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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
118 Sample Size Calculations for Clustered and Longitudinal Outcomes
define δ
j
= E(∆
kij
) to be the probability of a subject having an observation
at t
j
, and δ
jj
0
= E(∆
kij
kij
0
) to be the joint probability of a subject having
observations at both t
j
and t
j
0
.
Theorem 2 As n , the (K 1) ×(K 1) variance matrix
ˆ
W converges
to
W =
s
¯m
(1/r
1
1) 1 1 ··· 1
1 (1/r
2
1) 1 ··· 1
1 1 (1/r
3
1) ··· 1
··· ··· ··· ··· ···
1 1 1 ··· (1/r
K1
1)
.
Furthermore, we have W
1
=
¯m
2
s
[diag(r) + r
1
K
rr
0
]. Here s =
σ
2
P
m
j=1
P
m
j
0
=1
δ
jj
0
ρ
jj
0
, ¯m =
P
m
j=1
δ
j
, and r = (r
1
, . . . , r
K1
)
0
.
Proof. See the Appendix of Zhang and Ahn [44].
From Theorem 2 we have
η
0
W
1
η =
¯m
2
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Publisher Resources

ISBN: 9781466556270