sfLDOF {gsDesign} | R Documentation |
Lan-DeMets Spending function overview
Description
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. The spending function to approximate O'Brien-Fleming has been generalized as proposed by Liu, et al (2012)
With param=1=rho
, 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\left(\Phi^{-1}(1-\alpha/2)/ t^{\rho/2}\right).
For rho
otherwise in [.005,2]
, this is the generalized version of Liu et al (2012).
For param
outside of [.005,2]
, rho
is set to 1. The Lan-DeMets (1983)
spending function to approximate a Pocock design is implemented in the
function sfLDPocock()
:
f(t;\alpha)=\alpha ln(1+(e-1)t).
As shown in
examples below, other spending functions can be used to ge t as good or
better approximations to Pocock and O'Brien-Fleming bounds. In particular,
O'Brien-Fleming bounds can be closely approximated using
sfExponential
.
Usage
sfLDOF(alpha, t, param = NULL)
sfLDPocock(alpha, t, param)
Arguments
alpha |
Real value |
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 for |
Value
An object of type spendfn
. See spending functions for further
details.
Note
The gsDesign technical manual is available at https://keaven.github.io/gsd-tech-manual/.
Author(s)
Keaven Anderson keaven_anderson@merck.com
References
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.
Liu, Q, Lim, P, Nuamah, I, and Li, Y (2012), On adaptive error spending approach for group sequential trials with random information levels. Journal of biopharmaceutical statistics; 22(4), 687-699.
See Also
vignette("SpendingFunctionOverview")
, gsDesign
,
vignette("gsDesignPackageOverview")
Examples
library(ggplot2)
# 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
# plot spending functions for generalized Lan-DeMets approximation of
ti <-(0:100)/100
rho <- c(.05,.5,1,1.5,2,2.5,3:6,8,10,12.5,15,20,30,200)/10
df <- NULL
for(r in rho){
df <- rbind(df,data.frame(t=ti,rho=r,alpha=.025,spend=sfLDOF(alpha=.025,t=ti,param=r)$spend))
}
ggplot(df,aes(x=t,y=spend,col=as.factor(rho)))+
geom_line()+
guides(col=guide_legend(expression(rho)))+
ggtitle("Generalized Lan-DeMets O'Brien-Fleming Spending Function")