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

Description

These 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, 
             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 <= CVswitch. Also lower limit for the point estimate constraint. Defaults to 0.8 if not given explicitly.

theta2

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.

theta0

'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. Attention! In case of the 2x2x3 (TRT|RTR) design the order of n's is important if given as vector. n[1] is for sequence group 'TRT' and n[2] is for sequence group 'RTR'.

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 settings for the widening of the BE acceptance limits. May be given as character from the choices "EMA", "HC" "FDA" or as an object of class 'regSet' (see reg_const). Defaults to regulator="EMA" if missing. This argument may be given also in lower case if given as character. The former regulator="ANVISA" is no longer allowed. Use "EMA" since ANVISA now recommends the use of EMA regulatory settings.

nsims

Number of simulations to be performed to obtain the empirical power. Defaults to 100 000 = 1e+05. If simulations are aimed for empirical alpha nsims=1e+06 is recommended.

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 ... theta2. p(BE-ABE) is the simulated probability for the conventional ABE test.

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 if argument details=FALSE. Returns a named vector if argument details=TRUE. p(BE) is the power, p(BE-wABEL) is the power of the widened ABEL 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.

Warning

Cross-validation of the simulations as implemented here and via the 'classical' subject data simulation have shown somewhat unsatisfactory results for the 2x3x3 design if the variabilities for Test and Reference are different. The function power.scABEL() therefore gives a warning if calculations with different CVwT and CVwR are requested for the 2x3x3 partial replicate design. For more details see the above mentioned document "Implementation_scaledABE_simsVy.xx.pdf".

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 (~log(1.25)/0.29356) is used in case of regulator="EMA" or regulator="HC" 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 for CVwR=0.5. In case of regulator="HC" the capping is done such that the acceptance limits are 0.6666 ... 1.5 at maximum. The former inofficial regulatory settings for regulator="ANVISA" are now covered by regulator="EMA". 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. Function power.scABEL() implements the simulation via distributional characteristics of the 'key' statistics obtained from the EMA recommended evaluation via ANOVA if regulator="EMA" or if the regulator component est_method is set to "ANOVA" if regulator is an object of class 'regSet'. Otherwise the simulations are based on the distributional characteristis of the 'key' statistics obtained from evaluation via intra-subject contrasts (ISC), as recommended by the FDA.

References

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

Examples

Run this code

# NOT RUN {
# using all the defaults:
# design="2x3x3", EMA regulatory settings
# PE constraint 0.8-1.25, cap on widening if CV>0.5
# true ratio =0.90, 1E+6 simulations
power.scABEL(CV=0.4, n=29)
# should give:
# Unbalanced design. n(i)=10/10/9 assumed.
# [1] 0.66113
#
# with details=TRUE to view the computational time and components
power.scABEL(CV=0.5, n=54, theta0=1.15, details=TRUE)
# should give (times may differ depending on your machine):
# 1e+05sims. Time elapsed (sec): 0.07
# 
#      p(BE) p(BE-wABEL)    p(BE-pe)   p(BE-ABE) 
#    0.81727     0.82078     0.85385     0.27542
#
# exploring pure ABEL with the EMA regulatory constant
# (without mixed method, without capping, without pe constraint)
rs <- reg_const("EMA")
rs$CVswitch  <- 0
rs$CVcap     <- Inf
rs$pe_constr <- FALSE
power.scABEL(CV=0.5, n=54, theta0=1.15, regulator=rs)
# should give
# [1] 0.8519
# }

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