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 1.0-1 Index]