Sample size estimation for BE decision via linearized scaled ABE criterion

This function performs the Sample size estimation for the BE decision via linearized scaled ABE criterion based on simulations.

sampleN.RSABE(alpha = 0.05, targetpower = 0.8, theta0, theta1, theta2, CV,
              design = c("2x3x3", "2x2x4", "2x2x3"), regulator = c("FDA", "EMA"),
              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 body settings for the scaled ABE criterion. Defaults to design="FDA". Also the 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.


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, the 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 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. For more details see a document Implementation_scaledABE_simsVx.yy.pdf in the /doc sub-directory 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 Mu<U+00F1>oz et al. and is the standard behavior now if regulator="EMA" is choosen.


Returns a data.frame with the input 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.


The sample size estimation is done 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. The minimum sample size is n=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 theta0 >1.2 and <0.85 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 about 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.


Food and Drug Administration, Office of Generic Drugs (OGD). 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. open access

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

See Also

power.RSABE, power.scABEL

  • sampleN.RSABE
# using all the defaults:
# design=2x3x3 (partial replicate design), theta0=0.90, 
# ABE limits, PE constraint 0.8 - 1.25
# targetpower=80%, alpha=0.05, 1E5 simulations
sampleN.RSABE(CV = 0.3)
# should result in a sample size n=45, power=0.80344
# }
Documentation reproduced from package PowerTOST, version 1.4-9, License: GPL (>= 2)

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