sfHSD {gsDesign} | R Documentation |
The function sfHSD
implements a Hwang-Shih-DeCani spending function.
This is the default spending function for gsDesign()
.
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.
sfHSD(alpha, t, param)
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 real value specifying the gamma parameter for which Hwang-Shih-DeCani spending is to be computed; allowable range is [-40, 40] |
A Hwang-Shih-DeCani spending function takes the form
f(t; alpha, gamma) = alpha * (1-exp(-gamma * t))/(1 - exp(-gamma))
where gamma is the value passed in param
.
A value of gamma=-4 is used to approximate an O'Brien-Fleming design (see sfExponential
for a better fit),
while a value of gamma=1 approximates a Pocock design well.
An object of type spendfn
. See Spending function overview 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_anderson@merck.com
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
# design a 4-analysis trial using a Hwang-Shih-DeCani spending function # for both lower and upper bounds x <- gsDesign(k=4, sfu=sfHSD, sfupar=-2, sfl=sfHSD, sflpar=1) # print the design x # since sfHSD is the default for both sfu and sfl, # this could have been written as x <- gsDesign(k=4, sfupar=-2, sflpar=1) # print again x # plot the spending function using many points to obtain a smooth curve # show default values of gamma to see how the spending function changes # also show gamma=1 which is supposed to approximate a Pocock design t <- 0:100/100 plot(t, sfHSD(0.025, t, -4)$spend, xlab="Proportion of final sample size", ylab="Cumulative Type I error spending", main="Hwang-Shih-DeCani Spending Function Example", type="l") lines(t, sfHSD(0.025, t, -2)$spend, lty=2) lines(t, sfHSD(0.025, t, 1)$spend, lty=3) legend(x=c(.0, .375), y=.025*c(.8, 1), lty=1:3, legend=c("gamma= -4", "gamma= -2", "gamma= 1"))