ldPower {ldbounds}

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)])

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.

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.

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.

Author(s)

Charlie Casper [e-mail], Thomas Cook [e-mail], and Oscar A. Perez

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.ldPower and plot.ldPower.

ldBounds for computation of boundaries using alpha spending function method.

commonbounds for boundaries that do not use alpha spending.

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)
   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)