U 1 and U 2 are unmeasured
Should we control for C?
E
U 1
C
U 2
D
E
U 1 U 2
C D
By controlling for C we create an
unblocked path from E to D:
E–U 1 – U 2 – D
Do not control forC
Is it too much to expect that we
correctly and completely specify
the underlying causal structure?
Answer : Yes
Do we run the risk of inducing bias
if we do not consider the causal
structure at all?
Answer : Yes
Analytic goal:
EstimateE–Drelationship
)Concern about causal
structure confounding,
interaction
Predict the outcome
)Causal structure of less
concern
For a more complicated example, consider the
causal diagram on the left. SupposeU 1 andU 2
are unmeasured factors, withU 1 being a com-
mon cause ofEandC, and withU 2 being a
common cause ofDandC. If we are interested
in estimating an unbiased measure of effect
betweenEandD, should we control forC?U 1 is a cause ofE, andU 2 is a cause ofDbut
there is no common cause ofEandD, thus
there is no confounding. However, if we condi-
tion onC, a common effect ofU 1 andU 2 , then
we create a link betweenU 1 and U 2 (i.e., a
spurious association) and an unblocked back-
door path fromEtoDleading to a spurious
association betweenEandD. The backdoor
path is E–U 1 – U 2 – D. Since U 1 and U 2 are
unmeasured we cannot adjust for either of
these variables and block that backdoor path.
Therefore, we should not control forC.Correctly specifying the causal structure of all
the relevant variables for assessing the E–D
relationship is close to impossible. However,
this does not mean that we should not think
about the underlying causal structure.We should certainly be aware that decisions to
include or not include covariates in the model
may induce or remove bias depending on the
causal relationships. In particular, we should
be aware that conditioning on a common effect
can induce bias.Central to this discussion and to all our dis-
cussion on model strategy is that our goal is
to obtain a valid estimate of an exposure–
disease relationship. If our goal was to obtain
the best predictive model, we would not be
so concerned about the causal structure, con-
founding, or interaction.Presentation: V. Causal Diagrams 179