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

power.tsd.GS

R Documentation

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 \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/pst.1672")}

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))

Detlew/Power2Stage documentation built on Oct. 12, 2023, 9:08 p.m.