Description Usage Arguments Details Value Author(s) References See Also Examples
This function calculates the ‘empiric’ power of 2stage BE studies according to Potvin et al. via simulations. The Potvin methods are modified to include a futility criterion Nmax and to allow the sample size estimation step to be done with the point estimate (PE) and MSE (calculated from CV) of stage 1.
1 2 3 4 
method 
Decision schemes according to Potvin et.al. (defaults to 
alpha0 
Alpha value for the first step(s) in Potvin 
alpha 
Vector (two elements) of the nominal alphas for the two stages. Defaults to
Pocock’s setting 
n1 
Sample size of stage 1. 
GMR 
Ratio T/R to be used in decision scheme (power calculations in stage 1 and sample size estimation for stage 2). 
CV 
Coefficient of variation of the intrasubject variability (use e.g., 0.3 for 30%). 
targetpower 
Power threshold in the power monitoring steps and power to achieve in the sample size estimation step. 
pmethod 
Power calculation method, also to be used in the sample size estimation for
stage 2. 
usePE 
If 
Nmax 
Futility criterion. If set to a finite value, all studies simulated in which a
sample size 
min.n2 
Minimum sample size of stage 2. Defaults to zero. 
theta0 
True ratio of T/R for simulating. Defaults to the 
theta1 
Lower bioequivalence limit. Defaults to 0.8. 
theta2 
Upper bioequivalence limit. Defaults to 1.25. 
npct 
Percentiles to be used for the presentation of the distribution of

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.
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 an 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. 
nmean 
Mean of n(total), aka average total sample size (ASN). 
nrange 
Range (min, max) of n(total). 
nperc 
Vector of percentiles of the distribution of n(total). 
ntable 
Object of class 
D. Labes
Potvin D, DiLiberti CE, Hauck WW, Parr AF, Schuirmann DJ, Smith RA. Sequential design approaches for bioequivalence studies with crossover designs.
Pharm Stat. 2008; 7(4):245–62. doi: 10.1002/pst.294
Montague TH, Potvin D, DiLiberti CE, Hauck WW, Parr AF, Schuirmann DJ. Additional results for ‘Sequential design approaches for bioequivalence studies with crossover designs’.
Pharm Stat. 2011; 11(1):8–13. doi: 10.1002/pst.483
Fuglsang A. Controlling type I errors for twostage bioequivalence study designs.
Clin Res Reg Aff. 2011; 28(4):100–5. doi: 10.3109/10601333.2011.631547
Fuglsang A. Sequential Bioequivalence Trial Designs with Increased Power and
Controlled Type I Error Rates.
AAPS J. 2013; 15(3):659–61. doi: 10.1208/s1224801394755
Fuglsang A. Futility Rules in Bioequivalence Trials with Sequential Designs.
AAPS J. 2014; 16(1):79–82. doi: 10.1208/s1224801395400
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.p
for analogous calculations for 2group parallel
design.
power.tsd.fC
for analogous calculations with futility check
based on point estimate of stage 1.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26  # using all the defaults and 24 subjects in stage 1, CV of 25%
power.tsd(n1=24, CV=0.25)
# computation time ~ 1 sec
#
# as above, but save results for further use
res < power.tsd(n1=24, CV=0.25)
## Not run:
# representation of the discrete distribution of n(total)
# via plot method of object with class "table" which creates a
# 'needle' plot
plot(res$ntable/sum(res$ntable), ylab="Density",
xlab=expression("n"[total]), las=1,
main=expression("Distribution of n"[total]))
#
# If you prefer a histogram instead (IMHO, not the preferred plot):
# reconstruct the ntotal values from the ntable
ntot < rep.int(as.integer(names(res$ntable)),
times=as.integer(res$ntable))
# annotated histogram
hist(ntot, freq=FALSE, breaks=res$nrange[2]res$nrange[1],
xlab=expression("n"[total]), las=1,
main=expression("Histogram of n"[total]))
abline(v=c(res$nmean, res$nperc[["50%"]]), lty=c(1, 3))
legend("topright", box.lty=0, legend=c("mean", "median"),
lty=c(1, 3), cex=0.9)
## End(Not run)

TSD with 2x2 crossover
Method B: alpha (s1/s2) = 0.0294 0.0294
Target power in power monitoring and sample size est. = 0.8
Power calculation via noncentral t approx.
CV1 and GMR = 0.95 in sample size est. used
No futility criterion
BE acceptance range = 0.8 ... 1.25
CV = 0.25; n(stage 1) = 24; GMR = 0.95
1e+05 sims at theta0 = 0.95 (p(BE) = 'power').
p(BE) = 0.84244
p(BE) s1 = 0.63203
Studies in stage 2 = 33.56%
Distribution of n(total)
 mean (range) = 29 (24 ... 86)
 percentiles
5% 50% 95%
24 24 48
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