gsDesign (version 3.0-1)

sfPoints: 4.5: 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.

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

# NOT RUN {
# 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

# }