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Sample Size Calculations for Clustered and Longitudinal Outcomes in Clinical Research
book

Sample Size Calculations for Clustered and Longitudinal Outcomes in Clinical Research

by Chul Ahn, Moonseoung Heo, Song Zhang
December 2014
Intermediate to advanced content levelIntermediate to advanced
260 pages
8h 51m
English
Chapman and Hall/CRC
Content preview from Sample Size Calculations for Clustered and Longitudinal Outcomes in Clinical Research
Sample Size Determination for Correlated Outcomes Using GEE 133
the independent working correlation structure, the GEE estimator
ˆ
b can be
obtained by solving U (b) = 0, where
U(b) =
1
n
1
P
n
1
i=1
P
m
j=1
(y
1ijµ
1ij
(b)
)
···
1
n
1
P
n
1
i=1
P
m
j=1
(y
1ijµ
1ij
(b)
)
.
We employ the Newton-Raphson algorithm to solve for
ˆ
b. At the lth iteration,
ˆ
b
(l)
=
ˆ
b
(l1)
+ n
1
2
A
1
n
(
ˆ
b
(l1)
)U(
ˆ
b
(l1)
),
where A
n
(b) is a K × K diagonal matrix with the kth diagonal ele-
ment being
1
n
k
P
n
k
i=1
P
m
j=1
e
b
k
. By Liang and Zeger [5],
ˆ
b b approxi-
mately has a normal distribution with mean 0 and variance matrix Σ
n
=
1
n
W A
1
n
(
ˆ
b)V
n
(
ˆ
b)A
1
n
(
ˆ
b)W . Here W is diagonal with main diagonal elements
(1
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Publisher Resources

ISBN: 9781466556270