Statistical Modelling 3 (2003), 233249
A mixed model formulation for designing cluster randomized trials
with binary outcomes
Thomas M. Braun,
Department of Biostatistics,
School of Public Health,
University of Michigan,
Ann Arbor, MI 48109,
U.S.A.
eMail: tombraun@umich.edu
Abstract:
Cluster randomized trials (CRTs) are unlike traditional individually
randomized trials because observations within the same cluster are
positively correlated and the sample size (number of clusters) is
relatively small. Although formulae for sample size and power
estimates of CRT designs do exist, these formulae rely upon
first-order asymptotic approximations for the distribution of the
average intervention effect and are inaccurate for CRTs that have
a small number of clusters. These formulae also assume that the
intracluster correlation (ICC) is the same for each cluster in the
CRT. However, for CRTs in which the clusters are classrooms or
medical practices, the degree of ICC is often a factor of how many
students are in each classroom or how many patients are in each
practice. Specifically, smaller clusters are expected to have
larger ICC than larger clusters. A weighted sum of the cluster
means, D, is the statistic often used to estimate the average
intervention effect in a CRT. Therefore, we propose that a
saddlepoint approximation is a natural choice to approximate
the distributions of the cluster means more precisely than a
standard large-sample approximation. We parameterize the ICC for
each cluster as a random effect with a pre-defined prior distribution
that is dependent upon the size of each cluster. After integrating
over the range of the random effect, we use Monte Carlo methods to
generate sample cluster means, which are in turn used to approximate the
distribution of D with saddlepoint methods. Through numerical examples
and an actual application, we show that our method has accuracy that is
equal to or better than that of existing methods. Futhermore, our
method accomodates CRTs in which the correlation within cluster is
expected to diminish with the cluster size.
Keywords:
Saddlepoint approximation; sample size; marginal model; power
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