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)
``` |

```
Loading required package: xtable
Loading required package: ggplot2
Symmetric two-sided group sequential design with
90 % power and 2.5 % Type I Error.
Spending computations assume trial stops
if a bound is crossed.
Sample
Size
Analysis Ratio* Z Nominal p Spend
1 0.384 2.29 0.011 0.0110
2 0.767 2.29 0.011 0.0079
3 1.151 2.29 0.011 0.0060
Total 0.0250
++ alpha spending:
Pocock boundary.
* Sample size ratio compared to fixed design with no interim
Boundary crossing probabilities and expected sample size
assume any cross stops the trial
Upper boundary (power or Type I Error)
Analysis
Theta 1 2 3 Total E{N}
0.0000 0.011 0.0079 0.0060 0.025 1.1276
3.2415 0.389 0.3421 0.1689 0.900 0.7210
Lower boundary (futility or Type II Error)
Analysis
Theta 1 2 3 Total
0.0000 0.011 0.0079 0.006 0.025
3.2415 0.000 0.0000 0.000 0.000
Symmetric two-sided group sequential design with
90 % power and 2.5 % Type I Error.
Spending computations assume trial stops
if a bound is crossed.
Sample
Size
Analysis Ratio* Z Nominal p Spend
1 0.384 2.29 0.011 0.0110
2 0.767 2.29 0.011 0.0079
3 1.151 2.29 0.011 0.0060
Total 0.0250
++ alpha spending:
Wang-Tsiatis boundary with Delta = 0.5.
* Sample size ratio compared to fixed design with no interim
Boundary crossing probabilities and expected sample size
assume any cross stops the trial
Upper boundary (power or Type I Error)
Analysis
Theta 1 2 3 Total E{N}
0.0000 0.011 0.0079 0.0060 0.025 1.1276
3.2415 0.389 0.3421 0.1689 0.900 0.7210
Lower boundary (futility or Type II Error)
Analysis
Theta 1 2 3 Total
0.0000 0.011 0.0079 0.006 0.025
3.2415 0.000 0.0000 0.000 0.000
Symmetric two-sided group sequential design with
90 % power and 2.5 % Type I Error.
Spending computations assume trial stops
if a bound is crossed.
Sample
Size
Analysis Ratio* Z Nominal p Spend
1 0.385 2.28 0.0112 0.0112
2 0.771 2.28 0.0112 0.0080
3 1.156 2.30 0.0107 0.0058
Total 0.0250
++ alpha spending:
Hwang-Shih-DeCani spending function with gamma = 1.
* Sample size ratio compared to fixed design with no interim
Boundary crossing probabilities and expected sample size
assume any cross stops the trial
Upper boundary (power or Type I Error)
Analysis
Theta 1 2 3 Total E{N}
0.0000 0.0112 0.0080 0.0058 0.025 1.1327
3.2415 0.3933 0.3418 0.1649 0.900 0.7213
Lower boundary (futility or Type II Error)
Analysis
Theta 1 2 3 Total
0.0000 0.0112 0.008 0.0058 0.025
3.2415 0.0000 0.000 0.0000 0.000
Symmetric two-sided group sequential design with
90 % power and 2.5 % Type I Error.
Spending computations assume trial stops
if a bound is crossed.
Sample
Size
Analysis Ratio* Z Nominal p Spend
1 0.122 2.34 0.0096 0.0096
2 0.244 2.34 0.0096 0.0070
3 1.221 2.34 0.0096 0.0084
Total 0.0250
++ alpha spending:
Pocock boundary.
* Sample size ratio compared to fixed design with no interim
Boundary crossing probabilities and expected sample size
assume any cross stops the trial
Upper boundary (power or Type I Error)
Analysis
Theta 1 2 3 Total E{N}
0.0000 0.0096 0.0070 0.0084 0.025 1.1864
3.2415 0.1135 0.1479 0.6386 0.900 0.9517
Lower boundary (futility or Type II Error)
Analysis
Theta 1 2 3 Total
0.0000 0.0096 0.007 0.0084 0.0250
3.2415 0.0003 0.000 0.0000 0.0003
Symmetric two-sided group sequential design with
90 % power and 2.5 % Type I Error.
Spending computations assume trial stops
if a bound is crossed.
Sample
Size
Analysis Ratio* Z Nominal p Spend
1 0.106 2.67 0.0038 0.0038
2 0.213 2.63 0.0043 0.0034
3 1.064 2.08 0.0189 0.0178
Total 0.0250
++ alpha spending:
Hwang-Shih-DeCani spending function with gamma = 1.
* Sample size ratio compared to fixed design with no interim
Boundary crossing probabilities and expected sample size
assume any cross stops the trial
Upper boundary (power or Type I Error)
Analysis
Theta 1 2 3 Total E{N}
0.0000 0.0038 0.0034 0.0178 0.025 1.0507
3.2415 0.0531 0.0939 0.7530 0.900 0.9328
Lower boundary (futility or Type II Error)
Analysis
Theta 1 2 3 Total
0.0000 0.0038 0.0034 0.0178 0.0250
3.2415 0.0001 0.0000 0.0000 0.0001
One-sided group sequential design with
90 % power and 2.5 % Type I Error.
Sample
Size
Analysis Ratio* Z Nominal p Spend
1 0.339 3.47 0.0003 0.0003
2 0.677 2.45 0.0071 0.0069
3 1.016 2.00 0.0225 0.0178
Total 0.0250
++ alpha spending:
O'Brien-Fleming boundary.
* Sample size ratio compared to fixed design with no interim
Boundary crossing probabilities and expected sample size
assume any cross stops the trial
Upper boundary (power or Type I Error)
Analysis
Theta 1 2 3 Total E{N}
0.0000 0.0003 0.0069 0.0178 0.025 1.0136
3.2415 0.0565 0.5288 0.3147 0.900 0.7987
One-sided group sequential design with
90 % power and 2.5 % Type I Error.
Sample
Size
Analysis Ratio* Z Nominal p Spend
1 0.339 3.47 0.0003 0.0003
2 0.677 2.45 0.0071 0.0069
3 1.016 2.00 0.0225 0.0178
Total 0.0250
++ alpha spending:
Wang-Tsiatis boundary with Delta = 0.
* Sample size ratio compared to fixed design with no interim
Boundary crossing probabilities and expected sample size
assume any cross stops the trial
Upper boundary (power or Type I Error)
Analysis
Theta 1 2 3 Total E{N}
0.0000 0.0003 0.0069 0.0178 0.025 1.0136
3.2415 0.0565 0.5288 0.3147 0.900 0.7987
```

gsDesign documentation built on May 31, 2017, 2:15 a.m.

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