Bioequivalence and Bioavailability Forum

Hi Maggie,

❝ I am exploring the hypothesis to use the within subject variability obtained on conventional 2 way crossover bioequivalence study and apply it in scale average bioequivalence as described for a replicated design used for HVD or NTI.

Since you mentioned RSABE for NTID, I guess you are interested in the FDA’s methods.

❝ I know that within subject variability of reference would be necessary […]. My doubt is if these values have any relation somehow like, for instance, the first one is larger than the second one or there is no relationship at all?

Sorry, there is no relationship since one formulation doesn’t “care” about the other one behaves.
Try this one (which pools the within-subject CV from CV_wT and CV_wR):

library(PowerTOST)
CVwR    <- CVwT <- seq(0.3, 0.5, 0.05)
res     <- data.frame(CVwT=rep(CVwT, each=length(CVwR)),
                      CVwR=rep(CVwR, length(CVwT)), CVw=NA)
res$CVw <- mse2CV((CV2mse(res$CVwT)+CV2mse(res$CVwR))/2)
print(signif(res, 4), row.names=FALSE)

 CVwT CVwR    CVw
 0.30 0.30 0.3000
 0.30 0.35 0.3258
 0.30 0.40 0.3528
 0.30 0.45 0.3806
 0.30 0.50 0.4090
 0.35 0.30 0.3258
 0.35 0.35 0.3500
 0.35 0.40 0.3756
 0.35 0.45 0.4023
 0.35 0.50 0.4296
 0.40 0.30 0.3528
 0.40 0.35 0.3756
 0.40 0.40 0.4000
 0.40 0.45 0.4255
 0.40 0.50 0.4518
 0.45 0.30 0.3806
 0.45 0.35 0.4023
 0.45 0.40 0.4255
 0.45 0.45 0.4500
 0.45 0.50 0.4754
 0.50 0.30 0.4090
 0.50 0.35 0.4296
 0.50 0.40 0.4518
 0.50 0.45 0.4754
 0.50 0.50 0.5000

Say you found a CV_w of ~0.4 in a non-replicated crossover. That could mean CV_wT=CV_wR=0.4 but also extreme cases where one CV is 0.3 and the other one 0.5. Let’s explore it:

T.equal.R <- which(res$CVwT == 0.4 & res$CVwR == 0.4)
T.smaller <- which(res$CVwT == 0.3 & res$CVwR == 0.5)
R.smaller <- which(res$CVwT == 0.5 & res$CVwR == 0.3)

sampleN.RSABE(CV=c(res[T.equal.R, "CVwT"], res[T.equal.R, "CVwR"]),
              design="2x2x4", details=FALSE)

++++++++ Reference scaled ABE crit. +++++++++
           Sample size estimation
---------------------------------------------
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) = 0.4; CVw(R) = 0.4
True ratio = 0.9
ABE limits / PE constraints = 0.8 ... 1.25
Regulatory settings: FDA

Sample size
 n    power
24   0.80516

sampleN.RSABE(CV=c(res[T.smaller, "CVwT"], res[T.smaller, "CVwR"]),
              design="2x2x4", details=FALSE)

++++++++ Reference scaled ABE crit. +++++++++
           Sample size estimation
---------------------------------------------
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) = 0.3; CVw(R) = 0.5
True ratio = 0.9
ABE limits / PE constraints = 0.8 ... 1.25
Regulatory settings: FDA

Sample size
 n    power
18   0.82354

sampleN.RSABE(CV=c(res[R.smaller, "CVwT"], res[R.smaller, "CVwR"]),
              design="2x2x4", details=FALSE)

++++++++ Reference scaled ABE crit. +++++++++
           Sample size estimation
---------------------------------------------
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) = 0.5; CVw(R) = 0.3
True ratio = 0.9
ABE limits / PE constraints = 0.8 ... 1.25
Regulatory settings: FDA

Sample size
 n    power
54   0.80552

If you interested in the EMA’s ABEL, use sampleN.scABEL(...) and for Health Canada’s ABEL of AUC sampleN.scABEL(..., regulator="HC").

The FDA’s RSABE for NTIDs is more nasty because a comparison of σ_wT with σ_wR is part of the method. Code:

library(PowerTOST)
CVwR    <- CVwT <- seq(0.075, 0.15, 0.025)
res     <- data.frame(CVwT=rep(CVwT, each=length(CVwR)),
                      CVwR=rep(CVwR, length(CVwT)), CVw=NA)
res$CVw <- mse2CV((CV2mse(res$CVwT)+CV2mse(res$CVwR))/2)
print(signif(res, 4), row.names=FALSE)
T.equal.R <- which(res$CVwT == 0.100 & res$CVwR == 0.100)
T.smaller <- which(res$CVwT == 0.075 & res$CVwR == 0.125)
R.smaller <- which(res$CVwT == 0.125 & res$CVwR == 0.075)
sampleN.NTIDFDA(CV=c(res[T.equal.R, "CVwT"], res[T.equal.R, "CVwR"]),
                design="2x2x4", details=FALSE)
sampleN.NTIDFDA(CV=c(res[T.smaller, "CVwT"], res[T.smaller, "CVwR"]),
                design="2x2x4", details=FALSE)
sampleN.NTIDFDA(CV=c(res[R.smaller, "CVwT"], res[R.smaller, "CVwR"]),
                design="2x2x4", details=FALSE)

Gives

+++++++++++ FDA method for NTID's +++++++++++
           Sample size estimation
---------------------------------------------
Study design:  2x2x4
log-transformed data (multiplicative model)
1e+05 studies for each step simulated.

alpha  = 0.05, target power = 0.8
CVw(T) = 0.1, CVw(R) = 0.1
True ratio     = 0.975
ABE limits     = 0.8 ... 1.25
Regulatory settings: FDA

Sample size
 n     power
18   0.841790

+++++++++++ FDA method for NTID's +++++++++++
           Sample size estimation
---------------------------------------------
Study design:  2x2x4
log-transformed data (multiplicative model)
1e+05 studies for each step simulated.

alpha  = 0.05, target power = 0.8
CVw(T) = 0.075, CVw(R) = 0.125
True ratio     = 0.975
ABE limits     = 0.8 ... 1.25
Regulatory settings: FDA

Sample size
 n     power
12   0.827150

sampleN.NTIDFDA(CV=c(res[R.smaller, "CVwT"], res[R.smaller, "CVwR"]),
                 design="2x2x4", details=FALSE)

+++++++++++ FDA method for NTID's +++++++++++
           Sample size estimation
---------------------------------------------
Study design:  2x2x4
log-transformed data (multiplicative model)
1e+05 studies for each step simulated.

alpha  = 0.05, target power = 0.8
CVw(T) = 0.125, CVw(R) = 0.075
True ratio     = 0.975
ABE limits     = 0.8 ... 1.25
Regulatory settings: FDA

Sample size
 n     power
46   0.802330

Note that the FDA requires at least 24 dosed subjects in replicate designs for RSABE (though less eligibile due to dropouts are acceptable) and that for NTIDs a full replicate design is required.