Description Usage Arguments Details Value Author(s) References Examples
This function calculates the ‘empiric’ power of 2stage BE studies according to Potvin et al. via simulations. The Potvin methods are modified as described by Karalis & Macheras to include a futility criterion Nmax and to perform the power calculation steps and the sample size estimation step in the decision schemes with the MSE (calculated from CV) and the point estimate (PE) of T/R from stage 1.
1 2 3 4 
method 
Decision schemes according to Potvin et al. 
alpha0 
Alpha value for the first step(s) in Potvin C aka TSD of Karalis &
Macheras or TSD1 of Karalis, the power inspection and BE decision
if power > targetpower. 
alpha 
Vector (two elements) of the nominal alphas for the two stages. 
n1 
Sample size of stage 1. 
CV 
Coefficient of variation of the intrasubject variability (use e.g., 0.3 for 30%). 
targetpower 
Power threshold in the first step of Potvin 
pmethod 
Power calculation method, also to be used in the sample size estimation for
stage 2. 
Nmax 
Futility criterion. If set to a finite value all studies simulated in which
a sample size >Nmax is obtained will be regarded as BE=FAIL. Defaults to 150,
as recommended by Karalis & Macheras. 
theta0 
Assumed ratio of geometric means (T/R) for simulations. If missing,
defaults to 
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).
In contrast to Potvin et al. the power calculation steps as well as the
sample size adaption step of the decision schemes are done using the MSE
(calculated from CV) and the point estimate from
stage 1.
This resembles the methods described in Karalis & Macheras and Karalis.
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. 
nmean 
Mean of n(total). 
nrange 
Range (min, max) of n(total). 
nperc 
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
Karalis V, Macheras P. An Insight into the Properties of a TwoStage Design in Bioequivalence Studies.
Pharm Res. 2013; 30(7):1824–35. doi: 10.1007/s1109501310263
Karalis V. The role of the upper sample size limit in twostage bioequivalence designs.
Int J Pharm. 2013; 456(1):87–94. doi: 10.1016/j.ijpharm.2013.08.013
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
1 2 3 4 5 6  # using all the defaults
# but too low number of sims to complain with the CRAN policy:
# "check time only a few seconds per example"
# minimum number of sims should be 1E5 for power, 1E6 sims for 'alpha'
power.tsd.KM(n1=16, CV=0.2, nsims=1E4)
# ~3 sec if nsims=1E5

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