Bioequivalence and Bioavailability Forum

libaiyi ★ China, 2018-06-08 13:41 (2518 d 05:09 ago) Posting: # 18870 Views: 8,796	Calculate the BE limits for HVDPs based on EMA [RSABE / ABEL] Post reply
	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 Edit: Category changed; see also this post #1. [Helmut]

Shuanghe
★★

Spain,
2018-06-08 14:51
(2518 d 03:59 ago)

@ libaiyi
Posting: # 18872
Views: 7,693

Calculate the BE limits for HVDPs based on EMA

Post reply

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 CV_WR is between 30% and 50%, the lower and upper limit is EXP(-0.76*s_WR) and EXP(0.76*s_WR), respectively.
Relatioship between CV_WR and s_WR is described in EMA's guideline. you can check the formula there.

—
All the best,
Shuanghe

Helmut
★★★

Vienna, Austria,
2018-06-08 15:19
(2518 d 03:31 ago)

@ libaiyi
Posting: # 18873
Views: 7,808

(Expanded) BE limits, EMA-style

Post reply

Hi libaiyi,

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

The switching CV_wR is 30% and hence, the regulatory constant k should be $\log{(1.25)}/\sqrt{\log{(0.30^2+1)}} = 0.7601283\ldots $
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 CV_wR 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 77.23222 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

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 CV_wR ≤30%, and observes the upper cap of CV_wR 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!

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Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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libaiyi ★ China, 2018-06-11 09:21 (2515 d 09:28 ago) @ Helmut Posting: # 18881 Views: 7,446	(Expanded) BE limits, EMA-style Post reply
	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?

Helmut
★★★

Vienna, Austria,
2018-06-11 14:24
(2515 d 04:25 ago)

@ libaiyi
Posting: # 18882
Views: 7,623

CFDA: Yet another story?

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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.

Like the EMA (ABEL): SAS-code given in the Q&A-document. Proc GLM, not Proc Mixed.
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 (Y_T – Y_R)² – θs²_wR 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%.
Your story: Proc Mixed if the CFDA follows the FDA or Proc GLM if like the EMA.

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Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
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libaiyi ★ China, 2018-06-12 13:09 (2514 d 05:41 ago) @ Helmut Posting: # 18887 Views: 7,538	CFDA: Yet another story? Post reply
	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.

Helmut
★★★

Vienna, Austria,
2018-06-12 16:54
(2514 d 01:56 ago)

@ libaiyi
Posting: # 18889
Views: 7,647

CFDA: Draft guidance?

Post reply

Hi libaiyi,

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

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’).

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Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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Science Quotes

libaiyi ★ China, 2018-06-13 05:39 (2513 d 13:11 ago) @ Helmut Posting: # 18895 Views: 7,332	CFDA: Draft guidance? Post reply
	Thanks for you reply. Another question, how to write the null hypothesis and alternative hypothesis for BE based on FDA or EMA method?

Helmut
★★★

Vienna, Austria,
2018-06-13 13:39
(2513 d 05:11 ago)

@ libaiyi
Posting: # 18897
Views: 7,399

Hypotheses generated “in face of the data”

Post reply

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 s_wR (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 frameworks^a,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.

Endrényi L, Tóthfalusi L. Regulatory Conditions for the Determination of Bioequivalence of Highly Variable Drugs.
J Pharm Pharmaceut Sci. 2009;12(1):138–49. free resource.
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.
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.
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. View-only.
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.
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.
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.

RSABE
- If s_wR ≥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 s_wR <0.294 perform ABE with conventional limits (mixed effects model for all designs).
ABEL
- If CV_wR >30% expand the BE-limits based on s_wR. If CV_wR >50% expand the limits based on $s_{wr}^{*}=\sqrt{log{(0.50^2+1)}}$. 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 CV_wR ≤30% perform ABE with conventional limits (fixed effects model for all designs).

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Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

libaiyi ★ China, 2018-06-14 05:46 (2512 d 13:04 ago) @ Helmut Posting: # 18903 Views: 7,297	Hypotheses generated “in face of the data” Post reply
	The replies and the materials enlighten me a lot. Thanks for your patience.

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

Calculate the BE limits for HVDPs based on EMA

(Expanded) BE limits, EMA-style

(Expanded) BE limits, EMA-style

CFDA: Yet another story?

CFDA: Yet another story?

CFDA: Draft guidance?

CFDA: Draft guidance?

Hypotheses generated “in face of the data”

Hypotheses generated “in face of the data”