Description Usage Arguments Details Value Designs Warning Note Author(s) References See Also Examples
This function iteratively adjusts alpha for the BE decision via Average Bioequivalence with Expanding Limits (ABEL) based on simulations in order to maintain the consumer risk at the nominal level.
1 2 3 4 5 
alpha 
Type I Error (TIE) probability (nominal level of the test). Per convention commonly set to 0.05. 
theta0 
‘True’ or assumed T/R ratio. Defaults to 0.90 according to the two Lászlós if not given explicitly. 
theta1 
Conventional lower ABE limit to be applied in the mixed procedure
if 
theta2 
Conventional upper ABE limit to be applied in the mixed procedure
if 
CV 
Intrasubject coefficient(s) of variation as ratio (not percent).

design 
Design of the study. 
regulator 
Regulatory settings for the expanding of the BE acceptance limits.
Choose from 
n 
Total sample size of the study or a vector of sample size / sequences.
If 
alpha.pre 
Prespecified alpha (optional). Must be 
imax 
Maximum number of steps in sample size search. Defaults to 100. 
tol 
Desired accuracy (convergence tolerance). Defaults to 1E6. 
print 
If 
details 
If 
setseed 
Simulations are dependent on the starting point of the (pseudo)
random number generator. To avoid differences in power for different
runs 
nsims 
Number of simulations to be performed to estimate the (empirical) TIE error and in each iteration of adjusting alpha. The default value 1,000,000 = 1E+6 should not be lowered. 
sdsims 
If 
progress 
Set to 
The simulations are done via the distributional properties of the statistical
quantities necessary for assessing BE based on ABEL.
Simulations for the TIE are performed at the upper (expanded) limit U
of the acceptance range. Due to the symmetry around 1 results are valid for the lower
(expanded) limit L as well.
U at the EMA’s and Health Canada’s CVcap
, the GCC’s for any CVwR > 0.3:
1 2 3 4 5 6 
Simulated studies are evaluated by ANOVA (Method A) as recommended in the
EMA’ Q&Adocument and by intrasubject contrasts if regulator="HC"
.
Health Canada requires a mixedeffects model which cannot be implemented in R.
However, intrasubjects contrasts are a sufficiently close approximation.
The Type I Error in ABEL depends only on CVwR
and – to a
minor degree – the sample size. Algorithm:
The TIE is assessed based on alpha
(or alpha.pre
)
and compared to the nominal level of the test alpha
.
If no inflation of the TIE is found, the algorithm stops.
Otherwise, alpha is iteratively adjusted (i.e., alpha.adj <alpha
)
until no more relevant inflation of the TIE is detected (i.e.,
abs(TIE  alpha) <= tol
).
Sends results to the console if argument print=TRUE
(default).
Returns a list with the input, adjusted alpha, and Type I Error (for nominal
and adjusted alpha) if argument print=FALSE
.
If no adjustment is necessary, NAs
will be returned for the respective
variables (alpha.adj
, TIE.adj
, rel.change
, pwr.adj
, rel.loss
).
Although some designs are more ‘popular’ than others, power calculations are valid for all of the following designs:
"2x2x4"  TRTR  RTRT 
TRRT  RTTR  
TTRR  RRTT  
"2x2x3"  TRT  RTR 
TRR  RTT  
"2x3x3"  TRR  RTR  RRT 
See the Warning section of the function power.scABEL
concerning
the power value agreement to the one obtained by simulations via subject data.
Specifying theta0
is not necessary.
If theta0
is not given, achievable power for the common target
of 0.80 (both for alpha
and adjusted alpha) will be estimated. If
theta0
is specified, its value will be used; again for target power 0.80.
If you are interested in other levels of power, use sampleN.scABEL.ad
.
The EMA’s method is currently recommended in other jurisdictions as well (e.g., by the WHO;
in ASEAN States, Australia, Brazil, Egypt, the Eurasian Economic Union, New Zealand, the Russian Federation, and the East African Community).
If CVwR > 30%, fixed wider limits of 0.7500–1.3333 are recommended by the Gulf Cooperation Council (Bahrain, Kuwait, Oman, Qatar, Saudi Arabia, United Arab Emirates).
H. Schütz
Wonnemann M, Frömke C, Koch A. Inflation of the Type I Error: Investigations on Regulatory Recommendations for Bioequivalence of Highly Variable Drugs. Pharm Res. 2015;32(1):135–43. doi: 10.1007/s110950141450z
Muñoz J, Alcaide D, Ocaña J. Consumer’s risk in the EMA and FDA regulatory approaches for bioequivalence in highly variable drugs. Stat Med. 2015;35(12):1933–43. doi: 10.1002/sim.6834
Labes D, Schütz H. Inflation of Type I Error in the Evaluation of Scaled Average Bioequivalence, and a Method for its Control. Pharm Res. 2016;33(11):2805–14. doi: 10.1007/s1109501620061
Tóthfalusi L, Endrényi L. Algorithms for Evaluating Reference Scaled Average Bioequivalence: Power, Bias, and Consumer Risk. Stat Med. 2017;36(27):4378–90. doi: 10.1002/sim.7440
Molins E, Cobo E, Ocaña J. TwoStage Designs Versus European Scaled Average Designs in Bioequivalence Studies for Highly Variable Drugs: Which to Choose? Stat Med. 2017;36(30):4777–88. doi: 10.1002/sim.7452
European Medicines Agency, Committee for Medicinal Products for Human Use. Guideline on the Investigation of Bioequivalence. London, 20 January 2010. CPMP/EWP/QWP/1401/98 Rev. 1/ Corr **
European Medicines Agency, Committee for Medicinal Products for Human Use. Questions & Answers: positions on specific questions addressed to the Pharmacokinetics Working Party (PKWP). London, 19 November 2015. EMA/618604/2008 Rev. 13
Health Canada, Therapeutic Products Directorate. Policy on Bioequivalence Standards for Highly Variable Drug Products. Ottawa, 18 April 2016. 16104293140
Executive Board of the Health Ministers’ Council for GCC States. The GCC Guidelines for Bioequivalence. 30 March 2016. Version 2.4
sampleN.scABEL.ad
, power.scABEL
, power.scABEL.sdsims
, scABEL
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23  # Using all defaults:
# TRRRTRRRT, target power 80% for assumed ratio 0.90 (estimated sample size 54),
# EMA regulatory settings (ABE limits and PE constraint 0.80  1.25),
# 1E+6 simulated studies.
# Not run: due to timing policy of CRAN for examples
scABEL.ad(CV = 0.3)
# Should result in adjusted alpha 0.03389 (TIE 0.5000, TIE for nominal alpha 0.07189).
#
# As above but subject data simulations.
scABEL.ad(CV = 0.3, sdsims = TRUE)
# Should result in adjusted alpha 0.03336 (TIE 0.5000, TIE for nominal alpha 0.07237).
#
# TRTRTR, heteroscedasticity, sample size 48 (unbalanced), subject data simulations.
scABEL.ad(CV = c(0.25, 0.3), design = "2x2x3", n = c(23, 25), sdsims = TRUE)
# Should result in adjusted alpha 0.02465 (TIE 0.5000, TIE for nominal alpha 0.09050).
#
# TRTRRTRT, CV 0.35, sample size 33 (unbalanced).
scABEL.ad(CV = 0.35, design = "2x2x4", n = c(16, 17))
# Should result in adjusted alpha 0.03632 (TIE 0.5000, TIE for nominal alpha 0.06544).

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