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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
202 Sample Size Calculations for Clustered and Longitudinal Outcomes
the maximum likelihood estimate. Specifically, for the gth arm,
ˆη
g
=
N
3
P
i=1
N
2
P
j=1
N
1
P
k=1
T
k
¯
T

Y
ijk
¯
Y
g
,
N
3
P
i=1
N
2
P
j=1
N
1
P
k=1
T
k
¯
T
2
=
N
3
P
i=1
N
2
P
j=1
N
1
P
k=1
T
k
¯
T

Y
ijk
¯
Y
g
,
N
3
N
2
N
1
V ar
p
(T )
, (6.18)
where: (1)
¯
Y
g
(g = 0, 1) is the overall mean of the outcome Y for the gth
arm; (2)
¯
T =
P
N
1
k=1
T
k
/N
1
is the “mean” time point; and (3) V ar
p
(T ) =
P
N
1
k=1
T
k
¯
T
2
/N
1
is the “population variance” of the time variable T . The
variance of
ˆ
δ
(f)
can be obtained as
V ar(
ˆ
δ
(f)
) = V ar η
1
ˆη
0
) =
2(1 ρ
1
)σ
2
N
3
N
2
N
1
V ar
p
(T )
. (6.19)
It is worth noting that the variance of
ˆ
δ depends only on the residual
variance
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Publisher Resources

ISBN: 9781466556270