gsDesign (version 2.4-01)

gsBinomialExact: 3.4: One-Sample Exact Binomial Boundary Crossing Probabilities

Description

Computes power/Type I error and expected sample size for a group sequential design in a single-arm trial with a binary outcome. The print function has been extended using print.gsBinomialExact to print gsBinomialExact objects; see examples.

Usage

gsBinomialExact(k=2, theta=c(.1, .2), n.I=c(50, 100), a=c(3, 7), b=c(20,30))

Arguments

k

Number of analyses planned, including interim and final.

theta

Vector of possible underling binomial probabilities for a single binomial sample.

n.I

Sample size at analyses (increasing positive integers); vector of length k.

a

Number of "successes" required to cross lower bound cutoffs for futility or harm at each analysis; vector of length k; -1 means no lower bound.

b

Number of "successes" required to cross upper bound cutoffs for futility or harm at each analysis; vector of length k.

Value

• gsBinomialExact() returns a list of class gsBinomialExact and gsProbability (see example); when displaying one of these objects, the default function to print is print.gsProbability(). The object returned from gsBinomialExact() contains the following elements:
• k
  As input.
• theta
  As input.
• n.I
  As input.
• lower
  A list containing two elements: bound is as input in a and prob is a matrix of boundary crossing probabilities. Element i,j contains the boundary crossing probability at analysis i for the j-th element of theta input. All boundary crossing is assumed to be binding for this computation; that is, the trial must stop if a boundary is crossed.
• upper
  A list of the same form as lower containing the upper bound and upper boundary crossing probabilities.
• en
  A vector of the same length as theta containing expected sample sizes for the trial design corresponding to each value in the vector theta.

Details

Based on the book "Group Sequential Methods with Applications to Clinical Trials," Christopher Jennison and Bruce W. Turnbull, Chapter 12, Section 12.1.2 Exact Calculations for Binary Data. This computation is often used as an approximation for the distribution of the number of events in one treatment group out of all events when the probability of an event is small and sample size is large. An object of class gsBinomialExact is returned. On output, the values of theta input to gsBinomialExact will be the parameter values for which the boundary crossing probabilities and expected sample sizes are computed. Note that a[1] equal to -1 lower bound at n.I[1] means 0 successes continues at interim 1; a[2]==0 at interim 2 means 0 successes stops trial for futility at 2nd analysis. For final analysis, set a[k] equal to b[k]-1 to incorporate all possibilities into non-positive trial; see example.

References

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

See Also

gsProbability

Examples

zz <- gsBinomialExact(k=3,theta=seq(0,1,0.1), n.I=c(12,24,36),
        a=c(-1, 0, 11),  b=c( 5, 9, 12))

# let's see what class this is
class(zz)

# because of "gsProbability" class above, following is equivalent to 
# print.gsProbability(zz)
zz