power.tsd.GS: Power calculation for non-adaptive group sequential (2-stage)...
In Power2Stage: Power and Sample-Size Distribution of 2-Stage Bioequivalence Studies

Description Usage Arguments Details Value Note Author(s) References See Also Examples

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).

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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. 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`.

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).

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. 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

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

# 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))