gsBoundCP: 2.5: Conditional Power at Interim Boundaries
In gsDesign: Group Sequential Design

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

gsBoundCP() computes the total probability of crossing future upper bounds given an interim test statistic at an interim bound. For each interim boundary, assumes an interim test statistic at the boundary and computes the probability of crossing any of the later upper boundaries.

1	gsBoundCP(x, theta="thetahat", r=18)

`x`	An object of type `gsDesign` or `gsProbability`
`theta`	if `"thetahat"` and `class(x)!="gsDesign"`, conditional power computations for each boundary value are computed using estimated treatment effect assuming a test statistic at that boundary (`zi/sqrt(x$n.I[i])` at analysis `i`, interim test statistic `zi` and interim sample size/statistical information of `x$n.I[i]`). Otherwise, conditional power is computed assuming the input scalar value `theta`.
`r`	Integer value controlling grid for numerical integration as in Jennison and Turnbull (2000); default is 18, range is 1 to 80. Larger values provide larger number of grid points and greater accuracy. Normally `r` will not be changed by the user.

See Conditional power section of manual for further clarification. See also Muller and Schaffer (2001) for background theory.

A list containing two vectors, CPlo and CPhi.

`CPlo`	A vector of length `x$k-1` with conditional powers of crossing upper bounds given interim test statistics at each lower bound
`CPhi`	A vector of length `x$k-1` with conditional powers of crossing upper bounds given interim test statistics at each upper bound.

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\_anderson@merck.

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

Muller, Hans-Helge and Schaffer, Helmut (2001), Adaptive group sequential designs for clinical trials: combining the advantages of adaptive and classical group sequential approaches. Biometrics;57:886-891.

gsDesign, gsProbability, gsCP

# set up a group sequential design
x <- gsDesign(k=5)
x

# compute conditional power based on interim treatment effects
gsBoundCP(x)

# compute conditional power based on original x$delta
gsBoundCP(x, theta=x$delta)

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  0.220 -0.90    0.1836 0.0077 3.25    0.0006  0.0006
         2  0.441 -0.04    0.4853 0.0115 2.99    0.0014  0.0013
         3  0.661  0.69    0.7563 0.0171 2.69    0.0036  0.0028
         4  0.881  1.36    0.9131 0.0256 2.37    0.0088  0.0063
         5  1.101  2.03    0.9786 0.0381 2.03    0.0214  0.0140
     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      4      5  Total   E{N}
  0.0000 0.0006 0.0013 0.0028 0.0062 0.0117 0.0226 0.5726
  3.2415 0.0417 0.1679 0.2806 0.2654 0.1444 0.9000 0.7440

Lower boundary (futility or Type II Error)
          Analysis
   Theta      1      2      3      4      5  Total
  0.0000 0.1836 0.3201 0.2700 0.1477 0.0559 0.9774
  3.2415 0.0077 0.0115 0.0171 0.0256 0.0381 0.1000
             CPlo      CPhi
[1,] 2.294534e-06 1.0000001
[2,] 2.238566e-03 0.9998352
[3,] 2.669114e-02 0.9922459
[4,] 1.296705e-01 0.9200502
          CPlo      CPhi
[1,] 0.4936972 0.9940265
[2,] 0.3676577 0.9954019
[3,] 0.3331896 0.9912361
[4,] 0.3871332 0.9590607