This function performs the sample size estimation for the BE decision for the FDA’s method for NTIDs based on simulations. The study design is the full replicate design 2x2x4 (TRTR|RTRT) or the 3-period replicate design with sequences TRT|RTR.
sampleN.NTID(alpha = 0.05, targetpower = 0.8, theta0, theta1, theta2, CV,
design = c("2x2x4", "2x2x3"), nsims = 1e+05, nstart, imax = 100,
print = TRUE, details = TRUE, setseed = TRUE)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 re-starting.
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.
Attention! Defaults here to 0.975 if not given explicitly. The value was chosen
closer to 1 because the potency (contents) settings for NTIDs are tightened
by the FDA.
Conventional lower ABE limit to be applied in the FDA procedure.
Defaults to 0.8 if not given explicitly.
Conventional upper ABE limit to be applied in the FDA procedure.
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.
"2x2x4" is the full replicate with 2 sequences and 4 periods (TRTR|RTRT).
"2x2x3" is the full replicate with 2 sequences and 3 periods (TRT|RTR).
Defaults to design = "2x2x4".
Number of simulations to be performed to obtain the empirical power. Defaults to 100,000 = 1e+5.
Set this to a start value for the sample size if a previous run failed.
May be missing.
Maximum number of steps in sample size search. Defaults to 100.
If TRUE (default) the function prints its results. If FALSE only the resulting dataframe will be returned.
If set to TRUE, the default, the steps during sample size search are shown.
Moreover the details of the method settings are printed.
Simulations are dependent on the starting point of the (pseudo) random number
generator. To avoid differences in power values for different runs a
set.seed(123456) is issued if setseed = TRUE, the default.
D. Labes
For some input combinations the sample size search may be very time
consuming and will eventually even fail since the start values chosen may
not really reasonable for them. This applies especially for theta0 values
close to the implied scaled limits according to
exp(∓1.053605 × swR).
In case of a failed sample size search you may restart with setting the argument
nstart.
In case of theta0 values outside the implied scaled (tightened/widened) ABE limits
no sample size estimation is possible and the function throws an error
(f.i. CV = 0.04, theta0 = 0.95).
The linearized scaled ABE criterion is calculated according to the SAS code
given in the FDA’s guidances. For deciding BE the study must pass that criterion,
the conventional ABE test, and that the upper confidence limit of
σwT/σwR ≤ 2.5.
The simulations are done via the distributional properties of the statistical
quantities necessary for deciding BE based on this method.
Details can be found in a document Implementation_scaledABE_sims located in
the /doc sub-directory of the package.
The estimated sample size gives always the total number of subjects (not subject / sequence -- like in some other software packages).
Food and Drug Administration, Office of Generic Drugs (OGD). Draft Guidance on Warfarin Sodium. Recommended Dec 2012. download
Food and Drug Administration, Center for Drug Evaluation and Research (CDER). Draft Guidance for Industry. Bioequivalence Studies with Pharmacokinetic Endpoints for Drugs Submitted Under an ANDA. August 2021. download
Yu LX, Jiang W, Zhang X, Lionberger R, Makhlouf F, Schuirmann DJ, Muldowney L, Chen ML, Davit B, Conner D, Woodcock J. Novel bioequivalence approach for narrow therapeutic index drugs. Clin Pharmacol Ther. 2015;97(3):286--91. tools:::Rd_expr_doi("10.1002/cpt.28")
Jiang W, Makhlouf F, Schuirmann DJ, Zhang X, Zheng N, Conner D, Yu LX, Lionberger R. A Bioequivalence Approach for Generic Narrow Therapeutic Index Drugs: Evaluation of the Reference-Scaled Approach and Variability Comparison Criterion. AAPS J. 2015;17(4):891--901. tools:::Rd_expr_doi("10.1208/s12248-015-9753-5")
Endrényi L, Tóthfalusi L. Determination of Bioequivalence for Drugs with Narrow Therapeutic Index: Reduction of the Regulatory Burden. J Pharm Pharm Sci. 2013;16(5):676--82. open access
power.NTID
and power.HVNTID, sampleN.HVNTID for NTIDs with
high variability
sampleN.NTID(CV = 0.04,theta0 = 0.975)
# should give
# n=54 with an (empirical) power of 0.809590
#
# Test formulation with lower variability
sampleN.NTID(CV = c(0.04,0.06),theta0 = 0.975)
# should give
# n=20 with an (empirical) power of 0.0.814610
#
# alternative 3-period design
sampleN.NTID(CV = 0.04,theta0 = 0.975, design="2x2x3")
# should give
# n=86 with power = 0.80364
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