sampSize {DoseFinding} R Documentation

## Sample size calculations

### Description

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.

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.

### 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. lowerN defaults to floor(upperN/2). 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). 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. The ‘⁠placAdj⁠’ argument needs to be ‘⁠FALSE⁠’ (which is the default value for this argument). If sample size calculations are desired for a placebo-adjusted formulation use ‘⁠sampSize⁠’ or ‘⁠targN⁠’ directly. In case 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 ‘⁠Ntype == "total"⁠’ needs to be used if S is specified. When S is specified, automatically ‘⁠df = Inf⁠’ is assumed in the underlying ‘⁠powMCT⁠’ calls. For a homoscedastic normally distributed response variable only ‘⁠sigma⁠’ needs to be specified, as the sample size ‘⁠n⁠’ is iterated in the different ‘⁠powMCT⁠’ calls. power, sumFct power is a numeric defining the desired summary power to achieve (in ‘⁠sampSizeMCT⁠’). sumFct needs to be a function that combines the power values under the different alternatives into one value (in ‘⁠sampSizeMCT⁠’). 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.

### Author(s)

Jose Pinheiro, Bjoern Bornkamp

### 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

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,
## 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
## Not run:
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,
## 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))

## End(Not run)


[Package DoseFinding version 1.0-2 Index]