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
powMCTfunction 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. C., Bornkamp, B., and Bretz, F. (2006). Design and analysis of dose finding studies combining multiple comparisons and modeling procedures, Journal of Biopharmaceutical Statistics, 16, 639–656
Pinheiro, J.C., Bornkamp, B. (2017) Designing Phase II Dose-Finding Studies: Sample Size, Doses and Dose Allocation Weights, in O'Quigley, J., Iasonos, A. and Bornkamp, B. (eds) Handbook of methods for designing, monitoring, and analyzing dose-finding trials, CRC press
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))
} # }