d_labes ★★★ Berlin, Germany, 20080326 14:15 (5728 d 06:02 ago) Posting: # 1721 Views: 9,201 

Dear all, i wonder about the precision of the pharmacokinetic metrics used in bioequivalence studies. Can anybody enlighten me? How do you act in this respect? Do you have any standard regarding the significant digits or decimal places in reporting AUC, Cmax and so on? Does anybody know a regulative guideline? — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20080326 17:12 (5728 d 03:05 ago) @ d_labes Posting: # 1724 Views: 8,222 

Dear DLabes! ❝ […] precision of the pharmacokinetic metrics used in bioequivalence studies. Oh, that's an interesting question! A rather old (1988) reference from IUPAC (the International Union of Pure an Applied Chemistry) recommends giving location parameters (means, median) to two significant figures, and the relative standard deviation (RSD, CV) to three significant figures. You may download the reference here. I would suggest rising the significant figures by one digit. Problems arise if electronic data in full precision are transferred to the statistical database. Generally (paper)reports contain only modified results (rounded to decimal places or significant figures, or  even worse  truncated values). If PKparameters have to be recalculated from the paperversion or a PDFfile (i.e., during an inspection), results may differ from the ones reported… Most likely affected parameters are C_{max} and t_{1/2}, whereas AUC as an integrated parameter is pretty robust. Two reasons call for rounding of analytical data before using them in PK: a pragmatic one – avoid discrepancies between paper and electronic data which may raise unnecessary questions, and a scientific one – use of full precision data implies a degree of accuracy/precision which is not correct. Example: 3.141592653589793 (result from data system)3.1416 (four decimal places)3.142 (four significant figures)Since the accuracy/precision of an analytical method is dependent on the concentration, it would be desirable to take this into account and perfom rounding based on results form the validation. If the method comes up with ±2.3% at 30, with ±5.8% at 3.0 and with ±15% at 0.3 a rounding function may be set up. However, I would always opt for significant digits – not decimal places. Imagine the situation, where the analytical method covers two orders of magnitude: ++++ What we (silently) imply in the second column (rounding to three decimal places) is suggesting our ability to distinguish between 31.4154 and 31.4165 – a difference of 0.0035% from the reported value! Of course it gets better going to lower concentrations: 0.32% at 0.314. In the third column (rounding to three significant figures) we obtain 0.32% regardless the concentration – which is too low anyway… For many analytical methods even rounding to two significant digits would be sufficient – but I would guess everybody would start screaming then: analysts, sponsors, regulators. Most analysts have swallowed Arlington Conferences IIII and are familiar with 15% accuracy/precison (20% at LLOQ); but routinely come up with 3.141592653589793 . Subconsciously they belief, that such a result is more correct than 3.14 .If I tell them, next time they should come up with 3.14159265358979323846264338327950288 , they tell me, that I am a funny person. ❝ How do you act in this respect? I do rounding of analytical data to three significant figures (I failed convincing sponsors that concentrationbased rounding is a reasonable procedure). ❝ Do you have any standard regarding the significant digits or decimal places in reporting AUC, Cmax and so on? C_{max} taken from rounded data, therefore three significant figures; AUC as an integrated parameter to four significant figures (this makes sense according to propagation of uncertainty). Location parameters to the same number of digits; SD one more. ❝ Does anybody know a regulative guideline? No… — Diftor 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, 20080327 11:10 (5727 d 09:07 ago) @ Helmut Posting: # 1726 Views: 7,764 

... thats the question (Hamlet). Dear HS, thanks for lighten me a candle . Most of your reasoning meets my feeling about this topic. But some minor comments and questions for clarifying: ❝ However, I would always opt for significant digits  not decimal places. This is very resonable regarding your reasoning that follows in your post. But I have seen almost always constant decimal places (mostly 23) in the result from analysts. May be this is because they all use M$EXCEL . Have you convinced your analysts in using significant digits? Or is the discrepancy to the analytical report not an issue? ❝ For many analytical methods even rounding to two significant digits would be sufficient – but I would guess everybody would start screaming then ... Thats a pity, but "The customer is king". ❝ I do rounding of analytical data to three significant figures ... Am I right in assuming that you use the rounded values for further processing (PK analysis)? Or only for reporting the values in the study report? What about 3 significant digits if LLOQ is given by the analyst with 2 decimals but only 2 significant digits (f.i. 0.88 nano/whatever)? ❝ C_{max}… three significant figures; AUC as an integrated parameter to four significant figures… AUC (roughly spoken summed conc. multiplied by time ...) gains precision in comparision to Cmax? I had expected the contrary. Again the question: Rounded values for further processing (statistical analysis of bioequivalence) ? — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20080327 21:43 (5726 d 22:34 ago) @ d_labes Posting: # 1727 Views: 7,865 

Dear DLabes! ❝ … thats the question (Hamlet). ❝ But I have seen almost always constant decimal places (mostly 23) in the result from analysts. Yes, it’s a pity. ❝ May be this is because they all use M$EXCEL . Agree, but even for them help is on the way. In cell A1 : original value (to 15 significant figures, if they like)In cell B1 : =IF(A1>1000,ROUND(A1/10,0)*10, IF(A1>100,ROUND(A1,0), IF(A1>10,ROUND(A1,1), IF(A1>1,ROUND(A1,2),ROUND(A1,3))))) Custom format of column B : 0.??? … will handle values between 0.1 and 10000. ❝ Have you convinced your analysts in using significant digits? Since I’ve worked as an analyst myself for quite a long time, mainly I succeeded, because I speak the same language. ❝ Or is the discrepancy to the analytical report not an issue? Yes it is. As a precaution I describe the procedure in the SAP – which is submitted to the EC and the competent authority beforehand. I never experienced any problems. But still I try to avoid such situations and talk to the analysts… ❝ ❝ For many analytical methods even rounding to two significant ❝ ❝ digits would be sufficient – but I would guess everybody would ❝ ❝ start screaming then … ❝ Thats a pity, but "The customer is king". Yes, but I would say it’s also part of our job to do some education. Otherwise Rubbish in, rubbish out! applies.❝ ❝ I do rounding of analytical data to three significant figures … ❝ Am I right in assuming that you use the rounded values for further processing (PK analysis)? Exactly. ❝ What about 3 significant digits if LLOQ is given by the analyst with 2 decimals but only 2 significant digits (f.i. 0.88 nano/whatever)? I can only use the data I get. Three significant figures actually are too high for many analytical methods anyway. If the LLOQ is given with 0.88 I keep it as it is. As said in my previous post 0.88 implies everything between 0.875 and 0.884, or ~±0.5%, which is just ridiculous. I would prefer 0.9 (1 significant figure = ~±5%) ❝ ❝ C_{max}… three significant figures; AUC as an integrated ❝ ❝ parameter to four significant figures … ❝ AUC (roughly spoken summed conc. multiplied by time ...) gains precision in comparision to Cmax? I had expected the contrary. If I look at AUC as an integrated function, most (if actual rather than scheduled sampling times are used – all) the error is contributed by the concentrations. I expected some kind of dampening effect – but to be honest I never checked it before. According to the propagation of errors the muliplication of two erroneous values leads to an addition of errors. If we assume no error in sampling times, AUC should be given to the same degree of precision as concentrations. I will modify my SOP, thanks! ❝ Again the question: Rounded values for further processing (statistical analysis of bioequivalence) ? Yes. — Diftor 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, 20080328 12:00 (5726 d 08:17 ago) @ Helmut Posting: # 1729 Views: 7,731 

Dear HS, thanks for sharing your "humble" opinion. — Regards, Detlew 