Bioequivalence and Bioavailability Forum • Reference scaled approach for HVD

KR
★

India,
2009-02-07 12:29
(5918 d 16:06 ago)

Posting: # 3197
Views: 18,865

Reference scaled approach for HVD [RSABE / ABEL]

Dear all,
I have some confusion regarding statistical analysis of highly variable drug like lansoprazole which are mentioned below:

Sample size: how can we calculate sample size as we do not have any in-house study data of partial/full replicate data? Can anyone suggest me the procedure for sample size for highly variable drug (HVD) using reference scale approach. Can we use the data of two way crossover for sample size calculation in such case?
Bioequivalence criteria: How and when to decide bioequivalence limits of HVD using reference scale for a new study? i.e after statistical analysis of the study or should be pre-defined in the protocol. How to mention the criteria in the protocol?
Statistical analysis: How to do statistical analysis using reference scale?

Waiting for your valuable reply,

Thanks and regards,

KR

Edit: Category changed. Maybe you consider using a different name in your signature; 'Dear KR' in a reply would sound strange to me.. ;-)

[Helmut]

Helmut
★★★

Vienna, Austria,
2009-02-07 16:58
(5918 d 11:37 ago)

@ KR
Posting: # 3202
Views: 17,072

Reference scaled approach for HVD

Post reply

Dear KR!

❝ statistical analysis of highly variable drug like lansoprazole

I guess you are referring to FDA's drafted product-specific guideline from Oct 2008.
For details of the design and evaluation see the guideline itself and the quoted paper:
Haidar SH, Davit B, Chen M-L, Conner D, Lee LM, Li QH, Lionberger R, Makhlouf F, Patel D, Schuirmann DJ, and LX Yu
Bioequivalence Approaches for Highly Variable Drugs and Drug Products
Pharmaceutical Research 25/1, 237-241 (2008, DOI: 10.1007/s11095-007-9434-x)
free online resource

❝ 1. Sample size: how can we calculate sample size as we do not have any in-house study data of partial/full replicate data? Can anyone suggest me the procedure for sample size for highly variable drug (HVD) using reference scale approach.

See [msg]this post[/msg] from David Dubins. Essentially in the proposed RSABE procedure it’s not necessary to perfom studies in more than 34 subjects in a 3-period replicate design regardless the variability.

❝ Can we use the data of two way crossover for sample size calculation in such case?

No, these studies give you just a hint of high variability. But you may justify RSABE by such studies. If FDA is of concern, two guidelines have been published so far – for other drugs/drug products you should contact FDA's review staff beforehand. In the EU RSABE is not acceptable anyhow.

❝ 2. Bioequivalence criteria: How and when to decide bioequivalence limits of HVD using reference scale for a new study? i.e after statistical analysis of the study or should be pre-defined in the protocol. How to mention the criteria in the protocol?

It's the aim of RSABE to scale the acceptance range according to the intra-subject variability of the reference (therefore, you have to use a replicated design). Since the acceptance limits are scaled based on the variability obtained in the actual study, you cannot set them beforehand.

❝ 3. Statistical analysis: How to do statistical analysis using reference scale?

First you have to have suitable software (SAS, WinNonlin,…) which will give you CV_intra of the reference. Then follow Method C2 given in Haidar et al. to calculate to scaled BE limits. You may download David's FARTSSIE.xls, activate Macros, navigate to the Scaled BE - HVD-tab and enjoy. But remember: FARTSSIE.xls comes “as-is” (Excel is not a statistical software); therefore you should set up the method in your preferred software and validate it there.

Procedure: if you have sigma²_WR (the intra-subject variance of the reference formulation) already, fine; if not, calculate it from CV_intra,R:
sigma²_WR = ln(CV_intra,R²+1)
FDA's goalpost for scaling (sigma_W0) is 0.2936; i.e., the limit corresponds to 30% CV (that's the commonly accepted limit for a HVDP):
0.2936 = sqrt(ln(0.3²+1)).
Next calculate the scaling parameter theta_s:
theta_s = ln(1.25)²/sigma²_W0
The scaled BE-limits in ln-scale are:
±sqrt(theta_s×sigma²_WR)

Your CI should lie within the scaled BE limits and the point estimate - in FDA-speak the GMR (geometric mean ratio) - should lie within 0.80-1.25.

For example:

CV_intra,R| BE-limits (lin)

--------+-----------------

 0.3924 | 0.7500 - 1.3333

 0.4    | 0.7462 - 1.3402

 0.4964 | 0.7000 - 1.4286

 0.5    | 0.6984 - 1.4319

 0.6    | 0.6561 - 1.5242

 0.7    | 0.6188 - 1.6160

 0.8    | 0.5859 - 1.7067

 0.9    | 0.5569 - 1.7958

 1      | 0.5311 - 1.8828

 1.1    | 0.5082 - 1.9676

 1.1390 | 0.5000 - 2.0000

—
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

d_labes
★★★

Berlin, Germany,
2009-02-09 12:26
(5916 d 16:09 ago)

@ Helmut
Posting: # 3212
Views: 16,083

Reference scaled approach for HVD

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Dear Helmut! Dear All!

❝ ❝ 3. Statistical analysis: How to do [...]

❝

❝ First you have to have suitable software (SAS, WinNonlin,...) which will give you CV_intra of the reference. Then follow Method C2 given in Haidar et al. to calculate to scaled BE limits [...]

❝ [...]

❝ Procedure: if you have sigma²_WR [...]

Is it really that simple? :ponder:

I have read up to now from Haidar et. al.:
"[...] Furthermore,
theta=(ln Delta)²/sigma²_W0
where Delta is 1.25, the usual average BE upper limit for the untransformed test/reference ratio of geometric means, and sigma_W0=0.25. [...] A 95% upper confidence bound for (µ_T-µ_R)²/sigma²_WR determined in a BE study must be < theta, or equivalently, a 95% upper confidence bound for (µ_T-µ_R)²-theta*sigma²_WR must be <0. [...]".
(emphasis by me)

Thus I think the statistical method must calculate a confidence interval, recommended is that for the linearized SABE criterion (last in the excerpt above). This is so because we have only estimates of (µ_T-µ_R) and sigma²_WR with a certain variability.

Dave Dubins has given this above quote in his Fartssie.xls also, but I can not find a confidence interval calculation there in.

—
Regards,

Detlew

ddubins
☆

Toronto,
2009-03-12 04:34
(5886 d 00:01 ago)

@ d_labes
Posting: # 3353
Views: 16,492

Reference scaled approach for HVD

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Hi D. Labes, Helmut, and KR.

I'm far more of a PK scientist than a statistician. When I first read the FDA paper on scaled reference limits, I did simple algebra so I wouldn't have to alter my SAS program in ways that would make my head spin. The FDA asked for:

a 95% upper bound for (µT - µR)² / (sig_wr)² < theta

or

a 95% upper bound for (µT - µR)² / (sig_wr)² - theta < 0

The FDA wants you to use this formula to calculate theta:

theta = [ln(1.25)]² / sig_w₀², where sig_w₀ = 0.25.
theta = 0.796689

Theta is a constant, and sig_wr is also a constant once you calculate what it is.

For convenience, I re-arranged the 95% upper bound formula to:

a 95% upper bound for (µT - µR) < sqrt[theta × (sig_wr)²]
Now you can use your PROC MIXED program on the ln-transformed data as is without the headache. All you need to do is change "alpha = 0.1" to "alpha = 0.05" in the ESTIMATE statement to get SAS to spit out a 95% confidence interval instead of the typical 90% confidence interval. Here is my PROC MIXED code, nothing proprietary about this:

proc mixed data=ABEexample1;

  class Subject Sequence Period Treatment;

  model logcmax = Sequence Period Treatment / DDFM=SATTERTH;

  random Treatment/TYPE=FA0(2) SUB=Subject G;

  repeated/Group=Treatment SUB=Subject;

  lsmeans Treatment / pdiff;

  estimate 'Average Bioequivalence for log(cmax)' Treatment 1 -1/CL alpha=0.05;

  ods output estimates=se_lncmax;

  make "CovParms" out=cov_lncmax;

  ods output "Least Squares Means"=LSM_lncmax;

run;

If you examine the "CovParms" output you'll see the mean square residual of the reference in there (sig_wr²).

However, since the FDA isn't asking for the 95%CI on (µT-µR), I'm assuming you can calculate it back to what they want to see, or you can just get a biostatistician to write you a proper program rather than use a work-around.

My program (FARTSSIE) does calculate theta, but that's not what I report in big green numbers - I report the limits that would have been imposed on (uT-uR). In retrospect, looking at what the FDA wants to see, this isn't terrifically helpful for people. I can't exactly get it to calculate your adjusted 95% confidence interval though, since Excel can't perform PROC MIXED.

Does this make any sense? Has anyone else performed this analysis more elegantly? I'd be interested to see some SAS code from someone who's done the job properly and knows what they're doing.

Best, -Dave

—
David Dubins, Ph.D., B.A.Sc.
Associate Professor, Teaching Stream
Director, Pharmaceutical Chemistry Specialist Program
Leslie Dan Faculty of Pharmacy
University of Toronto

144 College Street (room PB802), Toronto, ON M5S 3M2
Tel. +1 416-946-5303; FAX: +1 416 978-8511

d_labes
★★★

Berlin, Germany,
2009-03-12 15:55
(5885 d 12:40 ago)

@ ddubins
Posting: # 3354
Views: 16,255

Estimated knowledge

Post reply

Dear Dave,

❝ [...] The FDA asked for: [...]

❝

❝ a 95% upper bound for (uT - uR)² / (sig_wr)² - theta < 0

❝

❝ The FDA wants you to use this formula to calculate theta:

❝

❝ theta = [ln(1.25)]² / sig_w₀², where sig_w₀ = 0.25.

❝ theta = 0.796689

❝

❝ Theta is a constant, and sig_wr is also a constant once you calculate what it is.

(emphasis by me)

This emphasized sentence was the reason why I wondered about Helmut's suggestion.

We do not know sigma_WR, but have an estimate of it from our data!
From Proc MIXED or Methods of moments or whatever. This estimate has accompanying an uncertainty which must IMHO be taken into account in the calculation of the 95% upper bound for the scaled ABE criterion.
BTW the linearized criterion is stated as
(µ_T - µ_R)² - theta×sigma²_WR < 0
(lineal linear except the super- and subscripts :cool:

)

I recently found a paper from Tothfalusi et. al.¹⁾ in which the details of the calculations of the upper bound (bases on Hyslop's method invented for the IBE criterion, I think) are given to some extent.

Let me try to excerpt it:
"[...] The two terms of the criterion can be estimated by their respective expected values:

   E_m=(m_T-m_R)²

   E_w= Theta*s²_WR

where m_T and m_R are the observed overall means of the test and reference formulations, respectively and s²_WR the estimated within-subject variance for the reference product.

The confidence limits for the two terms in the rearranged BE criterion are:

   C_m=[Abs(m_T-m_R)+t(1-alpha,N-2)*SE]²

   C_w= Theta*(N-2)s_WR²/chi²(alpha,N-2)

Here as already noted, SE =(s²_Int/N)^1/2.
(this is for 4 period design as indicated in the heading not excerpted D.L.)
t and chisq are the respective tabulated statistics [...]
(here begins the Hyslop method I think, D.L.)
The squared length of the onfidence intervals from their respective means are:

   L_m=(C_m-E_m)²

   L_w=(C_w-E_w)²

Finally the confidence limit (CL) for the rearranged BE criterion is:
CL=E_m-E_w+(L_m+L_w)^½
[...]" (EoE end of excerpt)

Seems easy enough to implement (of course in R ;-)

) . Provided it is that easy.
My only doubt here is that I don't know, what they really mean with s²_Int in their formula for replicate design.
But this does not matter. Let your software calculate the SE for µ_T-µ_R for your design and use it in C_m.

¹⁾ Tothfalusi, L., L. Endrenyi, K.K. Midha, M.J. Rawson and J.W. Hubbard
Evaluation of the bioequivalence of highly-variable Drug products
Pharm. Res. Vol.18, No. 6 (2001), 728-733

Hope this helps someone.
I myself haven't used this up to now.
Anybody out there who has an example or knows one, preferably elaborated?

❝ [...] I'd be interested to see some SAS code from someone who's done the job properly and knows what they're doing.

(emphasis by me)
Bible, New testament, Luke 23:34

—
Regards,

Detlew

sdu
☆

2010-01-26 22:21
(5565 d 06:14 ago)

@ d_labes
Posting: # 4649
Views: 14,946

Estimated knowledge

Post reply

Thank you for the nice summary of Toutfalusi et al.'s paper
I also read the Hyslop et al article on "A small sample confidence interval approach to assess individual bioequivalence" (Statistic in Med 2000, 19, pp2885-2897).
I have few questions

How do you calculate the s_int? Based on the Hyslop's paper the subject by formulation interaction is calculated using sig_D, sig_wt, and sig_wr. Is this the way to calculate based on Hyslop et al. paper?
If above statement is correct do we assume sig_wt is equal to sig_wr, as stated by Ekbohm and Melander et al. in "The subject-by-formulation interaction as a criterion for interchangeability of drugs". (Biometrics 1989; 45:1249-1254).
It was my understanding that Reference scaled Average BE is the special case of the IBE where we assume sig_D is negligible and the sig_wt is equal or smaller than the sig_wr. Is this correct?

In advance thank you for your input on the above questions
Kindly
sdu

d_labes
★★★

Berlin, Germany,
2010-01-27 15:00
(5564 d 13:35 ago)

@ sdu
Posting: # 4651
Views: 14,978

SABE issues

Post reply

Dear sdu!

❝ I have few questions

You are welcome. But eventually I'm not the one to answer all your questions. But lets try.

Ad 1.

❝ How do you calculate the s_int?

As I said in my post above, I don't really understand what is meant with that s_int. But this may not be necessary to know because what we really need is SE, the standard error of the (log) difference. Each statistical package I know off will give this. Then you can proceed with the above shortly outlined Al Gore rhythm.
See here for a recent comprehensive paper on SABE issues. Maybe it helps (at least in producing new questions ;-)

).

Ad 2.

❝ If above statement is correct do we assume sig_wt is equal to sig_wr ...

I would not suggest this. As far as I understand the FDA, the assumption of equal variabilities between Test and Reference should be avoided if possible (even in the case of parallel group studies!).
I must confess that I don't know the Ekbohm and Melander paper in detail. But if they talk about subject-by-formulation interaction they definitely talk about different variabilities between Test and Reference, at least between subject variabilities.

Moreover a separate within variability for the Test formulation is not identifiable in the design suggested by Haidar et. al. for evaluating reference scaled average, namely a design with the sequences RTR, RRT and TRR, the so called partial replicate design.
See this thread.

Ad 3.

❝ It was my understanding that Reference scaled Average BE is the special case of the IBE where we assume sig_D is negligible and the ...

This is also my understanding ...

❝ ... sig_wt is equal or smaller than the sig_wr.

... but the second condition is not necessarily implied.
May be the sig_wt comes out as greater then sig_wr in a replicate design which allows for estimates of both.

Since you are posting from USA (at least the forum system tells it :yes:

), can you eventually contact FDA's people dealing with SABE and enlighten us how they do all the stuff?

—
Regards,

Detlew

BE
☆

2009-03-19 13:30
(5878 d 15:05 ago)

@ Helmut
Posting: # 3380
Views: 15,717

Reference scaled approach for HVD

Post reply

Dear HS,

❝ In the EU RSABE is not acceptable anyhow.

Please let me know when you state that RSABE approach is not accepted by EU, are you referring to any guideline. If such is the case, how you do recommend to conduct BE studies for HVD, especially to claim wider limits. I hope you agree that 2 way crossover is not the correct design the depict the innovator variability.

Best Regards,

BE

Edit: Quote restored. [Helmut]

MGR ★ India, 2009-04-01 09:59 (5865 d 19:36 ago) @ KR Posting: # 3428 Views: 15,750	Reference scaled approach for HVD Post reply
	Dear KR, The following site may help to get some information on this topic. http://biostatisticsinbe.blogspot.com/2009/01/scaled-average-concept-in.html Thank you, Edit: Next time please a permalink to your blog. [Helmut] — Regards, MGR