
Sample Size Determination for Clustered Outcomes 43
studies. Donner’s sample size formula accounts for clustering in a stratified
cluster randomization design.
Suppose that clusters are randomly assigned to the intervention and con-
trol groups within each stratum, and n
i
is the number of clusters in each in-
tervention group in stratum i (i = 1, . . . , k), where k is the number of strata.
The cluster sizes are assumed to be equal within each stratum, but may vary
across strata. Let m
i
be the cluster size in stratum i. Let P
iC
denote the
probability of response among subjects in stratum i of the control group, and
P
iT
denote the probability of response