## CVw pooled from CVwT and CVwR [Power / Sample Size]

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 CVwT and CVwR):

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$CVwR))/2) print(signif(res, 4), row.names=FALSE) CVwT CVwR CVw 0.30 0.30 0.3000 0.30 0.35 0.3258 0.30 0.40 0.3528 0.30 0.45 0.3806 0.30 0.50 0.4090 0.35 0.30 0.3258 0.35 0.35 0.3500 0.35 0.40 0.3756 0.35 0.45 0.4023 0.35 0.50 0.4296 0.40 0.30 0.3528 0.40 0.35 0.3756 0.40 0.40 0.4000 0.40 0.45 0.4255 0.40 0.50 0.4518 0.45 0.30 0.3806 0.45 0.35 0.4023 0.45 0.40 0.4255 0.45 0.45 0.4500 0.45 0.50 0.4754 0.50 0.30 0.4090 0.50 0.35 0.4296 0.50 0.40 0.4518 0.50 0.45 0.4754 0.50 0.50 0.5000 Say you found a CVw of ~0.4 in a non-replicated crossover. That could mean CVwT=CVwR=0.4 but also extreme cases where one CV is 0.3 and the other one 0.5. Let’s explore it: T.equal.R <- which(res$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$CVwR == 0.3) sampleN.RSABE(CV=c(res[T.equal.R, "CVwT"], res[T.equal.R, "CVwR"]), design="2x2x4", details=FALSE) ++++++++ Reference scaled ABE crit. +++++++++ Sample size estimation --------------------------------------------- Study design: 2x2x4 (full replicate) log-transformed data (multiplicative model) 1e+05 studies for each step simulated. alpha = 0.05, target power = 0.8 CVw(T) = 0.4; CVw(R) = 0.4 True ratio = 0.9 ABE limits / PE constraints = 0.8 ... 1.25 Regulatory settings: FDA Sample size n power 24 0.80516 sampleN.RSABE(CV=c(res[T.smaller, "CVwT"], res[T.smaller, "CVwR"]), design="2x2x4", details=FALSE) ++++++++ Reference scaled ABE crit. +++++++++ Sample size estimation --------------------------------------------- Study design: 2x2x4 (full replicate) log-transformed data (multiplicative model) 1e+05 studies for each step simulated. alpha = 0.05, target power = 0.8 CVw(T) = 0.3; CVw(R) = 0.5 True ratio = 0.9 ABE limits / PE constraints = 0.8 ... 1.25 Regulatory settings: FDA Sample size n power 18 0.82354 sampleN.RSABE(CV=c(res[R.smaller, "CVwT"], res[R.smaller, "CVwR"]), design="2x2x4", details=FALSE) ++++++++ Reference scaled ABE crit. +++++++++ Sample size estimation --------------------------------------------- Study design: 2x2x4 (full replicate) log-transformed data (multiplicative model) 1e+05 studies for each step simulated. alpha = 0.05, target power = 0.8 CVw(T) = 0.5; CVw(R) = 0.3 True ratio = 0.9 ABE limits / PE constraints = 0.8 ... 1.25 Regulatory settings: FDA Sample size n power 54 0.80552 If you interested in the EMA’s ABEL, use sampleN.scABEL(...) and for Health Canada’s ABEL of AUC sampleN.scABEL(..., regulator="HC"). The FDA’s RSABE for NTIDs is more nasty because a comparison of σwT with σwR is part of the method. Code: library(PowerTOST) CVwR <- CVwT <- seq(0.075, 0.15, 0.025) res <- data.frame(CVwT=rep(CVwT, each=length(CVwR)), CVwR=rep(CVwR, length(CVwT)), CVw=NA) res$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.

Dif-tor heh smusma 🖖
Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes Ing. Helmut Schütz 