Dear Jeroen, Nick, and colleagues The CV estimate most often reported in population PK papers is simply OMEGA. It does not formally equal the SD/mean ratio for log-normally distributed values, but it still aims at estimating the same quantity, i.e. the relative dispersion of the values. This approach is probably more appropriate than the calculation of SQRT(EXP(OMEGA^2)-1) i.e. the formal CV for a log-normal distribution, which still implicitly refers to a context of prevailing additivity. Both metrics converge asymptotically for reasonably low dispersion, while SQRT(EXP(OMEGA^2)-1) tends towards aberrant values for large OMEGA values. We should stick to Stuart Beal's suggestion and continue using OMEGA for estimating the relative dispersion of parameter values, while perhaps just stating that this CV is expressed in Neper units (Np) rather than continuing to use % units (see https://en.wikipedia.org/wiki/Neper). Best regards
Thierry CHUV - University Hospital Centre of the Canton de Vaud Pr Thierry BUCLIN, MD, honorary professor, registered hospital physician Service of Clinical Pharmacology Lausanne - SWITZERLAND -----Message d'origine----- De : [email protected] <[email protected]> De la part de Jeroen Elassaiss-Schaap (PD-value B.V.) Envoyé : lundi, 13. mai 2024 00:24 À : Nick Holford <[email protected]>; [email protected] Objet : Re: [NMusers] %RSE for IIV when expressed as %CV instead of variance Hi Nick, Thanks for bringing this up. Stuart Beal rightly pointed out that with larger variability the interpretation of the lognormal becomes more involved and merits additional discussion. Nowadays we also seem to encounter values of OMEGA much larger than those that he seemed to consider (i.e., >1). What is also new since than, described in the paper I mentioned earlier in the thread, we (credits to Kevin Duisters) have established values up to which the lognormal can be approximated by a normal distribution on formal grounds (Kullback-Leibler divergence): up to a gray zone between 0.25-0.67 (lognormal sd) (*) for most purposes. To label as "apparent CV" does not seem too helpful to me, as the CV is well defined (CV=SD/mean) at any value. The remaining question is, what are intuitive statistics to describe the lognormal distribution (probability density function, PDF) at larger values? Arguably, common statistics like skewness and yes, CV, seem to fall short. It may be more insightful to show: - the ratio between mean and median (MMR) - the increase in the peak at the mode compared to its minimum (for log-sd>1) (mode density inflation, MDI) - 10th percentile of the distribution Of these three, the MMR is the nice and actionable, as the reader can induce how large the mean is given the MMR and the parameter value, next to get a feeling for how the PDF extends to larger values. The MDI gives more of an idea of how sharp the density peak close to zero becomes, therefore perhaps intuitive but mostly provides an impression of the PDF rather than something actionable. The 10th percentile is completely actionable but does not provide a lot of insight on how the PDF looks like.(#) Whatever the approach, it seems fair to warn readers for a "large"-variability log-normal estimate. Best regards, Jeroen * Noting that the range of 0.25-0.67 corresponds to the notion of Stuart Beal (2-15% difference between CV and log-sd). # The statistics mentioned and than some can be compared in the aforementioned cheatsheet https://ascpt.onlinelibrary.wiley.com/action/downloadSupplement?doi=10.1002%2Fpsp4.12507&file=psp412507-sup-0002-TableS1.pdf showing e.g. that at log-sd of 1.33, the mode is below the 10th percentile and 7-fold more likely to occur compared to the mean. http://pd-value.com [email protected] @PD_value +31 6 23118438 -- More value out of your data! On 11-05-2024 20:59, Nick Holford wrote: > > Thanks to Karam who retrieved the quote I mentioned from Stuart Beal. > > -- > > Nick Holford, Professor Emeritus Clinical Pharmacology, MBChB, FRACP > > mobile: NZ+64(21) 46 23 53 ; FR+33(6) 62 32 46 72 > > email: [email protected] <mailto:[email protected]> > > web: http://holford.fmhs.auckland.ac.nz/ > <http://holford.fmhs.auckland.ac.nz/> > > *From:*karam alali <[email protected]> > *Sent:* Saturday, May 11, 2024 7:31 PM > *To:* Nick Holford <[email protected]> > *Subject:* Re: [NMusers] %RSE for IIV when expressed as %CV instead of > variance > > Hi Prof. Nick, > > I got a capture of the original quote from web archive: > > https://web.archive.org/web/20050117183801/http://gaps.cpb.ouhsc.edu/n > m/91sep2697.html > <https://web.archive.org/web/20050117183801/http:/gaps.cpb.ouhsc.edu/n > m/91sep2697.html> > > Best Regards, > > Karam Alali > > Ph.D. Candidate > > Universiti Sains Malaysia > > On Sun, 12 May 2024, 2:10 am Nick Holford, <[email protected]> > wrote: > > Hi Anita, > > Some history on expressing the variance estimate of the random > effects of a parameter can be found here: > > > https://web.archive.org/web/20050117183801/http://gaps.cpb.ouhsc.edu/nm/91sep2697.html > > <https://web.archive.org/web/20050117183801/http:/gaps.cpb.ouhsc.edu/n > m/91sep2697.html> > > Stuart Beal wrote about this issue in 1997 and cautioned that > the interpretation is in the eye of the user because NONMEM does > not require ETAs to be normally distributed: "Many discussions > state that ETA is assumed to be normal, but these are often > misleading. While there are sometimes good reasons for making this > assumption, the NONMEM methodology largely avoids > the assumption." He proposed the term "apparent coefficient of > variation" as a way of implying a normal distribution of > ETA. "Since we do not need to make the normality assumption, it > does not follow that the "extra accuracy" given by the lognormal > formula really represents extra accuracy; it can just as well be > garbage. Suppose we want to really do the right thing, and CV is > large (perhaps as a pragmatic matter, we will judge the CV to be > large when the results from the two formulas differ > substantially). Then we should probably avoid reporting the CV as > a "CV", but report it as an "apparent CV"." > > Unfortunately, the original quote that I cited from Stuart Beal > (the originator of NONMEM) no longer seems to be available. > > http://gaps.cpb.ouhsc.edu/nm/91sep2697.html > > In the example you provide you mention ETA so presumably you are > referring to random parameter variability not residual error. I > encourage you not to use the acronym “IIV” because without other > information is not clear if this means “inter individual > variability” (e.g. PPV, population parameter variability of a > parameter) or “intra individual variability” describing residual > unexplained variability, RUV (“residual error”). > > The relative standard error can be estimated using a > non-parametric bootstrap by dividing the standard deviation of the > bootstrap distribution by the average of the bootstrap > distribution of the parameters. The non-parametric BS does not > make the assumption that the uncertainty of the parameters is > normal and therefore symmetrical. > > Best wishes, > > Nick > > NOTE: The address for Anita Moein [email protected] was bounced > by the University of Auckland email server. This may be linked to > the red warning shown below. > > -- > > Nick Holford, Professor Emeritus Clinical Pharmacology, MBChB, > FRACP > > mobile: NZ+64(21) 46 23 53 ; FR+33(6) 62 32 46 72 > > email: [email protected] <mailto:[email protected]> > > web: http://holford.fmhs.auckland.ac.nz/ > <http://holford.fmhs.auckland.ac.nz/> > > *From:*[email protected] <[email protected]> > *On Behalf Of *Anita Moein > *Sent:* Saturday, May 11, 2024 3:09 PM > *To:* [email protected] > *Subject:* [NMusers] %RSE for IIV when expressed as %CV instead of > variance > > Caution - Forged External Domain! > This e-mail cannot be validated and may not have been sent by the > sender shown in the 'From' field. > If you were not expecting to receive this e-mail we recommend you > contact the sender to confirm that they sent it. > If you believe this email was legitimately sent, we suggest the > sender notify their e-mail administrator that it has been received > as a forged (fake) e-mail by the University of Auckland. > Please contact the Staff Service Centre on extension 86000 if you > require further assistance. > > Dear All: > > I have a question regarding reporting ETAs as %CV instead of > variance. > > In NONMEM the IIV estimate is reported as variance with associated > RSE%. > > How can I convert the IIV Estimate and RSE% to report it as CV%? > > Thank you! > > Best, > > Anita > > > *Anita Moein* > > Senior Scientist > > Modeling and Simulation | Clinical Pharmacology | Genentech > > Phone: (650) 866 7701 | Cell: (415) 254 7972 >
