Description Usage Arguments Details Value Designs Warning Note Author(s) References See Also Examples
These function performs the power calculation of the BE decision via scaled (widened) BE acceptance limits by simulations.
1 2 3  power.scABEL(alpha = 0.05, theta1, theta2, theta0, CV, n,
design = c("2x3x3", "2x2x4", "2x2x3"), regulator,
nsims, details = FALSE, setseed = TRUE)

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

theta2 
Conventional upper ABE limit to be applied in the mixed procedure if

theta0 
‘True’ or assumed T/R ratio. 
CV 
Intrasubject coefficient(s) of variation as ratio (not percent).

n 
Number of subjects under study. 
design 
Design of the study. 
regulator 
Regulatory settings for the widening of the BE acceptance limits. 
nsims 
Number of simulations to be performed to obtain the empirical power.
Defaults to 100,000 = 1e+05. 
details 
If set to 
setseed 
Simulations are dependent on the starting point of the (pseudo) random number
generator. To avoid differences in power for different runs a 
The methods rely on the analysis of logtransformed data, i.e., assume a
lognormal distribution on the original scale.
The widened BE acceptance limits will be calculated by the formula
[L, U] = 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 case of regulator="GCC"
is treatd as special case of ABEL with
CVswitch = CVcap = 0.3. The r_const = log(1.25)/CV2se(0.3) assures that for CV>0.3
the widened BE limits of 0.7 ... 1.3333 are used.
The simulations are done via the distributional properties of the statistical
quantities necessary for deciding BE based on widened ABEL.
For more details see the 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 intrasubject contrasts (ISC),
as recommended by the FDA.
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(BEABEL) is the power of the widened ABEL criterion alone
and p(BEpe) is the power of the criterion ‘point estimate within acceptance
range’ alone. p(BEABE) is the power of the conventional ABE test given for
comparative purposes.
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 
Crossvalidation 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 and/or sequences exteremly unbalanced.
The function power.scABEL()
therefore gives a warning if calculations
with different CVwT and CVwR are requested for the 2x3x3 partial replicate design. For "EMA"
subject simulations are provided in power.scABEL.sdsims
.
For more details see the above mentioned document Implementation_scaledABE_simsVy.xx.pdf
.
In case of regulator="FDA"
the (empirical) power is only approximate since
the BE decision method is not exactly what is expected by the FDA. But the “Two Laszlós” state that the scABEL method should be ‘operational equivalent’ to the
FDA method.
To get the power for the FDA favored method via linearized scaled ABE criterion
use function power.RSABE
.
In case of regulator="HC"
(based on ISC), power is also only approximative since Health Canada recommends an evaluation via mixed model approach. This could only implemented via
subject data simulations which are very time consuming. But ISC may be a good
substitute.
D. Labes
Tóthfalusi L, Endrényi L. Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs. J Pharm Pharmaceut Sci. 2011;15(1):73–84. open source
sampleN.scABEL, power.RSABE, reg_const
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26  # using all the defaults:
# design="2x3x3", EMA regulatory settings
# PE constraint 0.81.25, 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(BEwABEL) p(BEpe) p(BEABE)
# 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

Unbalanced design. n(i)=10/10/9 assumed.
[1] 0.66113
1e+05 sims. Time elapsed (sec): 0.078
p(BE) p(BEwABEL) p(BEpe) p(BEABE)
0.81727 0.82078 0.85385 0.27542
[1] 0.8519
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