These function performs the power calculation of the BE decision via scaled (widened) BE acceptance limits by simulations.
power.scABEL(alpha = 0.05, theta1, theta2, theta0, CV, n, design = c("2x3x3", "2x2x4", "2x2x3"), regulator, nsims, details = FALSE, setseed = TRUE)
Type I error probability, significance level. Conventionally mostly set to 0.05.
Conventional lower ABE limit to be applied in the mixed procedure if
Conventional upper ABE limit to be applied in the mixed procedure if
‘True’ or assumed T/R ratio.
Intra-subject coefficient(s) of variation as ratio (not percent).
Number of subjects under study.
Design of the study.
Regulatory settings for the widening of the BE acceptance limits.
Number of simulations to be performed to obtain the empirical power.
Defaults to 100,000 = 1e+05.
If set to
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 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
[L, U] = exp(-/+ r_const * sWR)
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="HC" and in case of
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 sub-directory of the package.
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.
Returns the value of the (empirical) power if argument
Returns a named vector if argument
p(BE) is the power, p(BE-ABEL) is the power of the widened ABEL criterion alone and p(BE-pe) is the power of the criterion ‘point estimate within acceptance range’ alone. p(BE-ABE) 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:
||TRTR | RTRT|
|TRRT | RTTR|
|TTRR | RRTT|
||TRT | RTR|
|TRR | RTT|
||TRR | RTR | RRT|
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 and/or sequences exteremly unbalanced.
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
For more details see the above mentioned document
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
To get the power for the FDA favored method via linearized scaled ABE criterion use function
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
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
# 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. #  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 #  0.8519
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