R: Pointwise Spending Function

sfPoints {gsDesign} | R Documentation

## Pointwise Spending Function

### Description

The function `sfPoints` implements a spending function with values specified for an arbitrary set of specified points. It is now recommended to use sfLinear rather than sfPoints. Normally `sfPoints` 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, just the points they wish to specify. If using `sfPoints()` in a design, it is recommended to specify how to interpolate between the specified points (e.g,, linear interpolation); also consider fitting smooth spending functions; see Spending_Function_Overview.

### Usage

    sfPoints(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 and <=1. Values of the proportion of sample size/information for which the spending function will be computed.
`param` | A vector of the same length as `t` specifying the cumulative proportion of spending to corresponding to each point in `t`; must be >=0 and <=1.

### Value

An object of type `spendfn`. See spending functions 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, sfLogistic

### Examples

    library(ggplot2)
    # example to specify spending on a pointwise basis
    x <- gsDesign(
      k = 6, sfu = sfPoints, sfupar = c(.01, .05, .1, .25, .5, 1),
      test.type = 2
    )
    x

    # get proportion of upper spending under null hypothesis
    # at each analysis
    y <- x$upper$prob[, 1] / .025

    # change to cumulative proportion of spending
    for (i in 2:length(y))
      y[i] <- y[i - 1] + y[i]

    # this should correspond to input sfupar
    round(y, 6)

    # plot these cumulative spending points
    plot(1:6 / 6, y,
      main = "Pointwise spending function example",
      xlab = "Proportion of final sample size",
      ylab = "Cumulative proportion of spending",
      type = "p"
    )

    # approximate this with a t-distribution spending function
    # by fitting 3 points
    tx <- 0:100 / 100
    lines(tx, sfTDist(1, tx, c(c(1, 3, 5) / 6, .01, .1, .5))$spend)
    text(x = .6, y = .9, labels = "Pointwise Spending Approximated by")
    text(x = .6, y = .83, "t-Distribution Spending with 3-point interpolation")

    # example without lower spending at initial interim or
    # upper spending at last interim
    x <- gsDesign(
      k = 3, sfu = sfPoints, sfupar = c(.25, .25),
      sfl = sfPoints, sflpar = c(0, .25)
    )
    x

[Package gsDesign version 3.2.0 Index]