getMonotoneFunction: Return Monotone Function Values

In optconerrf: Optimal Monotone Conditional Error Functions

Return Monotone Function Values

Description

Applies the provided monotonisation constants to a specified, possibly non-monotone function. The returned function values are non-increasing.

Usage

getMonotoneFunction(
  x,
  fun,
  lower = NULL,
  upper = NULL,
  argument = NULL,
  nSteps = 10^4,
  epsilon = 10^(-5),
  numberOfIterationsQ = 10^4,
  design
)

Arguments

x	Argument values.
fun	The function to be made monotone.
lower	The lower limit of the interval on which the function should be monotonised. Must be a numeric value.
upper	The upper limit of the interval on which the function should be monotonised.
argument	The argument in which the function should be monotonised, given as a character.
nSteps	The number of steps to be taken when checking the function for monotonicity. Must be a numeric value. Default 10^4.
epsilon	Maximum allowed difference between the initial and monotone integral. Must be a numeric value. Default 10^-5.
numberOfIterationsQ	Maximum number of iterations allowed to determine each value of q. Must be a numeric value. Default 10^4.
design	An object of class TrialDesignOptimalConditionalError created by getDesignOptimalConditionalErrorFunction(). Contains all necessary arguments to calculate the optimal conditional error function for the specified case.

Details

The exact monotonisation process is outlined in Brannath et al. (2024), but specified in terms of the first-stage test statistic z_1 rather than the first-stage p-value p_1.
The algorithm can easily be translated to the use of p-values by switching the maximum and minimum functions, i.e., replacing \min\{q, Q(z_1)\} by \max\{q, Q(p_1)\} and \min\{q, Q(z_1)\} by \max\{q, Q(p_1\}.

Value

Monotone function values.

References

Brannath, W., Dreher, M., zur Verth, J., Scharpenberg, M. (2024). Optimal monotone conditional error functions. https://arxiv.org/abs/2402.00814

optconerrf documentation built on Sept. 9, 2025, 5:29 p.m.