
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
1ij−µ
1ij
(b)
)
···
1
√
n
1
P
n
1
i=1
P
m
j=1
(y
1ij−µ
1ij
(b)
)
.
We employ the Newton-Raphson algorithm to solve for
ˆ
b. At the lth iteration,
ˆ
b
(l)
=
ˆ
b
(l−1)
+ n
−
1
2
A
−1
n
(
ˆ
b
(l−1)
)U(
ˆ
b
(l−1)
),
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