R: Hwang-Shih-DeCani Spending Function

sfHSD {gsDesign} | R Documentation

## Hwang-Shih-DeCani Spending Function

### Description

The function `sfHSD` implements a Hwang-Shih-DeCani spending function. This is the default spending function for `gsDesign()`. Normally it will be passed to `gsDesign` in the parameter `sfu` for the upper bound or `sfl` for the lower bound to specify a spending function family for a design. In this case, the user does not need to know the calling sequence. The calling sequence is useful, however, when the user wishes to plot a spending function as demonstrated below in examples.

A Hwang-Shih-DeCani spending function takes the form

f(t; alpha, gamma) = alpha * (1-exp(-gamma * t))/(1 - exp(-gamma))

where gamma is the value passed in `param`. A value of gamma=-4 is used to approximate an O'Brien-Fleming design (see `sfExponential` for a better fit), while a value of gamma=1 approximates a Pocock design well.

### Usage

    sfHSD(alpha, t, param)

### Arguments

`alpha` | Real value > 0 and no more than 1. Normally, `alpha=0.025` for one-sided Type I error specification or `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 specifying the gamma parameter for which Hwang-Shih-DeCani spending is to be computed; allowable range is [-40, 40]

### Value

An object of type `spendfn`. See Spending_Function_Overview for further details.

### Note

The manual is not linked to this help file, but is available in library/gsdesign/doc/gsDesignManual.pdf in the directory where R is installed.

### Author(s)

Keaven Anderson keaven\_anderson@merck.com

### References

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

### See Also

Spending_Function_Overview, `gsDesign`, gsDesign package overview

### Examples

    library(ggplot2)
    # 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

    # since sfHSD is the default for both sfu and sfl,
    # this could have been written as
    x <- gsDesign(k = 4, sfupar = -2, sflpar = 1)

    # print again
    x

    # plot the spending function using many points to obtain a smooth curve
    # show default values of gamma to see how the spending function changes
    # also show gamma=1 which is supposed to approximate a Pocock design
    t <- 0:100 / 100
    plot(t, sfHSD(0.025, t, -4)$spend,
      xlab = "Proportion of final sample size",
      ylab = "Cumulative Type I error spending",
      main = "Hwang-Shih-DeCani Spending Function Example", type = "l"
    )
    lines(t, sfHSD(0.025, t, -2)$spend, lty = 2)
    lines(t, sfHSD(0.025, t, 1)$spend, lty = 3)
    legend(
      x = c(.0, .375), y = .025 * c(.8, 1), lty = 1:3,
      legend = c("gamma= -4", "gamma= -2", "gamma= 1")
    )

[Package gsDesign version 3.2.0 Index]