sri Junior 20090709 13:01 Posting: # 3945 Views: 3,106 

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, 20090709 13:48 @ sri Posting: # 3946 Views: 2,735 

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) AUC_{t} ≥80% AUC_{∞}. The ULOQ should be chosen based on the expected C_{max} 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
Example: LLOQ 10, ULOQ 500, n=6–8
Now you have to adjust these values for practicability (while keeping the LLOQ and ULOQ fixed). — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
ElMaestro Hero Denmark, 20090709 18:38 @ Helmut Posting: # 3947 Views: 2,674 

Hi HS, » blah blah starting point:
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, 20090709 19:24 @ ElMaestro Posting: # 3948 Views: 2,705 

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/σ^{2} but by w=1/y^{2} (or w=1/x^{2}). 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 backcalculated 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 daytoday analyses without fiddling around with w=1/y^{2} or the like. But that’s another story. — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
ElMaestro Hero Denmark, 20090709 20:06 @ Helmut Posting: # 3949 Views: 2,625 

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/x^{2}. Lets for the time being forget the 1/y or 1/y^{2} (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 xvalues and more points at low xvalues" 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, 20090709 21:00 @ ElMaestro Posting: # 3950 Views: 2,738 

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/x^{2}. Lets for the time being forget the 1/y or 1/y^{2} (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 TI59 and HP41 were top instruments then) analysts went for logarithmic spacing. To be honest I started with eyeball 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 backcalculations). — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
Ohlbe Hero France, 20090710 10:33 @ Helmut Posting: # 3951 Views: 2,788 

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/X^{1.754} ). 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 Frenchspeaking 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) 169194 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) 81107 1998 They were later republished in English: New strategy for the validation of chromatographic bioanalytical methods SFSTP commission: E. Chapuzet, N. Mercier S.T.P. Pharma Pratiques 10(1) 2138 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) 79101 2000 Regards Ohlbe 
Helmut Hero Vienna, Austria, 20090710 14:07 @ Ohlbe Posting: # 3953 Views: 2,855 

Dear Ohlbe! » Weighing or weighting ? Oops! No balance (ENUK) or scale (ENUS) 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/X^{1.754} ). Yes, why not. Some other useful references:
— Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
yjlee168 Senior Kaohsiung, Taiwan, 20090716 12:05 @ Helmut Posting: # 3958 Views: 2,520 

Dear all, Please allow me to add one more ref. here for this thread. ref. NIST: Engineering Statistics Handbooks  4.6.3.4. Weighting to Improve Fit. — All the best, Yungjin Lee bear v2.8.32: created by Hsinya Lee & Yungjin Lee Kaohsiung, Taiwan http://pkpd.kmu.edu.tw/bear Download link (updated) > here 