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.
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.
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.
Real value > 0 and no more than 1. Normally,
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.
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
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# 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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