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d_labes ★★★ Berlin, Germany, 2008-10-16 15:39 (6031 d 13:10 ago) Posting: # 2544 Views: 13,546 |
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Dear all, sitting here and wondering once again about an old and often pondered problem: One of the things to be prepared in BE studies is the synoptic plot of mean concentrations versus time for the formulations under study. I pondering especially about dealing with entries <LLOQ (or whatever your entry for values below lower limit of quantitation is). So my question is to you:
I use the common arithmetic mean and consider entries <LLOQ as zero. But I have no rationale for that other than simplicity. Thus looking forward to your reasoning. — Regards, Detlew |
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martin ★★ Austria, 2008-10-17 15:23 (6030 d 13:26 ago) @ d_labes Posting: # 2549 Views: 11,604 |
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dear dlabes ! here is my personal point of view for the classical complete data designs (i.e. one concentration time profile per subject):
handling missing values for calculation of AUCs depend on the definition. you can define the truncated AUC as 1) AUC from 0 to the last quantifiable concentration or 2) AUC from 0 to x hours. for calculation of AUC from 0 to x hours I set values < LLQ as zero. hope this helps Martin Jaki T and Wolfsegger MJ. A theoretical framework for estimation of AUCs in complete and incomplete sampling designs. Statistics in Biopharmaceutical Research, in press. Anders Källen (2008). Computational Pharmacokinetics. Chapman and Hall / CRC, Boca Ration. |
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d_labes ★★★ Berlin, Germany, 2008-10-17 17:23 (6030 d 11:27 ago) @ martin Posting: # 2551 Views: 11,193 |
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Dear Martin, thanks for sharing your opinion  . Let me ask some puzzled things further. ❝ - for visualizing individual concentration time profiles I treat values <LLQ as missing. Is this also true for intermediate (between two values >LLOQ) or beginning values <LLOQ? ❝ for average concentration time profiles I use also arithmetic means [...] note that values of zero are not possible when using geometric means. If you use the definition geom. mean=n-th root of the product of the values, you can account for zero's  . But then every time point with only one zero for a volunteer results in zero geometric mean. Not so good I think. Omitting zero values results on the other hand in a geometric mean which is in certain cases to high for my feeling. F.i. all but one value <LLOQ would then result in a mean = that value not <LLOQ. Nevertheless the geometric mean was recommended in the pioneering paper Sauter R, Steinijans VW, Diletti E, Böhm A, Schulz HU. Presentation of results from bioequivalence studies. Int J Clin Pharmacol Ther Toxicol. 1992 Jul;30(7):233-56. and recently in the book D Hauschke, V Steinijans and I Pigeot Bioequivalence Studies in Drug Development John Wiley & Sons, Chichester (2007), chapter 6 I assume this is because the authors assume log-normal distribution of concentration values. But both literature do not explicitly explain how they deal with LLOQ. OK, the whole is only for illustrative purposes in the study reports, but nevertheless a standardization deems necessary. — Regards, Detlew |
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martin ★★ Austria, 2008-10-17 18:13 (6030 d 10:37 ago) @ d_labes Posting: # 2552 Views: 11,317 |
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Dear dlabes ! ad) values > LLOQ or beginning <LLOQ: I deal with large molecule drugs – I have only measured values or values below LOQ (limit of quantification) I do not have experience with a “fuzzy range”. ad) geometric mean. Yes of course your right  but using exp(mean(log(x))) - it is simply not defined. Omitting values to calculate the mean can give you a terrible wrong picture (personal experience: I had a data set that switched from a one-compartmental to a two-compartmental model - by visual inspection - simply by excluding values below LOQ). Values below limit of detection are informative missing and not missing at random! Ad textbooks: Most of them are applicable for problems in a perfect world. From a theoretical point of view one has to model values below LOQ as censored observations (like in survival studies). I think when you have a perfect situation the geometric mean is applicable whereas in the case of values below LOQ it can give you a terrible wrong picture. For standardization of figures I would go for the arithmetic mean as 1) figures should give an overall unbiased picture and the arithmetic allows to handle values below <LOQ and 2) is theoretically (i.e. asymptotically and on assumption of an intra-subject correlation of zero) justified (which may not be the case using medians or geometric means). Best regards martin PS.: what do you think on providing boxplots per time point instead of means? |
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d_labes ★★★ Berlin, Germany, 2008-10-19 15:55 (6028 d 12:54 ago) @ martin Posting: # 2559 Views: 11,229 |
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Dear Martin! ❝ ad) values > LLOQ or beginning <LLOQ: I deal with large molecule drugs – I have only measured values or values below LOQ (limit of quantification) I do not have experience with a “fuzzy range”. Eventually my question was misunderstandable. Let me give examples to make it clear. Beginning values <LLOQ: t=0h, c=0; t=0.25h c= <LLOQ; t=0.5h, c=<LLOQ;t=1h, c=10 Do you then take c <LLOQ as missing? Intermediate values <LLOQ: t=12h, c=15; t=18h c= <LLOQ; t=24h, c=2; Do you then take c <LLOQ as missing? ❝ PS.: what do you think on providing boxplots per time point instead of means? This is a good suggestion, I think, it calls for median as the mean function. But I think it is very unusual for BE reports I have seen so far. My sponsors always have difficulties if Box-plots are provided (until now for the PK parameters). The plots need some deeper understanding in statistics compared to mean plots which is not always there. — Regards, Detlew |
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martin ★★ Austria, 2008-10-19 21:09 (6028 d 07:41 ago) @ d_labes Posting: # 2560 Views: 11,419 |
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Dear dlabes ! I assume that you refer to extra vascular route of administration 1) beginning values <LLOQ: yes I would set values below LLOQ to zero as it is a classical informative missing scenario. This gives you a clear impression of a lag-time to for the drug reaching the systemic circulation 2) intermediate values <LLOQ: this is an interesting scenario - as far as I understand - this up and down would indicate a "re-release" of the drug during the elimination phase however, I would set these values to zero (informative missing as indicated by <LLOQ). the average concentration time profile should give you an impression of an potential re-release or simple of random variation. In the case of an unexpected behavior of the drug – the mean concentration time profile would indicate this by a distinct bump otherwise this individual values would be "averaged out". in the case that a re-release is definitely not possible from a physiological point of view - this up and down is simple due to random variation. I would add a data handling section in the protocol clearly describing that if a concentration level post study drug administration observed after Tmax is lower than LLOQ that this concentration level and all subsequent concentration levels will be not used for calculation of any PK parameters (and set to zero for individual and average concentration time profiles). ad boxplots) are you kidding? the sponsor would give a drug to humans based on interpretation of rather complicated confidence intervals but they are not able to read box plots. OH MY GOD ! by the way I would go for schematic-type boxplots (link, figure 18.4) indicating both, the median and the arithmetic mean. best regards martin |
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Frieda ☆ 2008-10-29 18:40 (6018 d 09:10 ago) @ d_labes Posting: # 2606 Views: 11,299 |
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Dear all, I'm a bit late in responding, just back from holiday. Nonetheless, to expose my method: I use the common arithmetic mean (±SD) and set values <LLOQ to zero in the absorption phase, use LLOQ/2 for values <LLOQ if the adjacent values are >LLOQ. I set the first terminal value <LLOQ to half the LLOQ and the subsequent ones to zero, and do not produce a mean if >50% of the actual values were <LLOQ. My rationale is that it setting terminal values to zero straight away seems abrupt… (gut feeling, no real rationale). The ones in the middle will on average be somewhere between the LLOQ and zero and so I use half the LLOQ, also for AUC calculations. Regards Frieda |
Ing. Helmut Schütz