Description Usage Arguments Details Value Note Author(s) References See Also Examples

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.

1 2 | ```
sfLDOF(alpha, t, param)
sfLDPocock(alpha, t, param)
``` |

`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 and need not be specified. It is here so that the calling sequence conforms
the to the standard for spending functions used with |

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)\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`

.

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.

Lan, KKG and DeMets, DL (1983), Discrete sequential boundaries for clinical trials. *Biometrika*;70: 659-663.

Spending function overview, `gsDesign`

, gsDesign package overview

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 | ```
# 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
``` |

```
Loading required package: xtable
Loading required package: ggplot2
[1] 2.495115 2.476907 2.454964 2.437262 2.423276 2.412059
[1] 2.453211 2.453211 2.453211 2.453211 2.453211 2.453211
[1] 2.507958 2.471981 2.443139 2.426686 2.420302 2.421749
[1] 2.469285 2.448341 2.436191 2.437278 2.448837 2.468360
[1] 5.366558 3.710340 2.969736 2.538677 2.252190 2.044790
[1] 5.028296 3.555542 2.903088 2.514148 2.248722 2.052793
[1] 3.325024 3.103223 2.860383 2.603454 2.330046 2.034988
[1] -4
[1] 4.998123 3.598098 2.933292 2.530838 2.253723 2.047082
```

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