power.tsd.GS {Power2Stage}

Power calculation for non-adaptive group sequential (2-stage) BE studies

Description

This function calculates the ‘empiric’ power of group sequential 2-stage BE in 2×2 crossover designs via simulations.
The number of subjects in both stages has to be prespecified (non-adaptive).

Usage

power.tsd.GS(alpha = c(0.0294, 0.0294), n, CV, theta0, theta1, theta2,
             fCrit = c("CI", "PE"), fClower, fCupper, nsims, setseed = TRUE,
             details = FALSE)

Arguments

alpha

Vector of the two nominal alpha values to be used in the 100(1–2α) confidence interval calculations in the two stages.
Use something like package ⁠ldbounds⁠ for choosing the nominal alphas.

n

Vector of the two sample sizes in stage 1 and stage 2. ⁠n(total)⁠ is ⁠n[1]+n[2]⁠ if a second stage is necessary. Otherwise it is ⁠n[1]⁠.

CV

Coefficient of variation of the intra-subject variability (use e.g., 0.3 for 30%).

theta0

Assumed ratio of geometric means (T/R) for simulations. If missing, defaults to 0.95.

theta1

Lower bioequivalence limit. Defaults to 0.80.

theta2

Upper bioequivalence limit. Defaults to 1.25.

fCrit

Futility criterion.
If set to ⁠"PE"⁠ the study stops after stage 1 if not BE and if the point estimate (PE) of stage 1 evaluation is outside the range defined in the next two arguments ⁠"fClower"⁠ and ⁠"fCupper"⁠.
If set to ⁠"CI"⁠ the study stops after stage 1 if not BE and if the 90% confidence interval of stage 1 evaluation is outside the range defined in the next two arguments.
Defaults to ⁠"CI"⁠.

fClower

Lower limit of the futility criterion. Defaults to ⁠0⁠ if missing, i.e., no futility criterion.

fCupper

Upper limit of the futility criterion. Defaults to ⁠1/fClower⁠ if missing.

nsims

Number of studies to simulate.
If missing, ⁠nsims⁠ is set to 1E+05 = 100,000 or to 1E+06 = 1 Mio if estimating the empiric Type I Error (⁠'alpha'⁠), i.e., with ⁠theta0⁠ at the border or outside the acceptance range ⁠theta1⁠ ... ⁠theta2⁠.

setseed

Simulations are dependent on the starting point of the (pseudo) random number generator. To avoid differences in power for different runs a set.seed(1234567) is issued if ⁠setseed=TRUE⁠, the default.
Set this argument to ⁠FALSE⁠ to view the variation in power between different runs.

details

If set to ⁠TRUE⁠ the function prints the results of time measurements of the simulation steps. Defaults to ⁠FALSE⁠.

Details

The calculations follow in principle the simulations as described in Potvin et al. for adaptive designs, but with no interim power inspection and pre-specified (fixed) number of subjects in stage 2.
The underlying subject data are assumed to be evaluated after log-transformation. But instead of simulating subject data, the statistics pe1, mse1 and pe2, SS2 are simulated via their associated distributions (normal and χ² distributions).

Value

Returns an object of class ⁠"pwrtsd"⁠ with all the input arguments and results as components.
The class ⁠"pwrtsd"⁠ has a S3 print method.
The results are in the components:

pBE

Fraction of studies found BE.

pBE_s1

Fraction of studies found BE in stage 1.

pct_s2

Percentage of studies continuing to stage 2.

Note

The code is reasonable fast. 1E6 sims take ~ 1 sec on my machine. Even 1E7 sims are meanwhile possible without too much beer. :-)

Author(s)

D. Labes

References

Gould AL. Group sequential extensions of a standard bioequivalence testing procedure.
J Pharmacokin Biopharm. 1995; 23(1):57–86 doi: 10.1007/BF02353786

Patterson SD, Jones B. Bioequivalence and Statistics in Clinical Pharmacology.
Boca Raton: CRC Press; 2^nd edition 2016. Chapter 5.6 Optional Designs.

Schütz H. Two-stage designs in bioequivalence trials.
Eur J Clin Pharmacol. 2015; 71(3):271–81. doi: 10.1007/s00228-015-1806-2

Kieser M, Rauch G. Two-stage designs for cross-over bioequivalence trials.
Stat Med. 2015; 34(16):2403–16. doi: 10.1002/sim.6487

Zheng Ch, Zhao L, Wang J. Modifications of sequential designs in bioequivalence trials.
Pharm Stat. 2015; 14(3):180–8. doi: 10.1002/pst.1672

See Also

power.tsd and power.tsd.p for adaptive sequential designs.

Examples

# using the Pocock alpha settings and no futility rule
# (defaults), a CV of 20% and 12 subjects in both stages,
# midway interim
power.tsd.GS(CV=0.2, n=c(12,12))