GroupSeq (version 1.0)

computeDrift: Computes drift

Description

here its original description in the Fortran-Implementation from http://www.biostat.wisc.edu/landemets/ : "Find drift resulting in power "conf". The drift will be that value producing exit probability conf at time t(n) given the bounds. If t(n) < 1, this is not the power of the study."

Usage

computeDrift(n, t, t2, lowerBounds, upperBounds, target, drift, nMax)

Arguments

n

the number of analyses.

t

the vector of analysis time point on (0,1).

t2

is the second or information time scale, for covariances

lowerBounds

the vector of lower bounds (standardized).

upperBounds

the vector of upper bounds (standardized).

target

desired power respectively confidence level

drift

vector of drift parameters

nMax

Number of interim analyses is by default limited to nMax=25

Value

• drift
  computed drift

Details

The Fortran-Implementation used a naive search algorithm to calculate the drift. I replaced it by an algorithm which is called in german "Sekanten-Verfahren". This one is based on the Newton Iteration but uses secants here considering we cannot derive our function The calculation obeys following pattern whereby $x_{k+1}$ converges against the value we are searching for. $x_{k+1} = x_{k}-x_{k-1}{f(x_{k})-f(x_{k-1})}*f(x_{k})$ The Fortran-Implementation usually does about 17 iterations to calculate the drift whereas my method does only 3 or 4 iterations! If my method fails in converging which usually should not happen the function tries to calculate one more time with that more conservative and carefully method of the Fortran Implementation.

References

http://www.biostat.wisc.edu/landemets/

See Also

groupseq, computeAlphaLevel findDrift

Examples

## fictious example
computeDrift(2, c(0.5,1.0), c(0.5,1.0), c(-8,-8), c(2.3,1.1), 0.3, 0, 25)
## with following result:
# [1] 0.5696356