Bioequivalence and Bioavailability Forum

Dear all,

up to v2.4 of 14 March 2019 FARTSSIE’s tab Bioequivalence, Replicate contained two boxes for reference-scaling. The sample size was wrong because no analytical solution for power exists and simulations are required instead.

In v2.5 of 13 October 2020 Dave deleted the boxes and suggests to install PowerTOST. He gives in two boxes the arguments for PowerTOST’s functions sampleN.scABEL() for Average Bioequivalence with Expanding Limts (EMA and many others, Health Canada) and sampleN.NTIDFDA() for the FDA’s reference-scaling for NTIDs.
However, in the former don’t use the argument regulator="FDA" as he suggests since RSABE ≠ ABEL. Not only that the regulatory constants are different, these are different approaches (upper limit of the linearized criterion ≤0 vs expansion of the BE limits).

library(PowerTOST) # show the regulatory conditions
reg_const(regulator = "EMA")
EMA regulatory settings
- CVswitch            = 0.3
- cap on scABEL if CVw(R) > 0.5
- regulatory constant = 0.76
- pe constraint applied
reg_const(regulator = "HC")
HC regulatory settings
- CVswitch            = 0.3
- cap on scABEL if CVw(R) > 0.57382
- regulatory constant = 0.76
- pe constraint applied
reg_const(regulator = "FDA")
FDA regulatory settings
- CVswitch            = 0.3
- no cap on scABEL
- regulatory constant = 0.8925742
- pe constraint applied

Use the function sampleN.RSABE() instead. Examples with comments at the end.

Since in the survey 20% of participants reported to never update their software: Not a good idea.

---

library(PowerTOST)
sampleN.scABEL(CV = 0.6, design = "2x2x4", regulator = "EMA") # correct

+++++++++++ scaled (widened) ABEL +++++++++++
            Sample size estimation
   (simulation based on ANOVA evaluation)
---------------------------------------------
Study design: 2x2x4 (4 period full replicate)
log-transformed data (multiplicative model)
1e+05 studies for each step simulated.

alpha  = 0.05, target power = 0.8
CVw(T) = 0.6; CVw(R) = 0.6
True ratio = 0.9
ABE limits / PE constraint = 0.8 ... 1.25
EMA regulatory settings
- CVswitch            = 0.3
- cap on scABEL if CVw(R) > 0.5
- regulatory constant = 0.76
- pe constraint applied

Sample size search
 n     power
30   0.7851
32   0.8101

sampleN.scABEL(CV = 0.6, design = "2x2x4", regulator = "HC") # correct

+++++++++++ scaled (widened) ABEL +++++++++++
            Sample size estimation
(simulations based on intra-subject contrasts)
----------------------------------------------
Study design:  2x2x4 (full replicate)
log-transformed data (multiplicative model)
1e+05 studies for each step simulated.

alpha  = 0.05, target power = 0.8
CVw(T) = 0.6; CVw(R) = 0.6
True ratio = 0.9
ABE limits / PE constraint = 0.8 ... 1.25
HC regulatory settings
- CVswitch            = 0.3
- cap on scABEL if CVw(R) > 0.57382
- regulatory constant = 0.76
- pe constraint applied

Sample size search
 n     power
24   0.7505
26   0.7851
28   0.8118

sampleN.scABEL(CV = 0.6, design = "2x2x4", regulator = "FDA") # wrong

+++++++++++ scaled (widened) ABEL +++++++++++
            Sample size estimation
(simulations based on intra-subject contrasts)
----------------------------------------------
Study design:  2x2x4 (full replicate)
log-transformed data (multiplicative model)
1e+05 studies for each step simulated.

alpha  = 0.05, target power = 0.8
CVw(T) = 0.6; CVw(R) = 0.6
True ratio = 0.9
ABE limits / PE constraint = 0.8 ... 1.25
FDA regulatory settings
- CVswitch            = 0.3
- no cap on scABEL
- regulatory constant = 0.8925742
- pe constraint applied

Sample size search
 n     power
16   0.7017
18   0.7476
20   0.7813
22   0.8071

sampleN.RSABE(CV = 0.6, design = "2x2x4") # correct

++++++++ Reference scaled ABE crit. +++++++++
           Sample size estimation
---------------------------------------------
Study design: 2x2x4 (4 period full replicate)
log-transformed data (multiplicative model)
1e+05 studies for each step simulated.

alpha  = 0.05, target power = 0.8
CVw(T) = 0.6; CVw(R) = 0.6
True ratio = 0.9
ABE limits / PE constraints = 0.8 ... 1.25
FDA regulatory settings
- CVswitch            = 0.3
- regulatory constant = 0.8925742
- pe constraint applied

Sample size search
 n     power
16   0.67580
18   0.72735
20   0.76531
22   0.79589
24   0.81947