
16 Sample Size Calculations for Clustered and Longitudinal Outcomes
If σ
2
1
= σ
2
2
= σ
2
, then the required sample size per group is
n =
2σ
2
(z
1−α
+ z
1−β
)
2
∆
2
. (1.6)
In some randomized clinical trials, more subjects are assigned to the treat-
ment group than to the control group to encourage participation of subjects
in a trial due to their higher chance of being randomized to the treatment
group than the control group. Let n
1
= n be the number of subjects in the
control group and n
2
= kn be the number of subjects in the treatment group.
Then, the sample size for the study will be
n
1
= n = (1 + 1/k)σ
2
(z
1−α
+ z
1−β
)
2
∆
2
. (1.7)
The total sample size for the trial is