getDesignInverseNormal {rpact}R Documentation

Get Design Inverse Normal


Provides adjusted boundaries and defines a group sequential design for its use in the inverse normal combination test.


  kMax = NA_integer_,
  alpha = NA_real_,
  beta = NA_real_,
  sided = 1L,
  informationRates = NA_real_,
  futilityBounds = NA_real_,
  typeOfDesign = c("OF", "P", "WT", "PT", "HP", "WToptimum", "asP", "asOF", "asKD",
    "asHSD", "asUser", "noEarlyEfficacy"),
  deltaWT = NA_real_,
  deltaPT1 = NA_real_,
  deltaPT0 = NA_real_,
  optimizationCriterion = c("ASNH1", "ASNIFH1", "ASNsum"),
  gammaA = NA_real_,
  typeBetaSpending = c("none", "bsP", "bsOF", "bsKD", "bsHSD", "bsUser"),
  userAlphaSpending = NA_real_,
  userBetaSpending = NA_real_,
  gammaB = NA_real_,
  bindingFutility = NA,
  betaAdjustment = NA,
  constantBoundsHP = 3,
  twoSidedPower = NA,
  tolerance = 1e-08



Ensures that all arguments (starting from the "...") are to be named and that a warning will be displayed if unknown arguments are passed.


The maximum number of stages K. Must be a positive integer of length 1 (default value is 3). The maximum selectable kMax is 20 for group sequential or inverse normal and 6 for Fisher combination test designs.


The significance level alpha, default is 0.025. Must be a positive numeric of length 1.


Type II error rate, necessary for providing sample size calculations (e.g., getSampleSizeMeans()), beta spending function designs, or optimum designs, default is 0.20. Must be a positive numeric of length 1.


Is the alternative one-sided (1) or two-sided (2), default is 1. Must be a positive integer of length 1.


The information rates t_1, ..., t_kMax (that must be fixed prior to the trial), default is (1:kMax) / kMax. For the weighted inverse normal design, the weights are derived through w_1 = sqrt(t_1), and w_k = sqrt(t_k - t_(k-1)). For the weighted Fisher's combination test, the weights (scales) are w_k = sqrt((t_k - t_(k-1)) / t_1) (see the documentation).


The futility bounds, defined on the test statistic z scale (numeric vector of length kMax - 1).


The type of design. Type of design is one of the following: O'Brien & Fleming ("OF"), Pocock ("P"), Wang & Tsiatis Delta class ("WT"), Pampallona & Tsiatis ("PT"), Haybittle & Peto ("HP"), Optimum design within Wang & Tsiatis class ("WToptimum"), O'Brien & Fleming type alpha spending ("asOF"), Pocock type alpha spending ("asP"), Kim & DeMets alpha spending ("asKD"), Hwang, Shi & DeCani alpha spending ("asHSD"), user defined alpha spending ("asUser"), no early efficacy stop ("noEarlyEfficacy"), default is "OF".


Delta for Wang & Tsiatis Delta class.


Delta1 for Pampallona & Tsiatis class rejecting H0 boundaries.


Delta0 for Pampallona & Tsiatis class rejecting H1 boundaries.


Optimization criterion for optimum design within Wang & Tsiatis class ("ASNH1", "ASNIFH1", "ASNsum"), default is "ASNH1", see details.


Parameter for alpha spending function.


Type of beta spending. Type of of beta spending is one of the following: O'Brien & Fleming type beta spending, Pocock type beta spending, Kim & DeMets beta spending, Hwang, Shi & DeCani beta spending, user defined beta spending ("bsOF", "bsP", "bsKD", "bsHSD", "bsUser", default is "none").


The user defined alpha spending. Numeric vector of length kMax containing the cumulative alpha-spending (Type I error rate) up to each interim stage: 0 <= alpha_1 <= ... <= alpha_K <= alpha.


The user defined beta spending. Vector of length kMax containing the cumulative beta-spending up to each interim stage.


Parameter for beta spending function.


Logical. If bindingFutility = TRUE is specified the calculation of the critical values is affected by the futility bounds and the futility threshold is binding in the sense that the study must be stopped if the futility condition was reached (default is FALSE).


For two-sided beta spending designs, if betaAdjustement = TRUE a linear adjustment of the beta spending values is performed if an overlapping of decision regions for futility stopping at earlier stages occurs, otherwise no adjustment is performed (default is TRUE).


The constant bounds up to stage kMax - 1 for the Haybittle & Peto design (default is 3).


For two-sided testing, if twoSidedPower = TRUE is specified the sample size calculation is performed by considering both tails of the distribution. Default is FALSE, i.e., it is assumed that one tail probability is equal to 0 or the power should be directed to one part.


The numerical tolerance, default is 1e-08.


Depending on typeOfDesign some parameters are specified, others not. For example, only if typeOfDesign "asHSD" is selected, gammaA needs to be specified.

If an alpha spending approach was specified ("asOF", "asP", "asKD", "asHSD", or "asUser") additionally a beta spending function can be specified to produce futility bounds.

For optimum designs, "ASNH1" minimizes the expected sample size under H1, "ASNIFH1" minimizes the sum of the maximum sample and the expected sample size under H1, and "ASNsum" minimizes the sum of the maximum sample size, the expected sample size under a value midway H0 and H1, and the expected sample size under H1.


Returns a TrialDesign object. The following generics (R generic functions) are available for this result object:

How to get help for generic functions

Click on the link of a generic in the list above to go directly to the help documentation of the rpact specific implementation of the generic. Note that you can use the R function methods to get all the methods of a generic and to identify the object specific name of it, e.g., use methods("plot") to get all the methods for the plot generic. There you can find, e.g., plot.AnalysisResults and obtain the specific help documentation linked above by typing ?plot.AnalysisResults.

See Also

getDesignSet() for creating a set of designs to compare different designs.

Other design functions: getDesignCharacteristics(), getDesignConditionalDunnett(), getDesignFisher(), getDesignGroupSequential(), getGroupSequentialProbabilities(), getPowerAndAverageSampleNumber()


# Calculate two-sided critical values for a four-stage 
# Wang & Tsiatis design with Delta = 0.25 at level alpha = 0.05
getDesignInverseNormal(kMax = 4, alpha = 0.05, sided = 2, 
    typeOfDesign = "WT", deltaWT = 0.25) 
# Defines a two-stage design at one-sided alpha = 0.025 with provision of early stopping  
# if the one-sided p-value exceeds 0.5 at interim and no early stopping for efficacy. 
# The futility bound is non-binding.
getDesignInverseNormal(kMax = 2, typeOfDesign = "noEarlyEfficacy", futilityBounds = 0)  
## Not run: 
# Calculate one-sided critical values and binding futility bounds for a three-stage 
# design with alpha- and beta-spending functions according to Kim & DeMets with gamma = 2.5
# (planned informationRates as specified, default alpha = 0.025 and beta = 0.2)
getDesignInverseNormal(kMax = 3, informationRates = c(0.3, 0.75, 1), 
    typeOfDesign = "asKD", gammaA = 2.5, typeBetaSpending = "bsKD", 
    gammaB = 2.5, bindingFutility = TRUE)
## End(Not run) 

[Package rpact version 4.0.0 Index]