# Bioequivalence and Bioavailability Forum 05:27 CEST

sri
Junior

2009-07-09 13:01

Posting: # 3945
Views: 3,106

## Regarding US FDA guidelines [Bioanalytics]

Dear all,
Please clarify me the below sentense which is present in 'Guidance for Industry Bioanalytical Method Validation'.

The calibration (standard) curve should cover the expected unknown sample concentration range in addition to a calibrator sample at lower limit of quantification.

Regards,
Sri
Helmut
Hero

Vienna, Austria,
2009-07-09 13:48

@ sri
Posting: # 3946
Views: 2,735

## Calibration curve issues

Dear Sri!

» The calibration (standard) curve should cover the expected unknown sample concentration range in addition to a calibrator sample at lower limit of quantification.

In method development you should target the calibration range based on the lowest and highest concentrations expected in the study.
The LLOQ should be chosen in such a way that you are able to reliably describe the plasma profile. Reliable in this sense means that you are able to estimate the apparent elimination and (in most regulations) AUCt ≥80% AUC.
The ULOQ should be chosen based on the expected Cmax in the majority of subjects.
The guidance suggests six to eight calibrators for a linear function (probably more for nonlinear functions). Although linear regression theory calls for equidistant points, in bioanalytics most (all?) people opt for a geometric progression of calibrators in order to
• reduce the variability at the lower range and
• deal with the multiplicative error due to serial dilutions.
You may use following formula as a starting point:

`Ci = Ci-1 × (Cn/C1)1/(n-1)`

where

`i` index of the respective calibrator (2, 3, …, `n`), `n` number of calibrators, `Ci` calculated calibrator at `i`, `Ci-1` previous calibrator, `C1` lowest calibrator (LLOQ), and `Cn` highest calibrator (ULOQ).

Example: LLOQ 10, ULOQ 500, n=6–8```  6    7    8 -------------  10   10   10  22   19   17  48   37   31 105   71   53 229  136   94 500  261  164      500  286           500```
Now you have to adjust these values for practicability (while keeping the LLOQ and ULOQ fixed).

Cheers,
Helmut Schütz

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ElMaestro
Hero

Denmark,
2009-07-09 18:38

@ Helmut
Posting: # 3947
Views: 2,674

## Calibration curve issues

Hi HS,

» blah blah starting point:

`Ci= Ci-1 (Cn/C1)1/(n-1)`

Je vous en prie, could you give a reference or explain where it comes from?
And how do weights fit (sorry, couldn't find better word) into the use of this approach?

Many thanks.
EM.
Helmut
Hero

Vienna, Austria,
2009-07-09 19:24

@ ElMaestro
Posting: # 3948
Views: 2,705

## Weighing

Hi ElMaestro!

» Je vous en prie, could you give a reference …

Malheureusement non!
I guess, you won’t accept my brain as a proper reference.

» … or explain where it comes from?

Just walk downstairs to the bioanalytical department and ask what they do. Just my two cents that they use some kind of logarithmic spacing for their calibrators if a wide range of concentrations is covered.

» And how do weights fit (sorry, couldn't find better word) into the use of this approach?

No, weights are the correct term. Theoretically weights should be set to the inverse of the variance. If only duplicates are used this doesn’t make sense. Actually the guidance allows single calibrators as well. In bioanalytics a commonly applied method is weighing not by w=1/σ2 but by w=1/y2 (or w=1/x2). In many cases the logarithmic spacing efficiently “handles” the higher variability in the lower range, so that no weighing must be used. However, the chosen weighing scheme has to be justified by looking at back-calculated concentrations (accuracy and precision, both for the CC and QCs). I never came across a situation where somebody asked for a justification of the location of calibrators.

Scientifically speaking it’s all rubbish anyway. The best method would be to run a (set of) calibration curve(s) with at least six replicates at each concentration in order to obtain proper estimates of the variance. Next establish an empiric relationship between concentration and variance – generally a second order polynomial does the job very well (yes, there are references out there). Once you have established the weighing function in validation, you may use this function in day-to-day analyses without fiddling around with w=1/y2 or the like. But that’s another story.

Cheers,
Helmut Schütz

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ElMaestro
Hero

Denmark,
2009-07-09 20:06

@ Helmut
Posting: # 3949
Views: 2,625

## Weighing

Dear HS,

thanks, but I think I formulated myself wrongly; I agree with almost everything you say but what I meant was something else. I will try to "reformulate" (that's a forbidden word otherwise!):

The weighting scheme I encounter now and then is the 1/x or 1/x2. Lets for the time being forget the 1/y or 1/y2 (which deserves discussion in another thread).
As you point out the choice of weights has to do with variabilities, if the variability goes up as x increases then we weight accordingly in order to make sure that the points corresponding to high x values are not given the same priority as the numbers corresponding to low x values. But we could in theory achieve the same by having "less points at high x-values and more points at low x-values" and then use no weights. Implementing the equation you have given above would correspond pretty well to that concept. Therefore, my intuition tells me that your equation is intended for a situation with no weights and where the variability is not constant.

Best regards
EM.
Helmut
Hero

Vienna, Austria,
2009-07-09 21:00

@ ElMaestro
Posting: # 3950
Views: 2,738

## Weighing

Dear ElMaestro!

» I will try to "reformulate" (that's a forbidden word otherwise!)

» The weighting scheme I encounter now and then is the 1/x or 1/x2. Lets for the time being forget the 1/y or 1/y2 (which deserves discussion in another thread).

Yes!

» […] the choice of weights has to do with variabilities […]
» Therefore, my intuition tells me that your equation is intended for a situation with no weights and where the variability is not constant.

Your intuition essentially told you the right thing. In bioanalytics variance is never constant. When weighing was not possible due to computational limitations (the famous TI-59 and HP-41 were top instruments then) analysts went for logarithmic spacing. To be honest I started with eye-ball regression by means of graph paper and a transparent ruler.
Even today people are disappointed that weighted regression is not available in M\$-Excel.
Actually nobody goes with equidistant calibrators if more than one order of magnitude is covered, so it’s difficult to tell. Like you I would expect that logarithmic spacing would more often lead to a unweighted fit of proper ‘quality’ (based on back-calculations).

Cheers,
Helmut Schütz

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Ohlbe
Hero

France,
2009-07-10 10:33

@ Helmut
Posting: # 3951
Views: 2,788

## Weighing or weighting ?

Dear Helmut and El Maestro,

Over 10 years ago the SFSTP (Société Française des Sciences et Techniques Pharmaceutiques) published two papers on bioanalytical method validation, in which they discussed linearity issues and weighting. The first paper presented theory, the second paper was a practical example (in which they concluded that for that method, weighting should be 1/X1.754 ).

The papers are so complex that I never saw anybody use them, and they were issued before the FDA guidance (even before the draft 1998 guidance), so they are very far from current recommendations. But they are worth having a look at for some aspects of the discussion.

They were originally published in French (I give the reference for the few French-speaking readers of this forum ):

Méthodes chromatographiques de dosage dans les milieux biologiques: stratégie de validation. Rapport d'une commission SFSTP.
E. Chapuzet, N. Mercier, et al.
S.T.P. Pharma Pratiques 7(3) 169-194 1997

Méthodes chromatographiques de dosage dans les milieux biologiques. Exemple d'application de la stratégie de validation. Rapport d'une commission SFSTP
E. Chapuzet, N. Mercier, et al.
S.T.P. Pharma Pratiques 8(2) 81-107 1998

They were later re-published in English:

New strategy for the validation of chromatographic bioanalytical methods
SFSTP commission: E. Chapuzet, N. Mercier
S.T.P. Pharma Pratiques 10(1) 21-38 2000

Example of application of the new strategy proposed for the validation of chromatographic bioanalytical methods
SFSTP commission: E. Chapuzet, N. Mercier
S.T.P. Pharma Pratiques 10(2) 79-101 2000

Regards
Ohlbe
Helmut
Hero

Vienna, Austria,
2009-07-10 14:07

@ Ohlbe
Posting: # 3953
Views: 2,855

## Weighting!

Dear Ohlbe!

» Weighing or weighting ?

Oops! No balance (EN-UK) or scale (EN-US) is involved (weighing), we apply weights on the data; the correct term is weighting.

» […] a practical example (in which they concluded that for that method, weighting should be 1/X1.754 ).

Yes, why not.

Some other useful references:
• Draper NR, Smith H. Applied Regression Analysis. New York: Wiley; 3rd ed, 1998.
The standard textbook, but requires basic knowledge of matrix algebra!
• Miller JN, Miller JC. Statistics and Chemometrics for Analytical Chemistry. London: Pearson; 5th ed, 2005.
My personal favourite; a must for the bookshelf of all analytical chemists.
• Almeida AM, Castel-Branco MM, Falcão AC. Linear regression for calibration lines revisited: weighting schemes for bioanalytical methods. J Chromatogr B. 2002;774:215–22. doi:10.1016/S1570-0232(02)00244-1
• Fox J. Applied Regression, Generalized Linear Models, and Related Methods. New York: Sage Publications; 2nd ed, 2008. website
For R nerds only!

Cheers,
Helmut Schütz

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yjlee168
Senior

Kaohsiung, Taiwan,
2009-07-16 12:05

@ Helmut
Posting: # 3958
Views: 2,520

## Weighting!

Dear all,

ref.
NIST: Engineering Statistics Handbooks - 4.6.3.4. Weighting to Improve Fit.

All the best,
---Yung-jin Lee
bear v2.8.3-2:- created by Hsin-ya Lee & Yung-jin Lee
Kaohsiung, Taiwan http://pkpd.kmu.edu.tw/bear