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PowerTOST (version 1.1-08)

power.scABEL: (Empirical) Power for BE decision via scaled (widened) BE acceptance limits

Description

This function performs the power calculation of the BE decision via scaled (widened) BE acceptance limits by simulations.

Usage

power.scABEL(alpha = 0.05, theta1, theta2, theta0, CV, n, 
             design = c("2x3x3", "2x2x4", "2x2x3"), regulator = c("EMA", "FDA"), 
             nsims = 1e+05, details = FALSE, setseed = TRUE)

Arguments

alpha
Type I error probability, significance level. Conventionally mostly set to 0.05.
theta1
Conventional lower ABE limit to be applied in the mixed procedure if CVsWR
theta2
Conventional upper ABE limit to be applied in the mixed procedure if CVsWR
theta0
'True' or assumed bioequivalence ratio. Defaults to 0.95 if not given explicitly.
CV
Coefficient(s) of variation as ratio. If length(CV) = 1 the same CV is assumed for Test and Reference. If length(CV) = 2 the CV for Test must be given in CV[1] and for Reference in CV[2].
n
Number of subjects under study. May be given as vector. In that case it is assumed that n contains the number of subjects in the sequence groups. If n is given as single number (total sample size) and this number is not divisible by the number of seque
design
Design of the study to be planned. 2x3x3 is the partial replicate design (TRR/RTR/RRT). 2x2x4 is the full replicate design with 2 sequences and 4 periods. 2x2x3 is the 3-period design with sequences TRT|RTR. Defaults to design="2x3x3".
regulator
Regulatory body settings for the widening of the BE acceptance limits. Defaults to design="EMA"
nsims
Number of simulations to be performed to obtain the empirical power. Defaults to 100 000 = 1e+05.
details
If set to TRUE the computational time is shown as well as the components for the BE decision. p(BE-wABEL) is the probability that the CI is within widened limits. p(BE-PE) is the probability that the point estimate is within theta1 ... theta
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() is issued if setseed=TRUE, the default.

Value

  • Returns the value of the 'empirical' power.

Warning

Preliminary cross-validation of the simulations as implemented here and via subject data simulation and subsequent evaluation via the EMA method have shown that the algorithm used in V1.1-02 may be to naively implemented. Both simulation algorithm gave sometimes quite different results in the magnitude. For more details see a document "Implementation_scaledABE_sims" in the doc subdirectory of the package. The new implemented simulation algorithm gave better agreement to the power values obtained via subject data sims if CVwT=CVwR. The calculations with different variabilities gave still unsatisfactory results for the 2x3x3 design. The function therefore gives a warning if calculations with different CVwT, CVwR are requested for the 2x3x3 partial replicate design.

Details

The methods rely on the analysis of log-transformed data, i.e. assume a log-normal distribution on the original scale. The widened BE acceptance limits will be calculated by the formula [lBEL,uBEL] =exp(-+ r_const*sWR) with r_const the regulatory constant and sWR the standard deviation of the within subjects variability of the Reference. r_const=0.76 is used in case of regulator="EMA" and in case of regulator="FDA" r_const=0.89257...=log(1.25)/0.25. If the CVwR of the Reference is < CVswitch=0.3 the conventional ABE limits apply (mixed procedure). In case of regulator="EMA" a cap is placed on the widened limits if CVwr>0.5, i.e. the widened limits are held at value calculated at CVwR=0.5. The simulations are done via the distributional properties of the statistical quantities necessary for deciding BE based on widened ABEL. For more details see a document "Implementation_scaledABE_simsVx.yy.pdf" in the doc subdirectory of the package.

References

Laszlo Tothfalusi and Laszlo Endrenyi "Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs" J. Pharm. Pharmaceut. Sci. (www.cspsCanada.org) 15(1) 73 - 84, 2011

See Also

sampleN.scABEL, power.RSABE

Examples

Run this code
# using all the defaults:
# design="2x3x3", EMA regulatory settings
# PE constraint 0.8-1.25, cap on widening if CV>0.5
# true ratio =0.95, 1E+6 simulations
power.scABEL(CV=0.4, n=29)
# should give:
# Unbalanced design. n(i)=10/10/9 assumed.
# [1] 0.82854
# with details=TRUE to view the computational time
power.scABEL(CV=0.5, n=54, theta0=1.15, details=TRUE)
# should give (times may differ depending on your machine).
# 1e+05 sims. Time elapsed (sec):
#    user  system elapsed 
#    0.09    0.00    0.10 
# p(BE-ABE)= 0.27542 ; p(BE-wABEL)= 0.82078 ; p(BE-PE)= 0.85385 
# 0.81727

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