% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/power.R
\name{mb_cluster_design}
\alias{mb_cluster_design}
\title{Cluster-RCT design effect}
\usage{
mb_cluster_design(individuals_per_cluster, icc, n_clusters = NULL)
}
\arguments{
\item{individuals_per_cluster}{Numeric. Number of individuals
sampled per cluster (\code{m}).}

\item{icc}{Numeric in \verb{[0, 1]}. Intra-class correlation
coefficient. Use \code{\link[=mb_icc_reference]{mb_icc_reference()}} for plausible values.}

\item{n_clusters}{Optional numeric. Number of clusters per arm.
If supplied, returns effective sample size per arm in addition
to the design effect.}
}
\value{
A list with elements \code{deff} and (if \code{n_clusters}
supplied) \code{n_total_per_arm} and \code{n_effective_per_arm}.
}
\description{
Computes the design effect (DEFF) for a parallel cluster
randomised trial: how much the variance of the treatment effect
inflates relative to an individually-randomised design with the
same total sample size, due to within-cluster correlation.
}
\details{
\deqn{\text{DEFF} = 1 + (m - 1) \, \rho}
where \code{m} is the cluster size and \code{rho} is the ICC. The
effective sample size for power is \code{n_total / DEFF}.

Standard reference values for \code{rho} across UK policy domains
are bundled and accessible via \code{\link[=mb_icc_reference]{mb_icc_reference()}}.
}
\examples{
mb_cluster_design(individuals_per_cluster = 30, icc = 0.05)
mb_cluster_design(individuals_per_cluster = 30, icc = 0.05, n_clusters = 20)
}
\references{
Donner, A., Klar, N. (2000). Design and Analysis of Cluster
Randomization Trials in Health Research. Arnold.

Hedges, L. V., Hedberg, E. C. (2007). Intraclass Correlation
Values for Planning Group-Randomized Trials in Education.
Educational Evaluation and Policy Analysis 29(1).
\url{doi:10.3102/0162373707299706}.
}
\seealso{
\code{\link[=mb_icc_reference]{mb_icc_reference()}}, \code{\link[=mb_stepped_wedge]{mb_stepped_wedge()}},
\code{\link[=mb_sample_size]{mb_sample_size()}}.

Other power: 
\code{\link{mb_icc_reference}()},
\code{\link{mb_mde}()},
\code{\link{mb_power}()},
\code{\link{mb_sample_size}()},
\code{\link{mb_stepped_wedge}()}
}
\concept{power}
