spendingFunction: Spending Function

In gsDesign: Group Sequential Design

Spending Function

Description

Spending Function

Usage

## S3 method for class 'spendfn'
summary(object, ...)

spendingFunction(alpha, t, param)

Arguments

object	A spendfn object to be summarized.
...	Not currently used.
alpha	Real value > 0 and no more than 1. Defaults in calls to gsDesign() are alpha=0.025 for one-sided Type I error specification and alpha=0.1 for Type II error specification. However, this could be set to 1 if, for descriptive purposes, you wish to see the proportion of spending as a function of the proportion of sample size/information.
t	A vector of points with increasing values from 0 to 1, inclusive. Values of the proportion of sample size/information for which the spending function will be computed.
param	A single real value or a vector of real values specifying the spending function parameter(s); this must be appropriately matched to the spending function specified.

Value

spendingFunction and spending functions in general produce an object of type spendfn.

name	A character string with the name of the spending function.
param	any parameters used for the spending function.
parname	a character string or strings with the name(s) of the parameter(s) in param.
sf	the spending function specified.
spend	a vector of cumulative spending values corresponding to the input values in t.
bound	this is null when returned from the spending function, but is set in gsDesign() if the spending function is called from there. Contains z-values for bounds of a design.
prob	this is null when returned from the spending function, but is set in gsDesign() if the spending function is called from there. Contains probabilities of boundary crossing at i-th analysis for j-th theta value input to gsDesign() in prob[i,j].

Note

The gsDesign technical manual is available at https://keaven.github.io/gsd-tech-manual/.

Author(s)

Keaven Anderson [e-mail]

References

Jennison C and Turnbull BW (2000), Group Sequential Methods with Applications to Clinical Trials. Boca Raton: Chapman and Hall.

See Also

gsDesign, sfHSD, sfPower, sfLogistic, sfExponential, sfTruncated, vignette("gsDesignPackageOverview")

Examples

# Example 1: simple example showing what most users need to know

# Design a 4-analysis trial using a Hwang-Shih-DeCani spending function
# for both lower and upper bounds
x <- gsDesign(k = 4, sfu = sfHSD, sfupar = -2, sfl = sfHSD, sflpar = 1)

# Print the design
x
# Summarize the spending functions
summary(x$upper)
summary(x$lower)

# Plot the alpha- and beta-spending functions
plot(x, plottype = 5)

# What happens to summary if we used a boundary function design
x <- gsDesign(test.type = 2, sfu = "OF")
y <- gsDesign(test.type = 1, sfu = "WT", sfupar = .25)
summary(x$upper)
summary(y$upper)

# Example 2: advanced example: writing a new spending function
# Most users may ignore this!

# Implementation of 2-parameter version of
# beta distribution spending function
# assumes t and alpha are appropriately specified (does not check!)
sfbdist <- function(alpha, t, param) {
  # Check inputs
  checkVector(param, "numeric", c(0, Inf), c(FALSE, TRUE))
  if (length(param) != 2) {
    stop(
      "b-dist example spending function parameter must be of length 2"
    )
  }

  # Set spending using cumulative beta distribution and return
  x <- list(
    name = "B-dist example", param = param, parname = c("a", "b"),
    sf = sfbdist, spend = alpha *
      pbeta(t, param[1], param[2]), bound = NULL, prob = NULL
  )

  class(x) <- "spendfn"

  x
}

# Now try it out!
# Plot some example beta (lower bound) spending functions using
# the beta distribution spending function
t <- 0:100 / 100
plot(
  t, sfbdist(1, t, c(2, 1))$spend,
  type = "l",
  xlab = "Proportion of information",
  ylab = "Cumulative proportion of total spending",
  main = "Beta distribution Spending Function Example"
)
lines(t, sfbdist(1, t, c(6, 4))$spend, lty = 2)
lines(t, sfbdist(1, t, c(.5, .5))$spend, lty = 3)
lines(t, sfbdist(1, t, c(.6, 2))$spend, lty = 4)
legend(
  x = c(.65, 1), y = 1 * c(0, .25), lty = 1:4,
  legend = c("a=2, b=1", "a=6, b=4", "a=0.5, b=0.5", "a=0.6, b=2")
)

gsDesign documentation built on Sept. 11, 2024, 5:58 p.m.