This function calculates the ‘empiric’ power of 2-stage 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 .
power.tsd.KM(method = c("C", "B"), alpha0 = 0.05, alpha = c(0.0294, 0.0294),
n1, CV, targetpower = 0.8, pmethod = c("nct", "exact"),
Nmax = 150, theta0, theta1, theta2, npct = c(0.05, 0.5, 0.95),
nsims, setseed = TRUE, details = FALSE)Decision schemes according to Potvin et al.
Default is "C" aka TSD in the paper of Karalis & Macheras
if setting alpha=c(0.0294, 0.0294).
TSD-1 of Karalis can be obtained by choosing "C" but
setting alpha=c(0.028, 0.028).
TSD-2 of Karalis can be obtained by choosing "B" and
setting alpha=c(0.0294, 0.0294).
Alpha value for the first step(s) in Potvin C aka TSD of Karalis & Macheras or TSD-1 of Karalis, the power inspection and BE decision if power > targetpower. Defaults to 0.05.
Vector (two elements) of the nominal alphas for the two stages.
Defaults to Pocock<U+2019>s alpha setting alpha=c(0.0294, 0.0294)
as in TSD of Karalis & Macheras.
Sample size of .
Coefficient of variation of the intra-subject variability (use e.g., 0.3 for 30%).
Power threshold in the first step of Potvin "C" and power to
achieve in the sample size estimation step.
Power calculation method, also to be used in the sample size estimation for
.
Implemented are ""nct" (approximate calculations via non-central
t-distribution and "exact" (exact calculations via Owen<U+2019>s Q).
Defaults to "nct" as a reasonable compromise between speed and
accuracy in the sample size estimation step.
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.
Set this argument to Inf, to work without that futility criterion.
Assumed ratio of geometric means (T/R) for simulations. If missing,
defaults to GMR.
Lower bioequivalence limit. Defaults to 0.8.
Upper bioequivalence limit. Defaults to 1.25.
Percentiles to be used for the presentation of the distribution of
n(total)=n1+n2.
Defaults to c(0.05, 0.5, 0.95) to obtain the 5% and 95% percentiles
and the median.
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.
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.
If set to TRUE the function prints the results of time measurements
of the simulation steps. Defaults to FALSE.
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:
Fraction of studies found BE.
Fraction of studies found BE in .
Percentage of studies continuing to .
Mean of n(total).
Range (min, max) of n(total).
Percentiles of the distribution of n(total).
Object of class "table" summarizing the discrete distribution
of n(total) via its distinct values and counts of occurences of these values.
This component is only given back if is.finite(Nmax).
The calculations follow in principle the simulations as described in Potvin et al. 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 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 . This resembles the methods described in Karalis & Macheras and Karalis.
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. 10.1002/pst.294
Karalis V, Macheras P. An Insight into the Properties of a Two-Stage Design in Bioequivalence Studies. Pharm Res. 2013; 30(7):1824--35. 10.1007/s11095-013-1026-3
Karalis V. The role of the upper sample size limit in two-stage bioequivalence designs. Int J Pharm. 2013; 456(1):87--94. 10.1016/j.ijpharm.2013.08.013
Fuglsang A. Futility Rules in Bioequivalence Trials with Sequential Designs. AAPS J. 2014; 16(1):79--82. 10.1208/s12248-013-9540-0
Sch<U+00FC>tz H. Two-stage designs in bioequivalence trials. Eur J Clin Pharmacol. 2015; 71(3):271--81. 10.1007/s00228-015-1806-2
# NOT RUN {
# 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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