powMCT {DoseFinding} R Documentation

## Calculate power for multiple contrast test

### Description

Calculate power for a multiple contrast test for a set of specified alternatives.

### Usage

```powMCT(contMat, alpha = 0.025, altModels, n, sigma, S, placAdj=FALSE,
alternative = c("one.sided", "two.sided"), df, critV,
control = mvtnorm.control())
```

### Arguments

 `contMat` Contrast matrix to use. The individual contrasts should be saved in the columns of the matrix `alpha` Significance level to use `altModels` An object of class Mods, defining the mean vectors under which the power should be calculated `n, sigma, S` Either a vector n and sigma or S need to be specified. When n and sigma are specified it is assumed computations are made for a normal homoscedastic ANOVA model with group sample sizes given by n and residual standard deviation sigma, i.e. the covariance matrix used for the estimates is thus `sigma^2*diag(1/n)` and the degrees of freedom are calculated as `sum(n)-nrow(contMat)`. When a single number is specified for n it is assumed this is the sample size per group and balanced allocations are used. When S is specified this will be used as covariance matrix for the estimates. `placAdj` Logical, if true, it is assumed that the standard deviation or variance matrix of the placebo-adjusted estimates are specified in sigma or S, respectively. The contrast matrix has to be produced on placebo-adjusted scale, see `optContr`, so that the coefficients are no longer contrasts (i.e. do not sum to 0). `alternative` Character determining the alternative for the multiple contrast trend test. `df` Degrees of freedom to assume in case S (a general covariance matrix) is specified. When n and sigma are specified the ones from the corresponding ANOVA model are calculated. `critV` Critical value, if equal to TRUE the critical value will be calculated. Otherwise one can directly specify the critical value here. `control` A list specifying additional control parameters for the qmvt and pmvt calls in the code, see also mvtnorm.control for details.

### Value

Numeric containing the calculated power values

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

`powN`, `sampSizeMCT`, `MCTtest`, `optContr`, `Mods`

### Examples

```## look at power under some dose-response alternatives
## first the candidate models used for the contrasts
doses <- c(0,10,25,50,100,150)
## define models to use as alternative
fmodels <- Mods(linear = NULL, emax = 25,
logistic = c(50, 10.88111), exponential= 85,
betaMod=rbind(c(0.33,2.31),c(1.39,1.39)),
doses = doses, addArgs=list(scal = 200),
placEff = 0, maxEff = 0.4)
## plot alternatives
plot(fmodels)
## power for to detect a trend
contMat <- optContr(fmodels, w = 1)
powMCT(contMat, altModels = fmodels, n = 50, alpha = 0.05, sigma = 1)

## Not run:
## power under the Dunnett test
## contrast matrix for Dunnett test with informative names
contMatD <- rbind(-1, diag(5))
rownames(contMatD) <- doses
colnames(contMatD) <- paste("D", doses[-1], sep="")
powMCT(contMatD, altModels = fmodels, n = 50, alpha = 0.05, sigma = 1)

## now investigate power of the contrasts in contMat under "general" alternatives
altFmods <- Mods(linInt = rbind(c(0, 1, 1, 1, 1),
c(0.5, 1, 1, 1, 0.5)),
doses=doses, placEff=0, maxEff=0.5)
plot(altFmods)
powMCT(contMat, altModels = altFmods, n = 50, alpha = 0.05, sigma = 1)

## now the first example but assume information only on the
## for balanced allocations and 50 patients with sigma = 1 one obtains
## the following covariance matrix
S <- 1^2/50*diag(6)
## now calculate variance of placebo adjusted estimates
CC <- cbind(-1,diag(5))
V <- (CC)%*%S%*%t(CC)
linMat <- optContr(fmodels, doses = c(10,25,50,100,150),
S = V, placAdj = TRUE)