## Reference-scaling: Don’t use FARTSSIE! [Power / Sample Size]

Hi Chirag,

❝ What BE limits should be taken into consideration while estimating sample size for replicate design studies for USFDA & EMA.

If you want to go with reference-scaling, none! The limits depend on the CVwR and are estimated in the actual study. Hence, you need simulations, where your assumed CVwR is the average. Either use the tables provided by the two Lászlós* or package PowerTOST for R. The software is open source and comes free of costs.

❝ Should it be 80-125% ?

No (see above). Only if you don’t want reference-scaling (i.e., conventional ABE). Actually reference-scaling was introduced to avoid the extreme sample sizes required for ABE.

❝ We normally use FARTSSIE

FARTSSIE cannot perform the necessary simulations and therefore, is not suitable for any of the reference-scaling methods.

❝ For a product with 51% ISCV (from a completed partial replicate study UKMHRA) by using FARTSSIE we arrived at different sample size for EMA

❝ - Sample size estimated = 27 (80% Power, 95-105% T/R, Method C1, BE Limits 69.84 to 143.19%)

❝ - Sample size estimated = 76 (80% Power, 95-105% T/R, No reference Scaled BE Limits-80-125%)

1. Do not assume a T/R of 95% for HVDP(s). The two Lászlós recommend a 10% difference and for good reasons. Therefore, 90% is the default in PowerTOST’s reference-scaling functions.
2. If ever possible avoid the partial replicate design. Though the evaluation works for the EMA’s methods, sometimes no convergence is achieved for the FDA’s mixed effects model (if CVwR <30%) – independent from the software. Study done, no result, you are fired.
Better to opt for full replicate 2-sequence designs: 4-periods (TRTR|RTRT) or – if you are afraid of drop­outs and/or want to avoid large sampling volumes – 3-periods (TRT|RTR). In the latter one you need at least twelve eligible subjects in sequence RTR according to the EMA’s Q&A-document (not relevant in practice).
After installing R and downloading PowerTOST, start the R-console, and type library(PowerTOST). If you want to make yourself familiar with PowerTOST, type help(package=PowerTOST).
Try these examples, where "2x2x4" denotes the 4-perod full replicate, "2x2x3" the 3-period full replicate, and "2x3x3" the 3-sequence 3-period (partial) replicate.
• The EMA’s ABEL
sampleN.scABEL(CV=0.51, design="2x2x4") sampleN.scABEL(CV=0.51, design="2x2x3") sampleN.scABEL(CV=0.51, design="2x3x3") 
sampleN.scABEL(CV=0.51, design="2x2x4", regulator="HC") sampleN.scABEL(CV=0.51, design="2x2x3", regulator="HC") sampleN.scABEL(CV=0.51, design="2x3x3", regulator="HC") 
• The FDA’s RSABE
sampleN.RSABE(CV=0.51, design="2x2x4") sampleN.RSABE(CV=0.51, design="2x2x3") sampleN.RSABE(CV=0.51, design="2x3x3") 
Sample sizes for the FDA (22, 34, 30) are always smaller than ones for the EMA (28, 42, 39) because in RSABE there is no 50% CVwR limit for scaling. On the other hand Health Canada’s ABEL sometimes require less subjects than the EMA’s ABEL because the upper cap is 57.38%. If your boss insist in a T/R of 95% add the argument theta0=0.95 to the function calls but don’t blame me if the study fails. If you want 90% power instead of the default 80%, add the argument targetpower=0.90.
I suggest to perform a power analysis (recommended by ICH E9) assessing the influence of deviations from assumptions (lower/higher CVwR, T/R deviating more than expected from 100%, less eligible subjects due to drop­outs). Try (with the default partial replicate):

pa.scABE(CV=0.51, regulator="EMA") pa.scABE(CV=0.51, regulator="HC") pa.scABE(CV=0.51, regulator="FDA")

For the FDA CVwR can be as high as ~97% until power drops to 70%, though the sample size is smaller (30) compared to the EMA’s and Health Canada’s (39). With the same sample size 39, the CVwR can rise to ~76% (Health Canada) and only to ~64% (EMA). This is a consequence of differing upper scaling caps.

• Endrényi L, Tóthfalusi L. Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs. J Pharm Pharmaceut Sci. 2011;15(1):73–84. free resource.

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