power.NTID {PowerTOST}

(Empirical) Power for BE decision via FDA method for NTIDs

Description

This function performs the power calculation of the BE decision via the FDA’s method for narrow therapeutic index drugs (NTIDs) by simulations. The study design could be the full replicate design 2x2x4 with 4-periods (TRTR|RTRT) or the 2x2x3 replicate design with sequences TRT|RTR.

Usage

power.NTID(alpha = 0.05, theta1, theta2, theta0, CV, n, design=c("2x2x4", "2x2x3"),
           nsims = 1e+05, details = FALSE, setseed = TRUE)

Arguments

alpha

Type I error probability, significance level. Conventionally mostly set to 0.05.

theta1

Conventional lower ABE limit to be applied in the FDA procedure.
Defaults to 0.8 if not given explicitly.

theta2

Conventional upper ABE limit to be applied in the FDA procedure.
Defaults to 1.25 if not given explicitly.

theta0

‘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.

CV

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].

n

Number of subjects under study.
May be given as vector. In that case it is assumed that n contains the number of subjects per sequence groups.
Attention! In case of the "2x2x3" (TRT|RTR) design the order of sample sizes important if given as vector. n[1] is for sequence group ‘TRT’ and n[2] is for sequence group ‘RTR’.

If n is given as single number (total sample size) and this number is not divisible by the number of sequences of the design an unbalanced design is assumed. A corresponding message is thrown showing the numbers of subjects in the sequence groups.

design

Design of the study to be planned.
"2x2x4" is the full replicate design with 2 sequences and 4 periods (TRTR|RTRT).
"2x2x3" is the full replicate design with 2 sequences and 3 periods (TRT|RTR).
Defaults to design="2x2x4".

nsims

Number of simulations to be performed to obtain the empirical power. Defaults to 100,000 = 1e+5.

details

If set to TRUE the computational time is shown as well as the components for the BE decision.
⁠p(BE-ABE)⁠ is the simulated probability for the conventional ABE test.
⁠p(BE-sABEc)⁠ is the probability that the 95% CI of the scaled ABE criterion is ≤ 0.
⁠p(BE-sratio)⁠ is the probability that the upper confidence limit of σ_wT/σ_wR ≤ 2.5.

setseed

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.

Details

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 σ_wT/σ_wR ≤ 2.5.

The simulations are done via the distributional properties of the statistical quantities necessary for deciding BE based on these method.
Details can be found in a document ⁠Implementation_scaledABE_sims⁠ located in the /doc sub-directory of the package.

Value

Returns the value of the (empirical) power if argument details = FALSE.
Returns a named vector if argument details = TRUE, where ⁠p(BE)⁠ is the (overall) power, ⁠p(BE-sABEc)⁠ is the power of the BE test via scaled ABE criterion alone, ⁠p(BE-ABE)⁠ is the power of the conventional ABE test alone, and ⁠p(BE-sratio)⁠ is the power of the criterion ‘upper confidence limit of σ_wT/σ_wR ≤ 2.5’ alone.

Note

The FDA’s method is described for the ABE limits 0.8 ... 1.25 only. Setting theta1, theta2 to other values may not be reasonable and is not tested.
The results for the design "2x2x3" are to be considered as experimental since at present not thorougly tested.

The method is also required by China’s Center of Drug Evaluation.

Author(s)

D. Labes

References

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. 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. 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

See Also

sampleN.NTID
and power.HVNTID, sampleN.HVNTID for NTIDs with high variability

Examples

# using the all defaults:
# GMR=0.975, theta1=0.8, theta2=1.25, 100,000 simulations
# and a CV of 0.1 (= 10%) with 12 subjects, balanced
power.NTID(CV = 0.1, n = 12)
# should give a power of 0.62553