sfLDOF {gsDesign} | R Documentation |
Lan and DeMets (1983) first published the method of using spending functions to set boundaries for group sequential trials. In this publication they proposed two specific spending functions: one to approximate an O'Brien-Fleming design and the other to approximate a Pocock design. Both of these spending functions are available here, mainly for historical purposes. Neither requires a parameter.
sfLDOF(alpha, t, param) sfLDPocock(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 |
This parameter is not used and need not be specified. It is here so that the calling sequence conforms
the to the standard for spending functions used with gsDesign() . |
The Lan-DeMets (1983) spending function to approximate an
O'Brien-Fleming bound is implemented in the function (sfLDOF()
):
f(t; alpha)=2-2*Phi(Phi^(-1)(1-alpha/2)/t^(1/2)).
The Lan-DeMets (1983) spending function to approximate a Pocock design is implemented in the function sfLDPocock()
:
f(t;alpha)=ln(1+(e-1)t).
As shown in examples below, other spending functions can be used to get as good or better approximations to Pocock and
O'Brien-Fleming bounds. In particular, O'Brien-Fleming bounds can be closely approximated using sfExponential
.
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_anderson@merck.
Jennison C and Turnbull BW (2000), Group Sequential Methods with Applications to Clinical Trials. Boca Raton: Chapman and Hall.
Lan, KKG and DeMets, DL (1983), Discrete sequential boundaries for clinical trials. Biometrika;70: 659-663.
Spending function overview, gsDesign
, gsDesign package overview
# 2-sided, symmetric 6-analysis trial Pocock # spending function approximation gsDesign(k=6, sfu=sfLDPocock, test.type=2)$upper$bound # show actual Pocock design gsDesign(k=6, sfu="Pocock", test.type=2)$upper$bound # approximate Pocock again using a standard # Hwang-Shih-DeCani approximation gsDesign(k=6, sfu=sfHSD, sfupar=1, test.type=2)$upper$bound # use 'best' Hwang-Shih-DeCani approximation for Pocock, k=6; # see manual for details gsDesign(k=6, sfu=sfHSD, sfupar=1.3354376, test.type=2)$upper$bound # 2-sided, symmetric 6-analysis trial # O'Brien-Fleming spending function approximation gsDesign(k=6, sfu=sfLDOF, test.type=2)$upper$bound # show actual O'Brien-Fleming bound gsDesign(k=6, sfu="OF", test.type=2)$upper$bound # approximate again using a standard Hwang-Shih-DeCani # approximation to O'Brien-Fleming x<-gsDesign(k=6, test.type=2) x$upper$bound x$upper$param # use 'best' exponential approximation for k=6; see manual for details gsDesign(k=6, sfu=sfExponential, sfupar=0.7849295, test.type=2)$upper$bound