power.tsd.GS: Power calculation for non-adaptive group sequential (2-stage)...

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

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

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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)

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 GMR.

theta1

Lower bioequivalence limit. Defaults to 0.8.

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; 2nd 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

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# 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))

Power2Stage documentation built on April 3, 2018, 9:04 a.m.