powerMM: Calculate power for different sample sizes

In MCPMod: Design and Analysis of Dose-Finding Studies

Description

Calculates the power under the assumed candidate set for different sample sizes.

Usage

powerMM(models, doses, base, maxEff, sigma, lower, upper, step,
        sumFct = c("min", "mean", "max"), off = 0.1 * max(doses),
        scal = 1.2 * max(doses), alpha = 0.025, twoSide = FALSE,
        control = mvtnorm.control(), muMat = NULL, alRatio = NULL,
        typeN = c("arm", "total"), ...)

Arguments

models	A list specifying the candidate models. This can also be a fullMod object, then the arguments base, maxEff, off and scal are ignored.
doses	Dose levels to be administered
base	Expected baseline effect
maxEff	Expected maximum change from baseline
sigma	Expected standard deviation
lower, upper	Maximum and minimum group sample size for which the power is calculated.
step	Stepsize for the sample size at which the power is calculated. It is calculated at seq(lower,upper,by=step).
sumFct	A character vector giving the names of the summary functions used to combine the power values into one value. By default the minimum, the mean and the maximum are used.
off	Offset parameter for the linear in log model (default 10 perc. of maximum dose).
scal	Scale parameter for the beta model (default 20 perc. larger than maximum dose).
alpha	Level of significance (default: 0.025)
twoSide	Logical indicating whether a two sided or a one-sided test should be performed. By default FALSE, so one-sided testing.
control	A list of options for the pmvt and qmvt functions as produced by mvtnorm.control.
muMat	An optional matrix with means in the columns, dimnames should be given (dose levels and names of contrasts), if specified the the models argument should not be specified, see examples below.
alRatio	Vector describing the relative patient allocations to the dose groups. See examples below, e.g. c(1,2,2) corresponds to allocating twice as many patients in dose groups two and three. Per default balanced allocations are assumed.
typeN	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. See examples below.
...	Possible additional arguments for sumFct.

Details

Given the candidate set of models and associated guesstimates the function calculates the power to detect every model in the candidate set for different group sample sizes. Additionally summary functions can be specified to calculate the combined power (by default the minimum, mean and maximum). The location and scale parameters are determined by forcing the model function to go through (0,base) and (dmax,maxEff), see Pinheiro et al. (2006) for details. There exists a plot method for the output of the powerMM function. See the examples below.

Value

A powerMM object, i.e. a matrix containing the power values for different sample sizes and models

References

Bornkamp B., Pinheiro J. C., and Bretz, F. (2009). MCPMod: An R Package for the Design and Analysis of Dose-Finding Studies, Journal of Statistical Software, 29(7), 1–23

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

plot.powerMM, powCalc

Examples

## Not run: 
doses <- c(0,10,25,50,100,150)                                         
models <- list(linear = NULL, emax = 25,                               
               logistic = c(50, 10.88111), exponential= 85,            
               betaMod=matrix(c(0.33,2.31,1.39,1.39), byrow=TRUE, nrow=2))
pM <- powerMM(models, doses, base = 0, maxEff = 0.4, sigma = 1,
            alpha = 0.05, lower = 10, upper = 100, step = 20, scal = 200)         
pM
# a graphical display provides plot method
plot(pM)                                
# reproduces plot in JBS 16, p.651      
plot(pM, line.at = 0.8, models = "none")


# the same with fullMod object and default alpha
fMod <- fullMod(models, doses, base = 0, maxEff = 0.4, scal=200) 
pM <- powerMM(fMod, sigma = 1, lower = 10, upper = 100, 
              step = 20, scal = 200)         
pM

# using unbalanced (but fixed) allocations
pM <- powerMM(models, doses, base = 0, maxEff = 0.4, sigma = 1,       
               lower = 10, upper = 100, step = 20, scal = 200,
               alRatio = c(3, 2, 2, 1, 1, 1), typeN = "arm") 
plot(pM, summ = "mean")

# example, where means are directly specified
# doses   
dvec <- c(0, 10, 50, 100)
# mean vectors
mu1 <- c(1, 2, 2, 2)
mu2 <- c(1, 1, 2, 2)
mu3 <- c(1, 1, 1, 2)
mMat <- cbind(mu1, mu2, mu3)
dimnames(mMat)[[1]] <- dvec
pM <- powerMM(muMat = mMat, doses = dvec, sigma = 2, lower = 10,
              upper = 100, step = 20)         
pM

## End(Not run)

Example output

Loading required package: mvtnorm
Loading required package: lattice
      linear      emax  logistic exponential  betaMod1  betaMod2       min
10 0.2164735 0.2178171 0.2874361   0.1995559 0.1969237 0.2096792 0.1969237
30 0.4969080 0.4858853 0.6509473   0.4657323 0.5052014 0.4755112 0.4657323
50 0.7019457 0.6843789 0.8517957   0.6708289 0.7335669 0.6776581 0.6708289
70 0.8333637 0.8176918 0.9425685   0.8099913 0.8695279 0.8131070 0.8099913
90 0.9119092 0.8999899 0.9796180   0.8961539 0.9408605 0.8978555 0.8961539
        mean       max
10 0.2213143 0.2874361
30 0.5133643 0.6509473
50 0.7200290 0.8517957
70 0.8477084 0.9425685
90 0.9210645 0.9796180
attr(,"alRatio")
[1] 1
attr(,"sumFct")
[1] "min"  "mean" "max" 
attr(,"class")
[1] "powerMM"
      linear      emax  logistic exponential  betaMod1  betaMod2       min
10 0.1396930 0.1392149 0.1950013   0.1264927 0.1239161 0.1333446 0.1239161
30 0.3787782 0.3645262 0.5344456   0.3490849 0.3864658 0.3572209 0.3490849
50 0.5917686 0.5693977 0.7720868   0.5591998 0.6292449 0.5646946 0.5591998
70 0.7507108 0.7287865 0.9006623   0.7218047 0.7983974 0.7252889 0.7218047
90 0.8554441 0.8366637 0.9599484   0.8337316 0.8982772 0.8351056 0.8337316
        mean       max
10 0.1429438 0.1950013
30 0.3950869 0.5344456
50 0.6143987 0.7720868
70 0.7709418 0.9006623
90 0.8698618 0.9599484
attr(,"alRatio")
[1] 1
attr(,"sumFct")
[1] "min"  "mean" "max" 
attr(,"class")
[1] "powerMM"
         mu1       mu2       mu3       min      mean       max
10 0.1900207 0.2558825 0.1898123 0.1898123 0.2119052 0.2558825
30 0.5348320 0.6795100 0.5348305 0.5348305 0.5830575 0.6795100
50 0.7750864 0.8925756 0.7750706 0.7750706 0.8142442 0.8925756
70 0.9052432 0.9701097 0.9052237 0.9052237 0.9268589 0.9701097
90 0.9634187 0.9925838 0.9634074 0.9634074 0.9731366 0.9925838
attr(,"alRatio")
[1] 1
attr(,"sumFct")
[1] "min"  "mean" "max" 
attr(,"class")
[1] "powerMM"

MCPMod documentation built on March 26, 2020, 7:28 p.m.