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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 Outcomes from Three-Level Trials 227
ϕ can be computed as
N
3
=
f
2
z
2
α,φ,p
N
2
N
1
(p
1
p
0
)
2
(6.48)
from the power function
ϕ = Φ
(
|p
1
p
0
|
p
N
1
N
2
N
3
/f
2
Φ
1
(1 α/2)
p
p (1 ¯p)
p
p
0
(1 p
0
) + p
1
(1 p
1
)
)
From Equation (6.48), sample size N
2
for given N
1
, and N
3
can be imme-
diately obtained as
N
2
=
f
2
z
2
α,φ,p
N
3
N
1
(p
1
p
0
)
2
since f
2
= 1 + (N
1
1)ρ
1
N
1
ρ
2
in (6.10) is not a function of N
2
. In other
words, the power is invariant over the product of N
3
N
2
Equation (6.48) should
be solved to obtain N
1
.
6.7.2.2 Unbalanced Allocations
For an unbalanced design with Σ
j
X
j
= λN
(0)
2
for λ > 0 and i =
1, 2, . . . , N
3
, j = 1, 2, . . . (1 + λ)N
(0)
2
, and k = 1,
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Publisher Resources

ISBN: 9781466556270