sampSize function

Sample size calculations

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.

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).

• 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.

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
## 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,
                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))
## End(Not run)

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

See Also

powMCT

Author(s)

Jose Pinheiro, Bjoern Bornkamp