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

Computes power/Type I error and expected sample size for a group sequential design
across a selected set of parameter values for a given set of analyses and boundaries.
The print function has been extended using `print.gsProbability`

to print `gsProbability`

objects; see examples.

1 2 3 | ```
gsProbability(k=0, theta, n.I, a, b, r=18, d=NULL, overrun=0)
## S3 method for class 'gsProbability'
print(x,...)
``` |

`k` |
Number of analyses planned, including interim and final. |

`theta` |
Vector of standardized effect sizes for which boundary crossing probabilities are to be computed. |

`n.I` |
Sample size or relative sample size at analyses; vector of length k. See |

`a` |
Lower bound cutoffs (z-values) for futility or harm at each analysis, vector of length k. |

`b` |
Upper bound cutoffs (z-values) for futility at each analysis; vector of length k. |

`r` |
Control for grid as in Jennison and Turnbull (2000); default is 18, range is 1 to 80. Normally this will not be changed by the user. |

`d` |
If not |

`x` |
An item of class |

`overrun` |
Scalar or vector of length |

`...` |
Not implemented (here for compatibility with generic print input). |

Depending on the calling sequence, an object of class `gsProbability`

or class `gsDesign`

is returned.
If it is of class `gsDesign`

then the members of the object will be the same as described in `gsDesign`

.
If `d`

is input as `NULL`

(the default), all other arguments (other than `r`

) must be specified
and an object of class `gsProbability`

is returned.
If `d`

is passed as an object of class `gsProbability`

or `gsDesign`

the only other argument required is `theta`

;
the object returned has the same class as the input `d`

.
On output, the values of `theta`

input to `gsProbability`

will be the parameter values for which the
design is characterized.

`k` |
As input. |

`theta` |
As input. |

`n.I` |
As input. |

`lower` |
A list containing two elements: |

`upper` |
A list of the same form as |

`en` |
A vector of the same length as |

`r` |
As input. |

Note: `print.gsProbability()`

returns the input `x`

.

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.

Plots for group sequential designs, `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 32 33 34 35 36 | ```
# making a gsDesign object first may be easiest...
x <- gsDesign()
# take a look at it
x
# default plot for gsDesign object shows boundaries
plot(x)
# plottype=2 shows boundary crossing probabilities
plot(x, plottype=2)
# now add boundary crossing probabilities and
# expected sample size for more theta values
y <- gsProbability(d=x, theta=x$delta*seq(0, 2, .25))
class(y)
# note that "y" below is equivalent to print(y) and
# print.gsProbability(y)
y
# the plot does not change from before since this is a
# gsDesign object; note that theta/delta is on x axis
plot(y, plottype=2)
# now let's see what happens with a gsProbability object
z <- gsProbability(k=3, a=x$lower$bound, b=x$upper$bound,
n.I=x$n.I, theta=x$delta*seq(0, 2, .25))
# with the above form, the results is a gsProbability object
class(z)
z
# default plottype is now 2
# this is the same range for theta, but plot now has theta on x axis
plot(z)
``` |

```
Loading required package: xtable
Loading required package: ggplot2
Asymmetric two-sided group sequential design with
90 % power and 2.5 % Type I Error.
Upper bound spending computations assume
trial continues if lower bound is crossed.
Sample
Size ----Lower bounds---- ----Upper bounds-----
Analysis Ratio* Z Nominal p Spend+ Z Nominal p Spend++
1 0.357 -0.24 0.4057 0.0148 3.01 0.0013 0.0013
2 0.713 0.94 0.8267 0.0289 2.55 0.0054 0.0049
3 1.070 2.00 0.9772 0.0563 2.00 0.0228 0.0188
Total 0.1000 0.0250
+ lower bound beta spending (under H1):
Hwang-Shih-DeCani spending function with gamma = -2.
++ alpha spending:
Hwang-Shih-DeCani spending function with gamma = -4.
* 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 0.0013 0.0049 0.0171 0.0233 0.6249
3.2415 0.1412 0.4403 0.3185 0.9000 0.7913
Lower boundary (futility or Type II Error)
Analysis
Theta 1 2 3 Total
0.0000 0.4057 0.4290 0.1420 0.9767
3.2415 0.0148 0.0289 0.0563 0.1000
[1] "gsDesign"
Asymmetric two-sided group sequential design with
90 % power and 2.5 % Type I Error.
Upper bound spending computations assume
trial continues if lower bound is crossed.
Sample
Size ----Lower bounds---- ----Upper bounds-----
Analysis Ratio* Z Nominal p Spend+ Z Nominal p Spend++
1 0.357 -0.24 0.4057 0.0148 3.01 0.0013 0.0013
2 0.713 0.94 0.8267 0.0289 2.55 0.0054 0.0049
3 1.070 2.00 0.9772 0.0563 2.00 0.0228 0.0188
Total 0.1000 0.0250
+ lower bound beta spending (under H1):
Hwang-Shih-DeCani spending function with gamma = -2.
++ alpha spending:
Hwang-Shih-DeCani spending function with gamma = -4.
* 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 0.0013 0.0049 0.0171 0.0233 0.6249
0.8104 0.0058 0.0279 0.0872 0.1209 0.7523
1.6208 0.0205 0.1038 0.2393 0.3636 0.8520
2.4311 0.0595 0.2579 0.3636 0.6810 0.8668
3.2415 0.1412 0.4403 0.3185 0.9000 0.7913
4.0519 0.2773 0.5353 0.1684 0.9810 0.6765
4.8623 0.4574 0.4844 0.0559 0.9976 0.5701
5.6727 0.6469 0.3410 0.0119 0.9998 0.4868
6.4830 0.8053 0.1930 0.0016 1.0000 0.4266
Lower boundary (futility or Type II Error)
Analysis
Theta 1 2 3 Total
0.0000 0.4057 0.4290 0.1420 0.9767
0.8104 0.2349 0.3812 0.2630 0.8791
1.6208 0.1138 0.2385 0.2841 0.6364
2.4311 0.0455 0.1017 0.1718 0.3190
3.2415 0.0148 0.0289 0.0563 0.1000
4.0519 0.0039 0.0054 0.0097 0.0190
4.8623 0.0008 0.0006 0.0009 0.0024
5.6727 0.0001 0.0001 0.0000 0.0002
6.4830 0.0000 0.0000 0.0000 0.0000
[1] "gsProbability"
Lower bounds Upper bounds
Analysis N Z Nominal p Z Nominal p
1 1 -0.24 0.4057 3.01 0.0013
2 1 0.94 0.8267 2.55 0.0054
3 2 2.00 0.9772 2.00 0.0228
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 0.0013 0.0049 0.0171 0.0233 0.6
0.8104 0.0058 0.0279 0.0872 0.1209 0.8
1.6208 0.0205 0.1038 0.2393 0.3636 0.9
2.4311 0.0595 0.2579 0.3636 0.6810 0.9
3.2415 0.1412 0.4403 0.3185 0.9000 0.8
4.0519 0.2773 0.5353 0.1684 0.9810 0.7
4.8623 0.4574 0.4844 0.0559 0.9976 0.6
5.6727 0.6469 0.3410 0.0119 0.9998 0.5
6.4830 0.8053 0.1930 0.0016 1.0000 0.4
Lower boundary (futility or Type II Error)
Analysis
Theta 1 2 3 Total
0.0000 0.4057 0.4290 0.1420 0.9767
0.8104 0.2349 0.3812 0.2630 0.8791
1.6208 0.1138 0.2385 0.2841 0.6364
2.4311 0.0455 0.1017 0.1718 0.3190
3.2415 0.0148 0.0289 0.0563 0.1000
4.0519 0.0039 0.0054 0.0097 0.0190
4.8623 0.0008 0.0006 0.0009 0.0024
5.6727 0.0001 0.0001 0.0000 0.0002
6.4830 0.0000 0.0000 0.0000 0.0000
```

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