266 Exposure-Response Modeling: Methods and Practical Implementation
For similar motivations, we will consider the distribution of c
ij
as
c
ij + 1
∼ h(c;
¯
G
ij
, v
i
) (9.38)
where
¯
G
ij
is defined as F
ij
but may also include d
ij
. Similarly, it is sufficient
to adjust factors in G
ij
for fitting exposure–response models.
9.5.2 Directional acyclic graphs and the decomposition of
the likelihood function
The mechanism of dose adjustment can also be presented in a DAG such as
Figure 9.2. Rules applied to DAGs can also be applied here. For example,
one a dvantage of using ER modeling is that it is not impacted by res ponse–
depe ndent dose adjustment. Indeed, one can find in Figure 9.2 that c
ij
blocks
the path from d
ij
to y
ij
, hence, if there is no confounding b etween u
i
and ...