
108 Sample Size Calculations for Clustered and Longitudinal Outcomes
For the CS correlation structure, a consistent estimator of ρ can be obtained
by
ˆρ =
2
P
n
i=1
P
m−1
j=1
P
m
j
0
=j+1
ˆ
ij
ˆ
ij
0
ˆσ
2
nm(m − 1)
.
For the AR(1) correlation structure, the consistent estimator of ρ can be
obtained from the equation
n
X
i=1
m−1
X
j=1
m
X
j
0
=j+1
ˆ
ij
ˆ
ij
0
− ˆσ
2
ρ
|t
ij
−t
ij
0
|
= 0.
Suppose we apply the GEE sample size method to a labor pain study
[36]. Eighty-three women in labor were randomly assigned to either receive
a pain medication (43 women) or a placebo (40 women). Self-reported pain
scores were collected at 30-minute intervals, with 0 indicating no pain and
100 indicating extreme ...