## [Opinion] Should the 90% CI for GMR be required to encompass 1 [RSABE / ABEL]

Hi bebac_fan,

» I am a new poster, long time lurker.

Welcome to the club. Do you know what Groucho Marx said about clubs?

» I am […] crazy (but not formally trained) about statistics.

Welcome to the Amateur League.

I try to respond not only to this post but to others of yours.

» My question involves the case where an entire GMR 90% confidence interval is outside of 100.00 […]. For HVD with wide therapeutic index, I believe this is reasonable. But what about for a NTID with doses that differ by less than 15%?
»
» I understand this is part of the reason that RSABE and ABEL are implemented. However, let us assume that the Swr is 22% and essentially expands reference scaling to ABE limits. Let us also assume that a 7% difference in BE is clinically significant.

You’ve chosen a nice swR! With the FDA’s RSABE for NTIDs the “implied BE limits” would be wider than the conventional ABE’s 80.00–125.00% for any CVwR >21.42% (swR 0.2118). Hence, according to the book you have to pass the conventional limits as well.

» […] I am saying that a large enough sample size can force a test product with e.g. 89% relative BA (e.g. 100mg/112mg) relative to RLD to pass. The difference between 100 and 112mg is clinically significant for this product. I am wondering if adding the condition I talked about from the beginning would help.

OK, let’s ignore ElMaestro’s and John’s concerns about potency for a minute and assume that both drugs have a true potency of 100% (of their labeled contents of 100 and 112 mg).
I know that you are R-geek. Do we really need a large sample size?

library(PowerTOST) sampleN.NTIDFDA(CV=0.22, theta0=100/112, design="2x2x4", details=FALSE) +++++++++++ FDA method for NTIDs ++++++++++++            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) = 0.22, CVw(R) = 0.22 True ratio     = 0.8928571 ABE limits     = 0.8 ... 1.25 Regulatory settings: FDA Sample size  n     power 36   0.810220

Nope!
If everything comes out exactly as assumed, what will we get?

round(100*CI.BE(pe=100/112, CV=0.22, n=36, design="2x2x4", robust=TRUE), 2) lower upper 83.98 94.93

Although we would be allowed to scale a tiny bit

 sigma0             <- 0.1 # CV 10.02505. Why? Ask the FDA. Impl.Limits        <- exp(c(-1, +1)*log(1.11111)*CV2se(0.22)/sigma0) names(Impl.Limits) <- c("L", "U") round(100*Impl.Limits, 2)      L      U  79.53 125.74

with such a CVwR the condition “must pass ABE” is important. If you want to explore the overall-power (plus the ones of the three tests) try:

power.NTIDFDA(theta0=100/112, CV=0.22, n=36, design="2x2x4", details=TRUE)    p(BE)  p(BE-sABEc)    p(BE-ABE) p(BE-sratio)  0.81022      0.83051      0.90737      0.99986

OK, the study passes despite that the GMR is with 82.64% below your clinically significant difference (–7%).

» […] is it reasonable to require the 90% CI for GMR to fall within 1?

But: θ is within the 90% CI of the GMR. The upper CL (94.93%) overlaps with your “relevant” lower limit of 93%.

BTW, for the EMA (fixed BE-limits of 90.00–111.11%) try this:

sampleN.TOST(CV=0.22, theta0=100/112, theta1=0.90, design="2x2x4", details=FALSE)

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Helmut Schütz

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