gsDesign (version 3.0-1)

sfLDOF: 4.4: 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. Both of these spending functions are available here, mainly for historical purposes. Neither requires a parameter.

Usage

sfLDOF(alpha, t, param)
sfLDPocock(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 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().

Value

An object of type spendfn. See spending functions for further details.

Details

The Lan-DeMets (1983) spending function to approximate an O'Brien-Fleming bound is implemented in the function (sfLDOF()): $$f(t; \alpha)=2-2\Phi\left(\Phi^{-1}(1-\alpha/2)/ t^{1/2}\right).$$ 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.

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.

See Also

Spending function overview, gsDesign, gsDesign package overview

Examples

# NOT RUN {
# 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
# }