R: Kim-DeMets (power) Spending Function

sfPower {gsDesign} | R Documentation

## Kim-DeMets (power) Spending Function

### Description

The function `sfPower()` implements a Kim-DeMets (power) spending function. This is a flexible, one-parameter spending function recommended by Jennison and Turnbull (2000). 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 Kim-DeMets spending function takes the form

f(t; alpha, rho) = alpha t^rho

where rho is the value passed in `param`. See examples below for a range of values of rho that may be of interest (`param=0.75` to `3` are documented there).

### Usage

    sfPower(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, positive value specifying the rho parameter for which Kim-DeMets spending is to be computed; allowable range is (0,15]

### 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.

### 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 Kim-DeMets spending function
    # for both lower and upper bounds
    x <- gsDesign(k = 4, sfu = sfPower, sfupar = 3, sfl = sfPower, sflpar = 1.5)

    # print the design
    x

    # plot the spending function using many points to obtain a smooth curve
    # show rho=3 for approximation to O'Brien-Fleming and rho=.75 for
    # approximation to Pocock design.
    # Also show rho=2 for an intermediate spending.
    # Compare these to Hwang-Shih-DeCani spending with gamma=-4,  -2,  1
    t <- 0:100 / 100
    plot(t, sfPower(0.025, t, 3)$spend,
      xlab = "Proportion of sample size",
      ylab = "Cumulative Type I error spending",
      main = "Kim-DeMets (rho) versus Hwang-Shih-DeCani (gamma) Spending",
      type = "l", cex.main = .9
    )
    lines(t, sfPower(0.025, t, 2)$spend, lty = 2)
    lines(t, sfPower(0.025, t, 0.75)$spend, lty = 3)
    lines(t, sfHSD(0.025, t, 1)$spend, lty = 3, col = 2)
    lines(t, sfHSD(0.025, t, -2)$spend, lty = 2, col = 2)
    lines(t, sfHSD(0.025, t, -4)$spend, lty = 1, col = 2)
    legend(
      x = c(.0, .375), y = .025 * c(.65, 1), lty = 1:3,
      legend = c("rho= 3", "rho= 2", "rho= 0.75")
    )
    legend(
      x = c(.0, .357), y = .025 * c(.65, .85), lty = 1:3, bty = "n", col = 2,
      legend = c("gamma= -4", "gamma= -2", "gamma=1")
    )

[Package gsDesign version 3.2.0 Index]