GroupSeq (version 1.0)

computeBounds: calculate boundaries

Description

Function to calculate boundaries corresponding to particular type I error spending rates and times of interim analyses, see Lan & DeMets 83.

Usage

computeBounds(n, drift, alpha, phi, t, t2, OneOrTwoSidedBounds, whatSpendingFunctionIsUsed, boundsTruncation)

Arguments

n

is the number of interim analyses

drift

drift is the true mean of the process, the noncentrality - drift is set to zero, and so does not affect function

alpha

is the total type I error.

phi

optional Parameter referring to Power Family

t

is the information times.

t2

is the 'second' time scale, used for the covariance of sequential statistics, usually number of events or subjects.

OneOrTwoSidedBounds

indicates one or two sided boundaries.

whatSpendingFunctionIsUsed

indicates type I error spending function.

boundsTruncation

is the user selected truncation on integration limits.

Value

• lowerBounds
  the vector of lower standardized boundaries
• upperBounds
  the vector of upper standardized boundaries
• probExit
  vector of exit probabilities
• probDifference(i)
  probExit(i)-probExit(i-1)

References

Lan & DeMets 1983 Biometrika http://www.biostat.wisc.edu/landemets/

See Also

groupseq, alphaByUseFunction stdDeviations, pnorm jointDensity, tailProbability, searchForBound

Examples

## fictious example
computeBounds(2,0,0.05,0,c(0.5,1.0),c(0.5,1.0),1,1,8)
##with following result:
#$lowerBounds
#[1] -8 -8
#
#$upperBounds
#[1] 2.537988 1.662070
#
#$exitProbabilities
#[1] 0.005574597 0.050000000
#
#$differencesExitProbabilities
#[1] 0.005574597 0.044425403