
Sample Size Determination for Correlated Outcomes Using GEE 113
with σ
2
r
= ¯r(1 − ¯r), ¯m =
P
m
j=1
δ
j
, and η =
P
m
j=1
P
m
j
0
=1
δ
jj
0
ρ
jj
0
. It is easy to
show that the (2,2)th component of Σ is
σ
2
2
=
σ
2
η
¯m
2
σ
2
r
.
Thus the required sample size is
n =
σ
2
η(z
1−α/2
+ z
1−γ
)
2
β
2
2
¯m
2
σ
2
r
. (4.20)
This closed-form sample size formula provides a flexible approach to sample
size estimation because it can accommodate a broad spectrum of experimental
designs, missing patterns, and correlation structures through the specification
of (¯r, δ
j
, δ
jj
0
, ρ
jj
0
). For example, ¯r = 0.5 indicates a balanced design while
¯r = 0.33 implies a 1:2 randomization ratio between the treatment and control
group. ...