
in which selected subjects were hospitalized
patients (Berkson, 1946). If condition A and
condition B can lead to hospitalization, then
selecting only hospitalized patients can yield a
biased estimated association between A and B.
Similarly, if factors X and Y influenced volun-
teerism, then restricting the study population
to volunteers could lead to a selection bias of
the X–Y association.
We have seen that conditioning on a common
cause (a confounder) can remove bias and con-
ditioning on a common effect can induce bias.
178 6. Modeling Strategy Guidelines
