ldPower: Power and Other Probabilities for Group Sequential Boundaries

Description

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

Usage

ldPower(t, za=NULL, zb=NULL, t2=t, pow=NULL, drift=NULL,
      conf=NULL, method=NULL, pvaltime=NULL,
      zval=zb[length(zb)])

Value

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

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

type: Type of computation performed: 1 is drift given power, 2 is exit probabilities given drift, 3 is confidence interval for drift given final Z-statistic, and 4 is adjusted p-value 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.
p.ordering: the ordering specified for p-value calculation (if given).
p.value: the adjusted p-value if pval, pvaltime, and zval are given.

Arguments

t: a vector of analysis times or an 'ldBounds' object (from either the 'ldBounds' or 'commonbounds' function). If a vector of analysis times, must be increasing and in (0,1].
za: the vector of lower boundaries. If not specified, made symmetric to zb.
zb: the vector of upper boundaries.
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.
drift: the true drift (i.e. treatment effect when t=1). Default is 0 when pow, conf, and method are also left unspecified.
conf: the confidence level when a confidence interval for drift is wanted.
method: the type of adjusted p-value desired. Possible values are 'SW' (stage-wise) and 'LR' (likelihood ratio).
pvaltime: the analysis time at which the final Z-statistic was observed and an adjusted p-value is desired.
zval: the final observed Z-statistic (i.e. when trial is stopped). Used for confidence interval or ajusted p-value. Default is final upper boundary value.

Author

Charlie Casper charlie.casper@hsc.utah.edu, Thomas Cook cook@biostat.wisc.edu, and Oscar A. Perez

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, drift, conf, or pval is to be specified and zval is only used in the latter two cases.

If t is an 'ldBounds' object, za, zb, t, and t2 are already defined and should not be specified.

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.

Examples

Run this code

   ## 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)
   bound.pr <- ldPower(t,zb=upper,drift=3.242)
   summary(bound.pr)

   t <- c(0.2292,0.3333,0.4375,0.5833,0.7083,0.8333)
   power.fam <- ldBounds(t,iuse=3,alpha=0.05)
   bound.ci <- ldPower(power.fam,conf=0.95,zval=2.82)
   bound.p <- ldPower(power.fam,method="LR",pvaltime=5,zval=2.82)
   summary(bound.ci)
   summary(bound.p)
   plot(bound.ci)

   obf.bd <- ldBounds(5)
   obf.dr <- ldPower(obf.bd,pow=0.9)
   summary(obf.dr)

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