gsDesign (version 3.0-1)

Wang-Tsiatis Bounds: 5.0: Wang-Tsiatis Bounds

Description

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.

Details

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, \(i=1,2,\ldots,k\). 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 $$ct_i^{\Delta-0.5}$$ for \(i= 1,2,\ldots,k\) 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.

References

Jennison C and Turnbull BW (2000), Group Sequential Methods with Applications to Clinical Trials. Boca Raton: Chapman and Hall.

See Also

Spending function overview, gsDesign, gsProbability

Examples

# NOT RUN {
# 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)
# }