Sample size estimation for BE decision via scaled (expanded) BE acceptance limits

This function performs the sample size estimation via power calculations of the BE decision via scaled (expanded) BE acceptance limits, based on simulations.

sampleN.scABEL(alpha = 0.05, targetpower = 0.8, theta0, theta1, theta2, CV, 
               design = c("2x3x3", "2x2x4", "2x2x3"), regulator,
               nsims = 1e+05, nstart, imax = 100, print = TRUE, details = TRUE,
               setseed = TRUE)

Type I error probability. Per convention mostly set to 0.05.


Power to achieve at least. Must be >0 and <1. Typical values are 0.8 or 0.9.


‘True’ or assumed T/R ratio. Defaults to 0.90 according to the two Laszl<U+00F3>s if not given explicitly.


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.


Intra-subject coefficient(s) of variation as ratio (not percent).

  • If given as a scalar (length(CV)==1) the same CV of Test and Reference is assumed (homoscedasticity, CVwT==CVwR).

  • If given as a vector (length(CV)==2), i.e., assuming heteroscedasticity, the CV of the Test must be given in CV[1] and the one of the Reference in the CV[2].


Design of the study to be planned. "2x3x3" is the partial replicate design. "2x2x4" is a full replicate design with 2 sequences and 4 periods. "2x2x3" is a full replicate design with 2 sequences and 3 periods. Defaults to design="2x3x3". Details are given the section about Designs.


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 argument regulator="ANVISA" is defunct. Use "EMA" since the ANVISA now recommends the use of EMA regulatory settings.


Number of simulations to be performed to obtain the (empirical) power. The default value 100,000 = 1e+5 is usually sufficient. Consider to rise this value if theta0<=0.85 or >=1.25. But see the warning section.


Set this to a start for the sample size search if a previous run failed. After reworking the start n in version 1.1-05 rarely needed.


Maximum number of steps in sample size search. Defaults to 100.


If TRUE (default) the function prints its results. If FALSE only the result data.frame will be returned.


If set to TRUE (default), the steps during sample size search are shown.


Simulations are dependent on the starting point of the (pseudo) random number generator. To avoid differences in power for different runs a set.seed(123456) is issued if setseed=TRUE, the default.


The simulations are done via the distributional properties of the statistical quantities necessary for deciding BE based on ABEL (‘Average Bioequivalence with Expanded Limits’). For more details see a description in the /doc sub-directory of the package. Function sampleN.scABEL() is based on power calculations via simulations using the 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. Function sampleN.scABEL2() is solely based on power calculations via simulation using the distributional characteristics of the ‘key’ statistics obtained from evaluation via ISC. This function is deprecated.


Returns a data.frame with the input settings and sample size results. The Sample size column contains the total sample size. The nlast column contains the last n value. May be useful for restarting.


We are doing the sample size estimation only for balanced designs since the break down of the total subject number in case of unbalanced sequence groups is not unique. Moreover the formulas used are only for balanced designs. In case of regulator="FDA" the sample size is only approximate since the BE decision method is not exactly what is expected by the FDA. But the two Laszl<U+00F3>s state that the scABEL method should be ‘operationally’ equivalent to the FDA method. Thus the sample size should be comparable. Consider in case of regulator="FDA" to use the function sampleN.RSABE(). In case of regulator="HC" the underlying power is only approximative since the Health Canada recommends evaluation by a mixed model approach. But this could only implemented via subject data simulations which are very time consuming. The minimum sample size is 6, even if the power is higher than the intended targetpower.


Although some designs are more ‘popular’ than others, sample size estimations are valid for all of the following designs:

"2x2x4" TRTR | RTRT
"2x2x3" TRT | RTR


The sample size estimation for very extreme theta0 (<0.83 or >1.21) may be very time consuming and will eventually also fail since the start values chosen are not really reasonable in that ranges. This is especially true in the range around CV = 0.3 and regulatory constant according to FDA. If you really need sample sizes in that range be prepared to restart the sample size estimation via the argument nstart. Since the dependence of power from n is very flat in the mentioned region you may also consider to adapt the number of simulations not to tap in the simulation error trap. If results of power.scABEL are expected to be inaccurate (partial replicate design with unbalanced sequences and/or heteroscedasticity where CVwT > CVwR), subject data via sampleN.scABEL.sdsims should be simulated instead. Very time consuming (easily 100times slower)! Subject data simulations are only supported for regulator="EMA".


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. open access

See Also

power.scABEL, sampleN.scABEL.sdsims, sampleN.RSABE, reg_const

  • sampleN.scABEL
# using all the defaults:
# partial replicate design, targetpower=80%,
# true assumed ratio = 0.90, 1E+5 simulated studies
# ABE limits, PE constraint 0.8 - 1.25
# EMA regulatory settings
sampleN.scABEL(CV = 0.3)
# should result in a sample size n=54, power=0.8159
# now with former (inofficial) ANVISA settings, CVswitch=40%
# (since 2016 ANVISA uses the same settings as EMA)
reg      <- reg_const("USER", r_const = 0.76, CVswitch = 0.4, CVcap = 0.5)
reg$name <- "Old ANVISA"
sampleN.scABEL(CV = 0.3, regulator = reg)
# should result in n=60, power=0.8101

# for the full replicate design, target power = 90%
# true assumed ratio = 0.9, FDA regulatory settings
# sims based on evalaution via ISC
sampleN.scABEL(CV = 0.4, targetpower = 0.9, theta0 = 0.9,
               design = "2x2x4", regulator = "FDA")
# should result in a sample size n=32, power=0.9125
# }
Documentation reproduced from package PowerTOST, version 1.4-9, License: GPL (>= 2)

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