
Sample Size Determination for Correlated Outcomes Using GEE 103
Under H
0
, the first term on the right-hand side of (4.13) equals 0. By applying
the central limit theorem to (4.13), under H
0
, B is approximately normal with
mean 0 and variance V that can be consistently estimated by
ˆ
V = (ˆv
kk
0
) with
ˆv
kk
0
=
1
n − 2K
K
X
l=1
n
l
X
i=1
m
X
j=1
(ξ
kl
w
lij
− ˜w
lij
) ˆ
lij
m
X
j=1
(ξ
k
0
l
w
lij
− ˜w
lij
) ˆ
lij
,
where ˆ
kij
= y
kij
−
ˆ
θ
k
−
ˆ
β
k
t
j
. In the denominator of ˆv
kk
0
, 2K corresponds
to the number of parameters {(θ
k
, β
k
), 1 ≤ k ≤ K} estimated to obtain the
residuals ˆ
kij
. We reject H
0
with type I error α if B
0
ˆ
V
−1
B > χ
2
K−1,1−α
where
χ
2
v,1−α
is the 100(1−α)th percentile of a c ...