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\name{sampSize}
\alias{sampSize}
\alias{sampSizeMCT}
\alias{targN}
\alias{plot.targN}
\alias{powN}
\title{
Sample size calculations
}
\description{
The \samp{sampSize} function implements a bisection search algorithm
for sample size calculation. The user can hand over a general target
function (via \samp{targFunc}) that is then iterated so that a certain
\samp{target} is achieved. The \samp{sampSizeMCT} is a convenience
wrapper of \samp{sampSize} for multiple contrast tests using the power
as target function.
The \samp{targN} functions calculates a general target function for
different given sample sizes. The \samp{powN} function is a
convenience wrapper of \samp{targN} for multiple contrast tests using
the power as target function.
}
\usage{
sampSize(upperN, lowerN = floor(upperN/2), targFunc, target,
tol = 0.001, alRatio, Ntype = c("arm", "total"),
verbose = FALSE)
sampSizeMCT(upperN, lowerN = floor(upperN/2), ..., power, sumFct = mean,
tol = 0.001, alRatio, Ntype = c("arm", "total"),
verbose = FALSE)
targN(upperN, lowerN, step, targFunc, alRatio,
Ntype = c("arm", "total"), sumFct = c("min", "mean", "max"))
powN(upperN, lowerN, step, ..., alRatio,
Ntype = c("arm", "total"), sumFct = c("min", "mean", "max"))
\method{plot}{targN}(x, superpose = TRUE, line.at = NULL,
xlab = NULL, ylab = NULL, ...)
}
\arguments{
\item{upperN, lowerN}{ Upper and lower bound for the target sample
size. \code{lowerN} defaults to \code{floor(upperN/2)}. }
\item{step}{
Only needed for functions \samp{targN} and \samp{powN}. Stepsize
for the sample size at which the target function is calculated. The
steps are calculated via \code{seq(lowerN,upperN,by=step)}.
}
\item{targFunc, target}{
The target function needs to take as an input the vector of sample
sizes in the different dose groups. For \samp{sampSize} it needs to
return a univariate number. For function \samp{targN} it should
return a numerical vector.\cr
\cr
Example: \samp{targFunc} could be a function that calculates the
power of a test, and \samp{target} the desired target power value.
\cr
For function \samp{sampSize} the bisection search iterates the
sample size so that a specific target value is achieved (the
implicit assumption is that targFunc is monotonically increasing in
the sample size).\cr
\cr
Function \samp{targN} simply calculates \samp{targFunc} for a given
set of sample sizes.
}
\item{tol}{
A positive numeric value specifying the tolerance level for the
bisection search algorithm. Bisection is stopped if the \samp{targFunc}
value is within \samp{tol} of \samp{target}.
}
\item{alRatio}{
Vector describing the relative patient allocations to the dose
groups up to proportionality, e.g. \samp{rep(1, length(doses))}
corresponds to balanced allocations.
}
\item{Ntype}{
One of "arm" or "total". Determines, whether the sample size in the
smallest arm or the total sample size is iterated in bisection
search algorithm.
}
\item{verbose}{
Logical value indicating if a trace of the iteration progress of the
bisection search algorithm should be displayed.
}
\item{...}{
Arguments directly passed to the \code{\link{powMCT}} function in
the \samp{sampSizeMCT} and \samp{powN} function.
The \samp{placAdj} argument needs to be \samp{FALSE} (which is the
default value for this argument). If sample size calculations are
desired for a placebo-adjusted formulation use \samp{sampSize} or
\samp{targN} directly.
In case \code{S} is specified, the specified matrix needs to be
proportional to the (hypothetical) covariance matrix of one single
observation. The covariance matrix used for sample size calculation
is 1/N*S, where N is the total sample size. Hence \samp{Ntype == "total"}
needs to be used if \code{S} is specified. When \code{S} is
specified, automatically \samp{df = Inf} is assumed in the
underlying \samp{powMCT} calls.
For a homoscedastic normally distributed response variable only \samp{sigma}
needs to be specified, as the sample size \samp{n} is iterated in
the different \samp{powMCT} calls.
}
\item{power, sumFct}{
power is a numeric defining the desired summary power to achieve (in
\samp{sampSizeMCT}).
sumFct needs to be a function that combines the power values under
the different alternatives into one value (in \samp{sampSizeMCT}).
}
\item{x, superpose, line.at, xlab, ylab}{
arguments for the plot method of \samp{targN} and \samp{powN},
additional arguments are passed down to the low-level lattice plotting
routines.
}
}
\references{
Pinheiro, J. C., Bornkamp, B., and Bretz, F. (2006). Design and analysis of dose finding studies
combining multiple comparisons and modeling procedures, \emph{Journal of Biopharmaceutical
Statistics}, \bold{16}, 639--656
}
\author{
Jose Pinheiro, Bjoern Bornkamp
}
\seealso{
\code{\link{powMCT}}
}
\examples{
## sampSize examples
## first define the target function
## first calculate the power to detect all of the models in the candidate set
fmodels <- Mods(linear = NULL, emax = c(25),
logistic = c(50, 10.88111), exponential=c(85),
betaMod=matrix(c(0.33,2.31,1.39,1.39), byrow=TRUE, nrow=2),
doses = c(0,10,25,50,100,150), placEff=0, maxEff=0.4,
addArgs = list(scal=200))
## contrast matrix to use
contMat <- optContr(fmodels, w=1)
## this function calculates the power under each model and then returns
## the average power under all models
tFunc <- function(n){
powVals <- powMCT(contMat, altModels=fmodels, n=n, sigma = 1,
alpha=0.05)
mean(powVals)
}
## assume we want to achieve 80\% average power over the selected shapes
## and want to use a balanced allocations
\dontrun{
sSize <- sampSize(upperN = 80, targFunc = tFunc, target=0.8,
alRatio = rep(1,6), verbose = TRUE)
sSize
## Now the same using the convenience sampSizeMCT function
sampSizeMCT(upperN=80, contMat = contMat, sigma = 1, altModels=fmodels,
power = 0.8, alRatio = rep(1, 6), alpha = 0.05)
## Alternatively one can also specify an S matrix
## covariance matrix in one observation (6 total observation result in a
## variance of 1 in each group)
S <- 6*diag(6)
## this uses df = Inf, hence a slightly smaller sample size results
sampSizeMCT(upperN=500, contMat = contMat, S=S, altModels=fmodels,
power = 0.8, alRatio = rep(1, 6), alpha = 0.05, Ntype = "total")
## targN examples
## first calculate the power to detect all of the models in the candidate set
fmodels <- Mods(linear = NULL, emax = c(25),
logistic = c(50, 10.88111), exponential=c(85),
betaMod=matrix(c(0.33,2.31,1.39,1.39), byrow=TRUE, nrow=2),
doses = c(0,10,25,50,100,150), placEff=0, maxEff=0.4,
addArgs = list(scal=200))
## corresponding contrast matrix
contMat <- optContr(fmodels, w=1)
## define target function
tFunc <- function(n){
powMCT(contMat, altModels=fmodels, n=n, sigma = 1, alpha=0.05)
}
powVsN <- targN(upperN = 100, lowerN = 10, step = 10, tFunc,
alRatio = rep(1, 6))
plot(powVsN)
## the same can be achieved using the convenience powN function
## without the need to specify a target function
powN(upperN = 100, lowerN=10, step = 10, contMat = contMat,
sigma = 1, altModels = fmodels, alpha = 0.05, alRatio = rep(1, 6))
}
}
|
