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bebac_fan
Junior

US,
2018-03-28 18:43

Posting: # 18601
Views: 2,484
 

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

Dear All -

I am a new poster, long time lurker. I am a clinical pharmacologist who is crazy (but not formally trained) about statistics.

My question involves the case where an entire GMR 90% confidence interval is outside of 100.00 (e.g. 103.00 - 110.00). 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.

In your opinion, is it reasonable to require the 90% CI for GMR to fall within 1?

Thanks,
bebac_fan
ElMaestro
Hero

Denmark,
2018-03-28 19:07

@ bebac_fan
Posting: # 18602
Views: 2,226
 

 [Opinion] Should the 90% CI for GMR be required to encompass 1

Hi bfan,

» I am a new poster, long time lurker. I am a clinical pharmacologist who is crazy (but not formally trained) about statistics.

I like that :-D:-D

The width of the confidence interval is generally sample size dependent. Whether or not 100% is included in your CI may have absolutely nothing to do with the performance of the two products, or the existence of a clinically relevant difference, but which may have everything to do with your chosen sample size.
If we implement the rule like you propose we will therefor be punishing those sponsors who have high sample sizes. Think about it - this isn't what anyone wants to do.

At the end of the day you know the two products are different (although they might not be different by any clinically meaningful margin). The fact that any two products are different is one you can generally prove by increasing the sample size until the CI no longer includes 100%.:-)

if (3) 4

Best regards,
ElMaestro

"(...) targeted cancer therapies will benefit fewer than 2 percent of the cancer patients they’re aimed at. That reality is often lost on consumers, who are being fed a steady diet of winning anecdotes about miracle cures." New York Times (ed.), June 9, 2018.
bebac_fan
Junior

US,
2018-03-28 19:23

@ ElMaestro
Posting: # 18603
Views: 2,217
 

 [Opinion] Should the 90% CI for GMR be required to encompass 1

Dear ElMaestro,

Thank you for your input. I agree that this rule would punish sponsors have high sample sizes.

I understand this is also a potential mechanism of abuse to get poor drugs approved: Sponsors may increase sample sizes arbitrarily to meet BE. Would my proposed approach prevent that?

Lets take a drug that comes in 100, 112, and 125. Theoretically, a sponsor could get 100, 112, AND 125 dosage forms (assuming CMC doesn't catch it) approved for 112 if they use sample sizes big enough :-) This is my biggest concern.

Thanks again for your input -
bebac_fan


Edit: Full quote removed. Please delete everything from the text of the original poster which is not necessary in understanding your answer; see also this post #5[Helmut]
ElMaestro
Hero

Denmark,
2018-03-28 19:44

@ bebac_fan
Posting: # 18604
Views: 2,200
 

 [Opinion] Should the 90% CI for GMR be required to encompass 1

Dear bebac_fan,

» I understand this is also a potential mechanism of abuse to get poor drugs approved: Sponsors may increase sample sizes arbitrarily to meet BE. Would my proposed approach prevent that?

This is the wrong thinking, in my opinion. If the CI is within the limits then the product is BE, full stop. If you have reason to think the product is BE, then you have reason to apply a sample size appropriate for demonstrating it. Bear in mind that absence of a result indicating bioequivalence does not necessarily imply that the products are bioinequivalent


» Lets take a drug that comes in 100, 112, and 125. Theoretically, a sponsor could get 100, 112, AND 125 dosage forms (assuming CMC doesn't catch it) approved for 112 if they use sample sizes big enough :) This is my biggest concern.

Can you re-word this? I cannot understand what you mean.

if (3) 4

Best regards,
ElMaestro

"(...) targeted cancer therapies will benefit fewer than 2 percent of the cancer patients they’re aimed at. That reality is often lost on consumers, who are being fed a steady diet of winning anecdotes about miracle cures." New York Times (ed.), June 9, 2018.
bebac_fan
Junior

US,
2018-03-28 20:05

@ ElMaestro
Posting: # 18605
Views: 2,215
 

 [Opinion] Should the 90% CI for GMR be required to encompass 1

Dear ElMaestro,

You said:
» If you have reason to think the product is BE, then you have reason to apply a sample size appropriate for demonstrating it.

I fully agree with this - which is why i brought up that example. In the previous post you mentioned that we don't want to punish folks with large sample sizes. My intent is prevent maliciously large sample sizes.

Perhaps one way to do so is impose a GMR of 1 within CI limit, and the other is to enforce appropriate sample size. The latter requires assumption of Swr and power, which could be potentially exaggerated.

» Can you re-word this? I cannot understand what you mean.

Sorry for my english. Assume there is a current drug approved at doses 100, 112, and 125mg. The difference in dosing is clinically important.

My motivation for the original question: it is conceivable that a one could find T(100mg) and R(112mg) BE with a large enough sample. It is also conceivable that one may find 125mg BE with 112mg. This would cause substantial risk of harm. I thought that perhaps imposing the CI through GMR of 1 limit may prevent this from happening.

Thanks,
BF
jag009
Hero

NJ,
2018-03-28 21:25

@ bebac_fan
Posting: # 18606
Views: 2,175
 

 [Opinion] Should the 90% CI for GMR be required to encompass 1

Hi,

» My motivation for the original question: it is conceivable that a one could find T(100mg) and R(112mg) BE with a large enough sample. It is also conceivable that one may find 125mg BE with 112mg. This would cause substantial risk of harm. I thought that perhaps imposing the CI through GMR of 1 limit may prevent this from happening.

I think your clarification above is even more confusing. Your example "T(100mg) vs R(112mg) is bioequivalent with a large enough sample size". Are you trying to say that a large enough sample size can force a 100 mg product and a 112 mg product to become bioequivalent because the BE window has a ± 20% around 100%? Please don't forget that there is a criteria on T/R total assay/potency to be within 5%. Your 110mg and 112 mg has >5% potency and that alone invalidates your example.

John
bebac_fan
Junior

US,
2018-03-28 21:59

@ jag009
Posting: # 18609
Views: 2,162
 

 [Opinion] Should the 90% CI for GMR be required to encompass 1

Hi John,

Thanks for your response. Let me see if I can clear this up.

» Are you trying to say that a large enough sample size can force a 100 mg product and a 112 mg product to become bioequivalent because the BE window has a ± 20% around 100%?

Kind of. 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.

I was using the 100/112/125 example rather than talking about relative F to try to elucidate the clinical scenario, which I am doing a poor job of.

» Please don't forget that there is a criteria on T/R total assay/potency to be within 5%. Your 110mg and 112 mg has >5% potency and that alone invalidates your example.

I haven't. Thanks!

Cheers,
BF
ElMaestro
Hero

Denmark,
2018-03-28 23:03

@ bebac_fan
Posting: # 18610
Views: 2,123
 

 [Opinion] Should the 90% CI for GMR be required to encompass 1

Hi bf,

» I was using the 100/112/125 example...

there are two things in this:
  1. In some cases the usual 80.00%-125.00% criterion may not be optimal and in those cases alternatives must be sought.
  2. I am not aware of any problem of any kind, which has practical relevance and which can be solved by imposing a mandatory span for the CI across the 100% mark.
The example you mention appears very hypothetical, doesn't it?
If it existed that way then you could definbitely do a Finney bioassay to derive relative potency and a CI of the same. Now that's a horse of another color.:-D:-D

if (3) 4

Best regards,
ElMaestro

"(...) targeted cancer therapies will benefit fewer than 2 percent of the cancer patients they’re aimed at. That reality is often lost on consumers, who are being fed a steady diet of winning anecdotes about miracle cures." New York Times (ed.), June 9, 2018.
bebac_fan
Junior

US,
2018-03-28 23:57

@ ElMaestro
Posting: # 18611
Views: 2,122
 

 [Opinion] Should the 90% CI for GMR be required to encompass 1

Hi ElMaestro,

» 2. I am not aware of any problem of any kind, which has practical relevance and which can be solved by imposing a mandatory span for the CI across the 100% mark.

This is what I was looking for. Thank you for lending your knowledge!

The problem I describe may already exist for e.g. levothyroxine, with a Swr around 0.2, and many narrowly separated strengths (e.g. 100, 112, 125 mcg).

Using FDA NTID guidelines, I think it would be plausible to pass a formulation with GMR of 1.03-1.09 and another with a GMR of 0.93 - 0.99. In that case, a 100mcg tablet w/ GMR of 1.03-1.09 and 112mcg tablet w/ GMR of 0.93-0.99 would be biologically indistinguishable, which is concerning.

So we figured out that my proposed solution is not a good idea. How would you go about solving it?

Cheers,
BF
mittyri
Senior

Russia,
2018-04-05 17:57

@ bebac_fan
Posting: # 18645
Views: 1,225
 

 Black Swan again

Hi bebac_fan,

» The problem I describe may already exist for e.g. levothyroxine, with a Swr around 0.2, and many narrowly separated strengths (e.g. 100, 112, 125 mcg).

that's why Helmut named it Black Swan

Kind regards,
Mittyri
Helmut
Hero
avatar
Homepage
Vienna, Austria,
2018-03-28 23:57

@ bebac_fan
Posting: # 18612
Views: 2,100
 

 [Opinion] Should the 90% CI for GMR be required to encompass 1

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. :-D

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%).

No qualified opinion about your
» […] 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)


Cheers,
Helmut Schütz
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bebac_fan
Junior

US,
2018-03-29 13:46

@ Helmut
Posting: # 18614
Views: 1,887
 

 [Opinion] Should the 90% CI for GMR be required to encompass 1

Hi Helmut,

Thank you for validating the issue (sort of?). I am having fun with this theoretical exercise.

Yes I am an R fanatic. I think I'm going to play with power.NTID and add a criteria that the GMR CI falls through 1.00.

I will report back.

Cheers,
BF


Edit: Full quote removed. Please delete everything from the text of the original poster which is not necessary in understanding your answer; see also this post #5[Helmut]
jag009
Hero

NJ,
2018-03-29 16:52

@ Helmut
Posting: # 18616
Views: 1,820
 

 [Opinion] Should the 90% CI for GMR be required to encompass 1

So basically he's questioning the validity of FDA's 20% window on BE then...
John
bebac_fan
Junior

US,
2018-03-29 16:57

@ jag009
Posting: # 18617
Views: 1,829
 

 [Opinion] Should the 90% CI for GMR be required to encompass 1

Dear John

» So basically he's questioning the validity of FDA's 20% window on BE then...

Actually, I am questioning the validity of FDA's Swr scaled 10% window on BE for NTID.

If a GMR of 1.1 is clinically relevant (i.e. a test should be sensitive for this), and the NTID with a Swr of .22 will pass by ABE, this is a failure IMO.

Thanks,
BF
jag009
Hero

NJ,
2018-03-29 19:55

@ bebac_fan
Posting: # 18619
Views: 1,799
 

 [Opinion] Should the 90% CI for GMR be required to encompass 1

Hi,

» Actually, I am questioning the validity of FDA's Swr scaled 10% window on BE for NTID.
»
» If a GMR of 1.1 is clinically relevant (i.e. a test should be sensitive for this), and the NTID with a Swr of .22 will pass by ABE, this is a failure IMO.

Before we go further, does your hypothetical example pass the other two criteria stated in the NTI guidance?
bebac_fan
Junior

US,
2018-03-29 20:30

@ jag009
Posting: # 18620
Views: 1,797
 

 [Opinion] Should the 90% CI for GMR be required to encompass 1

» Before we go further, does your hypothetical example pass the other two criteria stated in the NTI guidance?

Yes, it would. See Helmut's post further up in the thread.

The point is, at Swr of .22, if you pass criteria 1, you generally pass criteria 2. Criteria 3 passes.

Thanks,
BF
jag009
Hero

NJ,
2018-03-29 21:22

@ bebac_fan
Posting: # 18621
Views: 1,791
 

 [Opinion] Should the 90% CI for GMR be required to encompass 1

If I recall (or I am imagining things), FDA published a paper about NTI drug BE assessment (Helmut, help! Am I hallucinating again?)

Anyhow, Have you looked at this FDA slide presentation before?

NTI

John
Helmut
Hero
avatar
Homepage
Vienna, Austria,
2018-03-30 01:33

@ jag009
Posting: # 18622
Views: 1,735
 

 Paper & Presentations

Hi John,

» If I recall (or I am imagining things), FDA published a paper about NTI drug BE assessment (Helmut, help! Am I hallucinating again?)

[image]Too much absinthe? I guess you mean this goody:

Yu LX, Jiang W, Zhang X, Lionberger R, Makhlouf F, Schuirmann DF, Muldowney L, Chen M-L, Davit B, Conner D, Woodcock J. Novel Bioequivalence Approach for Narrow Thera­peutic Index Drugs. Clin Pharmacol Ther. 2015;97(3):286–91. doi:10.1002/cpt.28.


» Anyhow, Have you looked at this FDA slide presentation before?
» NTI

Yep. There are others with more background information. Most simulations were performed in R – Donald told me in 2016 that he grew up with APL and finds R difficult… See also this post. The presentations are gone with the wind. Webarchive #1 (June 2017), #2 (July 2017). In #1 navigate to page 51 and in #2 to page 57.

Cheers,
Helmut Schütz
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Helmut
Hero
avatar
Homepage
Vienna, Austria,
2018-04-10 14:41

@ bebac_fan
Posting: # 18660
Views: 871
 

 Donald Schuirmann’s opinion

Hi BF,

see Donald Schuirmann’s presentation (starting at page 57). For the question whether the CI should 1 (and his opinion), navigate to page 93.

R-code to reproduce his findings presented on page 94:
library(PowerTOST)
# only 1e5 sim's for speed!
# (1) pure scaled (without ABE and s-ratio)
n        <- seq(12, 48, 12)
GMR.min  <- 0.92
swR      <- 0.05
GMR      <- unique(sort(c(seq(GMR.min, 1/GMR.min, length.out=35), 1)))
res1     <- data.frame(GMR=GMR)
pwr.name <- paste0("pwr.", n)
res1[pwr.name] <- NA
col      <- c("darkblue", "magenta", "darkgreen", "red")
pch      <- c(18, 15, 17, 16)
for (j in seq_along(GMR)) {
  for (k in seq_along(n)) {
    res1[j, pwr.name[k]] <- power.NTIDFDA(theta0=GMR[j], CV=se2CV(swR), n=n[k],
                                          details=TRUE)[["p(BE-sABEc)"]]
  }
}
print(res1, row.names=FALSE)
op <- par(no.readonly=TRUE)
par(mar=c(3, 4, 2, 0) + 0.1)
split.screen(figs=c(2, 1))
screen(1)
main <- paste0("swR=swT=", swR, "\n\'pure\' NTID RSABE (without ABE and s-ratio)")
for (j in seq_along(n)) {
  pwr <- res1[[paste0("pwr.", n[j])]]
  if (j == 1) {
    plot(GMR, pwr, type="n", log="x", ylim=c(0, 1), ylab="power", las=1,
         cex.main=0.9, main=main)
    abline(h=c(0.05, seq(0, 1, 0.2)), lty=2, col="grey50")
    abline(v=1, lty=2, col="grey50")
  }
  points(GMR, pwr, col=col[j], pch=pch[j], cex=1.15)
  lines(GMR, pwr, col=col[j], lwd=2)
}
legend("bottomright", legend=c(paste("n =", n)), col=col, pch=pch,
       pt.cex=1.15, lwd=2, bg="white")
# (2) NTID-RSABE (with ABE and s-ratio)
res2     <- data.frame(GMR=GMR)
pwr.name <- paste0("pwr.", n)
res2[pwr.name] <- NA
for (j in seq_along(GMR)) {
  for (k in seq_along(n)) {
    res2[j, pwr.name[k]] <- power.NTIDFDA(theta0=GMR[j], CV=se2CV(swR), n=n[k],
                                          details=TRUE)[["p(BE)"]]
  }
}
print(res2, row.names=FALSE)
screen(2)
main <- paste0("swR=swT=", swR, "\nNTID RSABE (with ABE and s-ratio)")
for (j in seq_along(n)) {
  pwr <- res2[[paste0("pwr.", n[j])]]
  if (j == 1) {
    plot(GMR, pwr, type="n", log="x", ylim=c(0, 1), ylab="power", las=1,
         cex.main=0.9, main=main)
    abline(h=c(0.05, seq(0, 1, 0.2)), lty=2, col="grey50")
    abline(v=1, lty=2, col="grey50")
  }
  points(GMR, pwr, col=col[j], pch=pch[j], cex=1.15)
  lines(GMR, pwr, col=col[j], lwd=2)
}
legend("bottomright", legend=c(paste("n =", n)), col=col, pch=pch,
       pt.cex=1.15, lwd=2, bg="white")
close.screen(all=TRUE)
par(op)


» The point is, at Swr of .22, if you pass criteria 1, you generally pass criteria 2. Criteria 3 passes.

Yep. Run the code with
GMR.min <- 100/112
swR     <- 0.22

Cheers,
Helmut Schütz
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