R: Calculate power for multiple contrast test

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

### Author(s)

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

### See Also

`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
    ## 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)

[Package DoseFinding version 1.0-2 Index]