# powMCT: Calculate power for multiple contrast test In DoseFinding: Planning and Analyzing Dose Finding Experiments

## Description

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

## Usage

 ```1 2 3``` ```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`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44``` ```## 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 ## placebo-adjusted scale ## 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) powMCT(linMat, altModels = fmodels, placAdj=TRUE, alpha = 0.05, S = V, df=6*50-6) # match df with the df above ## End(Not run) ```