The sampSize function implements a bisection search algorithm for sample size calculation. The user can hand over a general target function (via targFunc) that is then iterated so that a certain target is achieved. The sampSizeMCT is a convenience wrapper of sampSize 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")
)
# S3 method for class 'targN'
plot(x, superpose = TRUE, line.at = NULL, xlab = NULL, ylab = NULL, ...)Arguments
- upperN, lowerN
Upper and lower bound for the target sample size.
lowerNdefaults tofloor(upperN/2).- targFunc, target
The target function needs to take as an input the vector of sample sizes in the different dose groups. For sampSize it needs to return a univariate number. For function targN it should return a numerical vector.
Example: targFunc could be a function that calculates the power of a test, and target the desired target power value.
For function 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).
Function targN simply calculates targFunc for a given set of sample sizes.- tol
A positive numeric value specifying the tolerance level for the bisection search algorithm. Bisection is stopped if the targFunc value is within tol of target.
- alRatio
Vector describing the relative patient allocations to the dose groups up to proportionality, e.g. rep(1, length(doses)) corresponds to balanced allocations.
- 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.
- verbose
Logical value indicating if a trace of the iteration progress of the bisection search algorithm should be displayed.
- ...
Arguments directly passed to the
powMCT()function in the sampSizeMCT and powN function.- power, sumFct
power is a numeric defining the desired summary power to achieve (in sampSizeMCT).
- step
Only needed for functions targN and powN. Stepsize for the sample size at which the target function is calculated. The steps are calculated via
seq(lowerN,upperN,by=step).- x, superpose, line.at, xlab, ylab
arguments for the plot method of targN and powN, additional arguments are passed down to the low-level lattice plotting routines.
Details
The targN functions calculates a general target function for different given sample sizes. The powN function is a convenience wrapper of targN for multiple contrast tests using the power as target function.
References
Pinheiro J, Bornkamp B, Bretz F (2006). “Design and Analysis of Dose Finding Studies Combining Multiple Comparisons and Modeling Procedures.” Journal of Biopharmaceutical Statistics, 16, 639-656. doi:10.1080/10543400600860428 .
Pinheiro J, Bornkamp B (2017). “Designing phase II dose-finding studies: sample size, doses, and dose allocation weights.” In Handbook of Methods for Designing, Monitoring, and Analyzing Dose-Finding Trials, 229–246. Chapman and Hall/CRC.
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
if (FALSE) { # \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))
} # }