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libaiyi
Junior

China,
2018-06-08 11:41

Posting: # 18870
Views: 1,176
 

 Calculate the BE limits for HVDPs based on EMA [RSABE / ABEL]

Hi,

I am so confused about how to calculate the suitable BE limits for HVDPs based on EMA criterion since the range changes all the time.

When we get a CVwr, how to get the BE limits?

Thanks in advance :lol3:


Edit: Category changed; see also this post #1. [Helmut]
Shuanghe
Regular

Spain,
2018-06-08 12:51

@ libaiyi
Posting: # 18872
Views: 1,051
 

 Calculate the BE limits for HVDPs based on EMA

Hi,

» I am so confused about how to calculate the suitable BE limits for HVDPs based on EMA criterion since the range changes all the time.
»
» When we get a CVwr, how to get the BE limits?

The easiest way is using R. Some nice guy in this forum :-D wrote a package so basically
library(powerTOST)
scABEL(CV, regulator)

will give you whatever you want, where CV is the CV of reference. And it's not limited to EMA. you can use it for calculations according to US FDA's and Canadian's guidance too (regulator="FDA" or "HC"). e.g.

scABEL(0.5, regulator="EMA") will give you
    lower     upper
0.6983678 1.4319102


and scABEL(0.4, regulator="EMA") will give
    lower     upper
0.746177 1.340165


If you like to reinventing the wheel then it is also pretty straightforward to do so. If your CVWR is between 30% and 50%, the lower and upper limit is EXP(-0.76*sWR) and EXP(0.76*sWR), respectively.
Relatioship between CVWR and sWR is described in EMA's guideline. you can check the formula there.

All the best,
Shuanghe
Helmut
Hero
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Vienna, Austria,
2018-06-08 13:19

@ libaiyi
Posting: # 18873
Views: 1,060
 

 (Expanded) BE limits, EMA-style

Hi libaiyi,

» When we get a CVwr, how to get the BE limits?

The switching CVwR is 30% and hence, the regulatory constant k should be log(1.25)/√log(0.30²+1) or 0.7601283…
In R (CVs and BE limits in %):

CVwR <- seq(0.25, 0.55, 0.05)
swR  <- sqrt(log(CVwR^2+1))
k    <- log(1.25)/sqrt(log(0.3^2+1))
EL1  <- data.frame(CVwR=100*CVwR, swR=swR, L=100*exp(-k*swR), U=100*exp(+k*swR))
EL1$L[EL1$CV <= 30] <-  80 # conventional
EL1$U[EL1$CV <= 30] <- 125 # BE limits
EL1$L[EL1$CV >= 50] <- 100*exp(-k*sqrt(log(0.5^2+1))) # upper scaling
EL1$U[EL1$CV >= 50] <- 100*exp(+k*sqrt(log(0.5^2+1))) # cap at CV 50%
print(EL1, row.names=FALSE)

CVwR       swR        L        U
  25 0.2462207 80.00000 125.0000
  30 0.2935604 80.00000 125.0000
  35 0.3399387 77.22885 129.4853
  40 0.3852532 74.61401 134.0231
  45 0.4294214 72.15055 138.5991
  50 0.4723807 69.83255 143.1997
  55 0.5140870 69.83255 143.1997


In its eternal wisdom (preferring “nice” numbers) the EMA demands a rounded k 0.76 (which implies a switching CVwR of 30.0053%).*

EL2 <- data.frame(CVwR=100*CVwR, swR=swR, L=100*exp(-0.76*swR), U=100*exp(+0.76*swR))
EL2$L[EL2$CV <= 30] <-  80
EL2$U[EL2$CV <= 30] <- 125
EL2$L[EL2$CV >= 50] <- 100*exp(-0.76*sqrt(log(0.5^2+1)))
EL2$U[EL2$CV >= 50] <- 100*exp(+0.76*sqrt(log(0.5^2+1)))
print(EL2, row.names=FALSE)

CVwR       swR        L        U
  25 0.2462207 80.00000 125.0000
  30 0.2935604 80.00000 125.0000
  35 0.3399387 77.2
3222 129.4796
  40 0.3852532 74.61770 134.0165
  45 0.4294214 72.15452 138.5915
  50 0.4723807 69.83678 143.1910
  55 0.5140870 69.83678 143.1910


More convenient by the function scABEL() of the R-package PowerTOST (by applying the default argument regulator="EMA"). The function then uses k 0.76, returns the conventional ABE limits if CVwR ≤30%, and observes the upper cap of CVwR 50%:

library(PowerTOST)
CVwR <- seq(0.25, 0.55, 0.05)
EL3  <- data.frame(CVwR=100*CVwR, swR=CV2se(CVwR),
                   L=100*scABEL(CV=CVwR)[, "lower"],
                   U=100*scABEL(CV=CVwR)[, "upper"])
print(EL3, row.names=FALSE)

CVwR       swR        L        U
  25 0.2462207 80.00000 125.0000
  30 0.2935604 80.00000 125.0000
  35 0.3399387 77.23222 129.4796
  40 0.3852532 74.61770 134.0165
  45 0.4294214 72.15452 138.5915
  50 0.4723807 69.83678 143.1910
  55 0.5140870 69.83678 143.1910


Don’t apply double rounding! Round the 90% CI in percent to two decimal places but compare it to the expanded limits in full precision.


  • Karalis V, Symillides, Macheras P. On the leveling-off properties of the new bioequivalence limits for highly variable drugs of the EMA guideline. Eur J Pharm Sci. 2011;44:497–505. doi:10.1016/j.ejps.2011.09.008.

Edit: Hey Shuanghe, you were faster!

Cheers,
Helmut Schütz
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libaiyi
Junior

China,
2018-06-11 07:21

@ Helmut
Posting: # 18881
Views: 903
 

 (Expanded) BE limits, EMA-style

Hi,

I want to know how to figure out that whether the results are bioequivalence?

According to CFDA (China Food and Drug Administration) guidelines, when CVwR of Cmax is larger than 0.3, BE limits are fixed at (69.83, 143.19). Can we use the results from Mixed Model by SAS directly to determine if it falls between the limits or not? :-D:-D:-D
Helmut
Hero
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Homepage
Vienna, Austria,
2018-06-11 12:24

@ libaiyi
Posting: # 18882
Views: 870
 

 CFDA: Yet another story?

Hi libaiyi,

» I want to know how to figure out that whether the results are bioequivalence?
  • If the 90% CI of the GMR lies entirely within the (expanded) BE limits
    bioequivalence demonstrated with p ≤0.05.
  • If at least one of the confidence limits is outside the (expanded) BE limits
    indecisive (BE not demonstrated due to lacking power; may be possible in another study with a higher sample size).
  • If the 90% CI of the GMR lies entirely outside the (expanded) BE limits (i.e., lower CL > upper limit or upper CL < lower limit)
    bioinequivalence proven with p ≤0.05. Don’t perform another study: Reformulate.

» According to CFDA (China Food and Drug Administration) guidelines, when CVwR of Cmax is larger than 0.3, BE limits are fixed at (69.83, 143.19).

Weird – do you have a reference? Feel free to post in Chinese; we have some native speakers here. ;-)
This would add another story to the two we already have (see this thread in all of its beauty). I have some doubts whether that is really what the CFDA wants. Would be a step back to what was used in some European countries 25+ years ago.

» Can we use the results from Mixed Model by SAS directly to determine if it falls between the limits or not?

First you have to clarify which method for HVD(P)s the CFDA accepts.
  1. Like the EMA (ABEL): SAS-code given in the Q&A-document. Proc GLM, not Proc Mixed.
  2. Like the FDA (RSABE): SAS-code given in the progesterone guidance. Decision not based on the “implied” scaled limits but the upper 95% confidence bound of (YT – YR)2 – θs²wR must be ≤0. Proc Mixed for full replicate studies (TRTR|RTRT, TTRR|RRTT, or TRT|RTR) and Proc GLM for partial replicate studies (TRR|RTR|RRT).
    If swR <0.294 (conventional ABE) Proc Mixed and BE if 90% CI within 80.00–125.00%.
  3. Your story: Proc Mixed if the CFDA follows the FDA or Proc GLM if like the EMA.

Cheers,
Helmut Schütz
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libaiyi
Junior

China,
2018-06-12 11:09

@ Helmut
Posting: # 18887
Views: 814
 

 CFDA: Yet another story?

Hi Helmut,

thanks for your help.

CFDA has relased the draft guidance for HVBE, which follows FDA method (RSABE).

I still have a question about EMA method. Do you mean if we follow EMA's guidance, the ABEL should be used rather than RSABE, please give me more advise.

thanks in advance. :-D:-D:-D
Helmut
Hero
avatar
Homepage
Vienna, Austria,
2018-06-12 14:54

@ libaiyi
Posting: # 18889
Views: 814
 

 CFDA: Draft guidance?

Hi libaiyi,

» CFDA has relased the draft guidance for HVBE, which follows FDA method (RSABE).

<nitpick>

There is nothing like “highly variable bioequivalence”. Either the drug itself is highly variable (if the clearance is HV already seen after an iv dose or after an oral solution the absorption is HV: HVD) or a drug product is HV: HVDP. Since it not always known whether the drug itself is HV, when talking about formulations people like me leave the question open and prefer the term HVD(P).
Example diclofenac: iv and a solution show pretty low CVs (<15%). Hence, it is not an HVD. Suspensions, IR, and rectal products are not HVDPs (CVs 20–25%). On the other hand, gastric resistant formulations are borderline HVDPs (CVs 30–40%). Topical products are definitely HVDPs (crazy CVs).

</nitpick>

I see. Is this link correct? Interesting the two attachments (#1, #2).
When it comes to replicate designs only the lousy partial replicate (TRR|RTR|RRT) and one full replicate (TRTR|RTRT) given in Tables 2&3. Never heard about the 3-period full replicate (TRT|RTR) and another 4-period full replicate (TTRR|RRTT)? Although not given in the tables, 4-sequence 4-period full replicates are also mentioned (TRTR|RTRT|TRRT|RTTR or TRRT|RTTR|TTRR|RRTT). Forget it; confounded effects.
From #2 it is clear that the FDA’s RSABE was 1:1 copied.

» I still have a question about EMA method. Do you mean if we follow EMA's guidance, the ABEL should be used rather than RSABE, …

Correct.

» … please give me more advise.

As I wrote previously, SAS-code is given in the EMA’s Q&A-document. The EMA prefers a fixed effects model (‘Method A’).

Cheers,
Helmut Schütz
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libaiyi
Junior

China,
2018-06-13 03:39

@ Helmut
Posting: # 18895
Views: 761
 

 CFDA: Draft guidance?

Thanks for you reply.

Another question,
how to write the null hypothesis and alternative hypothesis for BE based on FDA or EMA method?
Helmut
Hero
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Homepage
Vienna, Austria,
2018-06-13 11:39

@ libaiyi
Posting: # 18897
Views: 752
 

 Hypotheses generated “in face of the data”

Hi libaiyi,

» how to write the null hypothesis and alternative hypothesis for BE based on FDA or EMA method?

That's a legitimate question. May sound strange but the hypotheses don’t exist until we have estimated swR (the extent of scaling in RSABE and the expanded limits in ABEL are random variables and not fixed like in ABE). Hence, both hypotheses are generated “in face of the data” which may lead to inflation of the type I error.1–7

RSABE and ABEL are frameworksa,b where one cannot know beforehand which “path” to follow (see here and there). One can only specify the method and its conditions intended to follow in the protocol.


  1. Endrényi L, Tóthfalusi L. Regulatory Conditions for the Determination of Bio­equivalence of Highly Variable Drugs.
    J Pharm Pharmaceut Sci. 2009;12(1):138–49. [image] free resource.
  2. Wonnemann M, Frömke C, Koch A. Inflation of the Type I Error: Investigations on Regulatory Recommendations for Bioequivalence of Highly Variable Drugs.
    Pharm Res. 2015;32(1):135–43. doi:10.1007/s11095-014-1450-z.
  3. Muñoz J, Alcaide D, Ocaña J. Consumer's risk in the EMA and FDA regulatory approaches for bioequivalence in highly variable drugs.
    Stat Med. 2016;35(12):1933–43. doi:10.1002/sim.6834.
  4. Labes D, Schütz H. Inflation of Type I Error in the Evaluation of Scaled Average Bio­equivalence, and a Method for its Control.
    Pharm Res. 2016;33(11):2805–14. doi:10.1007/s11095-016-2006-1. [image] view-only.
  5. Tóthfalusi L, Endrényi L. Algorithms for evaluating reference scaled average bio­equivalence: Power, bias, and consumer risk.
    Stat Med. 2017;36(27):4378–90. doi:10.1002/sim.7440.
  6. Molins E., Cobo E., Ocaña J. Two-stage designs versus European scaled average designs in bioequivalence studies for highly variable drugs: Which to choose?
    Stat Med. 2017;36(30):4777–88. doi:10.1002/sim.7452.
  7. Knahl SIE, Lang B, Fleischer F, Kieser M. A comparison of group sequential and fixed sample size designs for bioequivalence trials with highly variable drugs.
    Eur J Clin Pharmacol. 2018;74(5):549–59. doi:10.1007/s00228-018-2415-7.

  1. RSABE
    • If swR ≥0.294 assess the upper 95% CL of the linearized criterion (mixed effects model for full replicate designs, fixed effects model for partial replicate designs).
      • If ≤0, the GMR has to be within 80.00–125%.
    • If swR <0.294 perform ABE with conventional limits (mixed effects model for all designs).
  2. ABEL
    • If CVwR >30% expand the BE-limits based on swR. If CVwR >50% expand the limits based on log(0.5²+1). Fixed effects model for all designs.
      • If the 90% CI lies entirely within the expanded limits, the GMR has to be within 80.00–125%.
    • If CVwR ≤30% perform ABE with conventional limits (fixed effects model for all designs).

Cheers,
Helmut Schütz
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The quality of responses received is directly proportional to the quality of the question asked. ☼
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libaiyi
Junior

China,
2018-06-14 03:46

@ Helmut
Posting: # 18903
Views: 692
 

 Hypotheses generated “in face of the data”

The replies and the materials enlighten me a lot.
Thanks for your patience. :-D:-D:-D
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