Description Usage Arguments Value Note Author(s) References See Also Examples

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.

1 |

`alpha` |
Real value |

`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 |

An object of type `spendfn`

. See spending functions for further details.

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.

Keaven Anderson keaven\[email protected]

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

Spending function overview, `gsDesign`

, gsDesign package overview, sfLogistic

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 | ```
# 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
``` |

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