Description Usage Arguments Details Value Note Author(s) References See Also Examples
This function calculates the ‘empiric’ power of group sequential
2stage BE in 2×2 crossover designs via simulations.
The number of subjects in both stages has to be prespecified (nonadaptive).
1 2 3  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)

alpha 
Vector of the two nominal alpha values to be used in the
100(1–2α)
confidence interval calculations in the two stages. 
n 
Vector of the two sample sizes in stage 1
and stage 2. 
CV 
Coefficient of variation of the intrasubject 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. 
fClower 
Lower limit of the futility criterion. Defaults to 
fCupper 
Upper limit of the futility criterion. Defaults to 
nsims 
Number of studies to simulate. 
setseed 
Simulations are dependent on the starting point of the (pseudo) random number
generator. To avoid differences in power for different runs a

details 
If set to 
The calculations follow in principle the simulations as described in Potvin
et al. for adaptive designs, but with no interim power inspection and
prespecified (fixed) number of subjects in stage 2.
The underlying subject data are assumed to be evaluated after logtransformation.
But instead of simulating subject data, the statistics pe1, mse1 and pe2, SS2 are
simulated via their associated distributions (normal and
χ^{2} distributions).
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. 
The code is reasonable fast. 1E6 sims take ~ 1 sec on my machine.
Even 1E7 sims are meanwhile possible without too much beer. :)
D. Labes
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. Twostage designs in bioequivalence trials.
Eur J Clin Pharmacol. 2015; 71(3):271–81. doi: 10.1007/s0022801518062
Kieser M, Rauch G. Twostage designs for crossover 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
power.tsd
and power.tsd.p
for adaptive sequential designs.
1 2 3 4  # 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))

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