
Confounding bias and caus al inference in exposure–response modeling 243
to adjust the confounding bias. But u
i
may not be entirely confounded. It is
the component correlated to v
i
that causes bias and has to be adjusted for.
The CF method uses the IV mo de l to predict this component, then includes
its prediction to adjust the y-part model. To this end, we need to assume that
u
i
can be written as
u
i
= av
i
+ ε
i
(8.49)
where ε
i
is a ra ndom term independent of v
i
. Therefore, u
i
has two compo-
nents; av
i
is the source of confounding and the error term ε
i
is independent
of c
i
. The re lationship (8.49) holds when u
i
and v
i
are jointly normally dis-
tributed. But it