Sequential and simultaneous exposure–response modeling 95
to fit them, e.g., availa ble in SAS proc MODEL. However, since our goal is
to predict the c oncentration and to fit ER models, considering the following
marginal model derived from (4.62) is sufficient:
log(c
i1
) = θ
01
+ θ
1
log(d
i1
) + θ
12
log(d
i2
) + v
i1
log(c
i2
) = θ
02
+ θ
2
log(d
i2
) + θ
21
log(d
i1
) + v
i2
. (4.63)
They are almost the same as model (4.62), apart from the interaction term
θ
kk
′
c
ik
′
, c
ik
being replaced with d
ik
′
. The two models are equivalent in terms
of the dos e–exposure rela tionship. However, all parameters and v
ik
s in model
(4.63), not only θ
kk
′
, have different meanings from those in model (4.62). But
we do not introduce new names for simplicity. Also, even if the v
i1
and v
i2
are independent ...