gsDesign (version 3.6.6)

gsBoundCP: Conditional Power at Interim Boundaries

Description

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.

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

Usage

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

Value

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.

Arguments

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 (>= 1 and <= 80) controlling the number of numerical integration grid points. Default is 18, as recommended by Jennison and Turnbull (2000). Grid points are spread out in the tails for accurate probability calculations. Larger values provide more grid points and greater accuracy but slow down computation. Jennison and Turnbull (p. 350) note an accuracy of \(10^{-6}\) with r = 16. This parameter is normally not changed by users.

Author

Keaven Anderson

References

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.

See Also

gsDesign, gsProbability, gsCP

Examples

# 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)