This function performs the power calculation of the BE decision via linearized scaled ABE criterion by simulations as recommended by the FDA.
power.RSABE(alpha = 0.05, theta1, theta2, theta0, CV, n,
design = c("2x3x3", "2x2x4", "2x2x3"), regulator,
nsims = 1e+05, details = FALSE, setseed=TRUE)Type I error probability, significance level. Conventionally mostly set to 0.05.
Conventional lower ABE limit to be applied in the mixed procedure if CVsWR <= CVswitch. Also lower limit for the point estimate constraint. Defaults to 0.8 if not given explicitly.
Conventional upper ABE limit to be applied in the mixed procedure if CVsWR <= CVswitch. Also upper limit for the point estimate constraint. Defaults to 1.25 if not given explicitly.
'True' or assumed bioequivalence ratio. Defaults to 0.90 according to the two Laszlo's if not given explicitly.
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].
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 sequences of the design an unbalanced design is
assumed. A corresponding message is thrown showing the numbers of subjects
in sequence groups used.
Attention! In case of the 2x2x3 (TRT|RTR) design the order of sample sizes / sequence is important
if given as a vector. n[1] is for sequence group 'TRT' and n[2] is for
sequence group 'RTR'.
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".
Regulatory settings for RSABE.
May be given as character from the choices "EMA" or "FDA" or as an object of
class 'regSet' (see reg_const).
Defaults to regulator="FDA" if missing.
This argument may be given also in lower case if given as character.
Also the linearized scaled ABE criterion is usually calculated with the FDA
constant r_const=log(1.25)/0.25 you can override this behavior to use the
EMA setting r_const=0.76 to avoid the discontinuity at CV=30% and be
more stringent.
Number of simulations to be performed to obtain the empirical power.
Defaults to 100 000 = 1e+5.
If simulations are aimed for empirical alpha nsims=1e+06 is recommended.
If set to TRUE the computational time is shown as well as the components
for the BE decision.
p(BE-sABEc) is the probability that the 95% CI of the ABE criterion is <0.
p(BE-PE) is the probability that the point estimate is within theta1 ... theta2.
p(BE-ABE) is the simulated probability for the conventional ABE test given for
comparision purposes.
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.
Returns the value of the (empirical) power if argument details=FALSE.
Returns a named vector if argument details=TRUE.
p(BE) is the power, p(BE-sABEc) is the power of the scaled ABE criterion alone
and p(BE-pe) is the power of the criterion 'point estimat within acceptance
range' alone.
p(BE-ABE) is the power of the conventional ABE test given for comparative purposes.
In case of the design 2x2x3 heteroscedasticity (i.e. CVwT not equal to CVwR) may lead to poor agreement of the power values compared to those calculated via the 'classical' way of subject data simulations if the design is unbalanced in respect to the number of subjects in the sequence groups. Therefore, the function issues a warning for that cases.
The linearized scaled ABE criterion is calculated according to the SAS code
given in the FDA progesterone guidance.
The simulations are done via the distributional properties of the statistical
quantities necessary for deciding BE based on scaled ABE criterion.
Details can be found in a document "Implementation_scaledABE_simsVx.yy.pdf"
located in the doc subdirectory of the package.
If a CVcap is defined for the regulator, the BE decision is based on the inclusion
of the CI in the capped widened acceptance limits in case of CVwR > CVcap. This
resembles method Howe-EMA in Munoz et al. and is the standard behavior now if
regulator="EMA" is choosen.
FDA Draft Guidance on Progesterone Recommended Apr 2010. Revised Feb 2011. download
T<U+00F3>thfalusi, L, Endr<U+00E9>nyi, L. Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs J Pharm Pharmaceut Sci. 2011;15(1):73--84. free download
T<U+00F3>thfalusi L, Endr<U+00E9>nyi L, Garc<U+00ED>a Arieta A. Evaluation of Bioequivalence for Highly Variable Drugs with Scaled Average Bioequivalence Clin Pharmacokin. 2009;48(11):725--43. 10.2165/11318040-000000000-00000
Mu<U+00F1>oz J, Alcaide D, Oca<U+00F1>a J. Consumer<U+2019>s risk in the EMA and FDA regulatory approaches for bioequivalence in highly variable drugs Stat Med. 2015;35(12):1933--43. 10.1002/sim.6834
# NOT RUN {
# using all the defaults:
# design="2x3x3" -> partial replicate
# ABE limits, PE constraint 0.8-1.25
# true ratio =0.90, 1E+5 simulations
power.RSABE(CV=0.4, n=36)
# should give
# [1] 0.83634
#
# to explore the simulation error due to the state of the
# random number generator
power.RSABE(CV=0.4, n=36, setseed=FALSE)
# will give something like
# [1] 0.83725
#
# explore pure RSABE (without mixed method, without pe constraint)
rs <- reg_const("FDA")
rs$CVswitch <- 0
rs$pe_constr <- FALSE
power.RSABE(CV=0.4, n=36, regulator=rs)
# should give
# [1] 0.84644
# }
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