drift {ldbounds}R Documentation

Drift and Probabilities for Group Sequential Boundaries

Description

'drift' calculates drift (effect), confidence interval for drift, or power and other probabilities given drift for specified group sequential boundaries for interim analyses of accumulating data in clinical trials.

Usage

drift(za = -zb, zb, t, t2 = t, pow = NULL, drft = NULL,
      conf = NULL, zval = zb[length(zb)])

Arguments

za the vector of lower boundaries. Symmetric to zb by default.
zb the vector of upper boundaries.
t the vector of analysis times, which must be increasing and in (0,1].
t2 the second time scale, usually in terms of amount of accumulating information. By default, same as t.
pow the desired power when drift is not specified.
drft the true drift (i.e. treatment effect when t=1).
conf the confidence level when a confidence interval for drift is wanted.
zval the final observed Z statistic (i.e. when trial is stopped). Used for confidence interval.

Details

This is based on a Fortran program, 'ld98', by Reboussin, DeMets, Kim, and Lan. It has some advantages, like making use of probability distributions in R. Only one of pow, drft, and conf is to be specified and zval is only used in the last case.

Value

'drift' returns an object of 'class' '"drift"'.

An object of class '"drift"' is a list containing the following components:

type Type of computation performed: 1 is drift given power, 2 is exit probabilities given drift, and 3 is confidence interval for drift given final Z statistic.
time the original time scale.
time2 the second (information) time scale.
lower.bounds the vector of lower boundaries given.
upper.bounds the vector of upper boundaries given.
power the power. If power is given, it is returned here. If drift is given, the resulting power is calculated.
drift the drift. If drift is given, it is returned here. If power is given, the drift resulting in given power is calculated.
lower.probs the vector of exit probabilities across the lower boundary. Returned if power or drift is given.
upper.probs the same for upper boundary.
exit.probs the probability at each analysis of crossing the boundary. The sum of lower.probs and upper.probs.
cum.exit the cumulative probability of crossing.
conf.level the desired confidence level, if given.
final.zvalue the final Z statistic, if given.
conf.interval the confidence interval for drift, if conf and zval are given.

Author(s)

Charlie Casper casper@stat.wisc.edu and Oscar A. Perez perez@stat.wisc.edu

References

Reboussin, D. M., DeMets, D. L., Kim, K. M., and Lan, K. K. G. (2000) Computations for group sequential boundaries using the Lan-DeMets spending function method. Controlled Clinical Trials, 21:190-207.

Fortran program 'ld98' by the same authors as above.

DeMets, D. L. and Lan, K. K. G. (1995) Recent Advances in Clinical Trial Design and Analysis, Thall, P. F. (ed.). Boston: Kluwer Academic Publishers.

Lan, K. K. G. and DeMets, D. L. (1983) Discrete sequential boundaries for clinical trials. Biometrika, 70:659-63.

See Also

Generic functions summary.drift and plot.drift.

bounds for computation of boundaries using alpha spending function method.

Examples

   ## From Reboussin, et al. (2000)

   t <- c(0.13,0.4,0.69,0.9,0.98,1)
   upper <- c(5.3666,3.7102,2.9728,2.5365,2.2154,1.9668)
   drift.pr <- drift(zb=upper,t=t,drft=3.242)
   summary(drift.pr)

   t <- c(0.2292,0.3333,0.4375,0.5833,0.7083,0.8333)
   upper <- c(2.53,2.61,2.57,2.47,2.43,2.38)
   drift.ci <- drift(zb=upper,t=t,conf=0.95,zval=2.82)
   summary(drift.ci)
   plot(drift.ci)

   ## Using output from 'bounds'
   t <- seq(0.2,1,length=5)
   obf.bd <- bounds(t,iuse=c(1,1),alpha=c(0.025,0.025))
   drift.dr <- drift(obf.bd$lower.bounds,obf.bd$upper.bounds,t,pow=0.9)
   summary(drift.dr)





[Package ldbounds version 1.0-1 Index]