Skip to Main Content
Exposure-Response Modeling
book

Exposure-Response Modeling

by Jixian Wang
July 2015
Intermediate to advanced content levelIntermediate to advanced
351 pages
10h 2m
English
Chapman and Hall/CRC
Content preview from Exposure-Response Modeling
80 Exposure-Response Modeling: Methods and Practical Implementation
we examine the idea behind the RC approach. Since only c
i
is observed, we
would like to fit y
i
with its conditional mean E(y
i
|c
i
) = βE(c
i
|c
i
), i.e., we fit
y
i
= βE(c
i
|c
i
) + ε
i
, (4.24)
where ε
i
= ε
i
+ β(c
i
E(c
i
|c
i
)). It can be verified that as long as E(c
i
|c
i
) is
sp ecified correctly, fitting this model gives a consistent estimate for β, although
ε
i
depe nds on β. To this end, note that the RC estimate
ˆ
β
RC
is the solution
to
S
RC
(β) =
n
X
i=1
E(c
i
|c
i
)(y
i
βE(c
i
|c
i
))/n = 0, (4.25)
we check E(S
RC
(β)) = 0, which is the key condition for consistency of
ˆ
β
RC
(A.6). E(S
RC
(β)) can be calculated by first conditioning on c
i
:
E(S
RC
(β)) = E
c
(E(c
i
|c
i
)E(y
i
βE(c
i
|c
i
)|c
i
)) (4.26)
in which E(y
i
βE(c
i
|c
i
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Computational Pharmacokinetics

Computational Pharmacokinetics

Anders Kallen
Deep Learning through Sparse and Low-Rank Modeling

Deep Learning through Sparse and Low-Rank Modeling

Zhangyang Wang, Yun Fu, Thomas S. Huang

Publisher Resources

ISBN: 9781466573215