Description Details Note Author(s) References See Also Examples

`gsDesign`

offers the option of using Wang-Tsiatis bounds as an alternative to
the spending function approach to group sequential design.
Wang-Tsiatis bounds include both Pocock and O'Brien-Fleming designs.
Wang-Tsiatis bounds are currently only available for 1-sided and symmetric 2-sided designs.
Wang-Tsiatis bounds are typically used with equally spaced timing between analyses, but
the option is available to use them with unequal spacing.

Wang-Tsiatis bounds are defined as follows.
Assume *k* analyses and let *Z_i* represent the upper bound and *t_i* the proportion of the
total planned sample size for the *i*-th analysis,
*i=1,2,…,k*.
Let *Delta* be a real-value.
Typically *Delta* will range from 0 (O'Brien-Fleming design) to 0.5 (Pocock design).
The upper boundary is defined by

*ct_i^{Δ-0.5}*

for *i= 1,2,…,k* where *c* depends on the other parameters.
The parameter *Delta* is supplied to `gsDesign()`

in the parameter `sfupar`

.
For O'Brien-Fleming and Pocock designs there is also a calling sequence that does not require a parameter.
See examples.

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.

`Spending function overview, gsDesign`

, `gsProbability`

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 | ```
# Pocock design
gsDesign(test.type=2, sfu="Pocock")
# alternate call to get Pocock design specified using
# Wang-Tsiatis option and Delta=0.5
gsDesign(test.type=2, sfu="WT", sfupar=0.5)
# this is how this might work with a spending function approach
# Hwang-Shih-DeCani spending function with gamma=1 is often used
# to approximate Pocock design
gsDesign(test.type=2, sfu=sfHSD, sfupar=1)
# unequal spacing works, but may not be desirable
gsDesign(test.type=2, sfu="Pocock", timing=c(.1, .2))
# spending function approximation to Pocock with unequal spacing
# is quite different from this
gsDesign(test.type=2, sfu=sfHSD, sfupar=1, timing=c(.1, .2))
# One-sided O'Brien-Fleming design
gsDesign(test.type=1, sfu="OF")
# alternate call to get O'Brien-Fleming design specified using
# Wang-Tsiatis option and Delta=0
gsDesign(test.type=1, sfu="WT", sfupar=0)
``` |

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