Re: Log transformation of concentration

Dear all, log-transformation has also some practical value. It adds stability to the parameter estimation process when the observations cover a wide range. I just had an example running with data from a phase I dose ranging study . The doses increased during the execution of the study over a 50-fold range. With fairly complete profiles I had concentrations which differed up to 500-fold. I fit the data on the linear scale and then log-transformed. Only with the log-transformed data was I able to fit a full BLOCK(5) OMEGA matrix. Rounding error terminations were diminished. The VPC was much easier as I had no negative predictions. These are all just practical observations, and I cannot give you an eloquent statistical explanation (Leonid may). But I will log-transform my concentration data in the future, especially when they cover a wide range. Thanks also to Mats for pointing that out in his workshop. Joachim __________________________________________ Joachim GREVEL, Ph.D. Merck Serono S.A. - Genève Human Pharmacology 1202 Geneva Tel: +41.22.414.4751 Fax: +41.22.414.3059 Email: [email protected] Leonid Gibiansky <[email protected]> Sent by: [email protected] 03/26/2009 11:52 PM To "Elassaiss - Schaap, J. \(Jeroen\)" <[email protected]> cc [email protected] Subject Re: [NMusers] Log transformation of concentration Jeroen, I think that the goal of modeling is to recover (predict) the underlying quantity (concentration, pd effect, whatever we are modeling). Our assumptions about the model (error model, in particular) help us (if they are correct) to recover those quantities. So there is no such thing as "prediction mode": we should always predict the underlying quantity. If the "true" error model is additive or proportional, then, given 1000 observations at the same true-concentration level, true concentration is equal to the mean of those observations. If the "true" error model is exponential, then, given the same 1000 observations, concentration is equal to the geometric mean of the observations. If the true model is exponential but we fit an additive model, then the fit is biased (relative to the true value), and vice versa. Investigation of the data should allow (in theory, given sufficient amount of data) to recover the true model, including the true error model. Log-transformation is just the trick that allows to implement the exponential error model in nonmem. Thanks Leonid -------------------------------------- Leonid Gibiansky, Ph.D. President, QuantPharm LLC web: www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel: (301) 767 5566 Elassaiss - Schaap, J. (Jeroen) wrote: > Dear Chenguang, > > There is one difference that could be added to the excellent explanation > by Leonid; this has been previously brought forward by Mats in another > thread (Calculation of AUC) this week. When log-transforming on both > sides (TBS) your model will predict the median (geometric mean) rather > than the average of your data on the normal scale. This only will be > noticable when the residual error is large, see the values provided by > Mats. This effect does not depend on between-subject variability, i.e. > it also holds for single-subject models. > > So while the log-transformation does not change the meaning of the > parameters, it will change the prediction 'mode' from average to median. > > Best regards, > Jeroen > > > *Jeroen Elassaiss-Schaap, PhD* > Modeling & Simulation Expert > Pharmacokinetics, Pharmacodynamics & Pharmacometrics (P3) > Early Clinical Research and Experimental Medicine > Schering-Plough Research Institute > T: +31 41266 9320 > > > > ------------------------------------------------------------------------ > *From:* [email protected] > [mailto:[email protected]] *On Behalf Of *Chenguang Wang > *Sent:* Thursday, 26 March, 2009 14:40 > *To:* Leonid Gibiansky > *Cc:* nmusers > *Subject:* Re: [NMusers] Log transformation of concentration > > Dear Leonid, > Thank you very much for your explaination! I think I am now much clearer > about this. > > Regards! > > Chenguang > > > > 2009/3/26 Leonid Gibiansky <[email protected] > <mailto:[email protected]>> > > Hi Chenguang, > The main reason to do the log transformation is the numerical > algorithm used in nonmem for error model. If you try to fit the > error model > Y=F*EXP(eps) > nonmem will take only the first term of the EXP function expansion > and will use the error model > Y=F*(1+EPS) > > Therefore, the only way to get true exponential (not proportional) > model is to log-transform both parts: > LOG(Y)=LOG(F)+EPS > > Note that this is done on the very last step. All parameters have > the same meaning. All differential equations are written and solved > for F. Then, after you obtain F, you take the log. In the DV column, > you put the log of observed concentrations, so that your actual code is > Y=LOG(F)+EPS > > Last year I compared the performance of FOCE with interaction for > models with and without log-transformation, and found the > performance to be similar (in terms of bias and precision of > parameter estimates): you can find the poster on PAGE web site. > Still, for several real data sets, I've seen that the > log-transformed model provided slightly better fit, especially for > data with large residual error. > > Leonid > > -------------------------------------- > Leonid Gibiansky, Ph.D. > President, QuantPharm LLC > web: www.quantpharm.com http://www.quantpharm.com/ > e-mail: LGibiansky at quantpharm.com http://quantpharm.com/ > tel: (301) 767 5566 > > > > > > Chenguang Wang wrote: > > Dear NONMEM users, > > I am working on a PK model and using the log-transformed > concentration data. I'v read some discussions in the NONMEM user > group about the log-transformed concentration. But I am still > not very clear about this. Could anybody give me a reason to do > the transform on concentration? Also, I am curious that after > the transform, will the fixed effect have the same meaning as > that in the untransformed model? For example, theta1 is the > clearance, after log-transform of concentration, would the > estimation of theta1 still stands for the population clearance? > To my simple thinking about the differential equation, > > d(lnc)/dt= (dc/dt)*(1/c). Therefore, a "c" will be multiplied to > the right term of the orginal differential equation. I think the > solution of that equation might be different from the original > one. If it is different, how can I explain the theta1 in the log > transformed model? > > Would anyone please give me some explainations or references? > > Thanks a lot! > > Chenguang > > > ------------------------------------------------------------------------ > This message and any attachments are solely for the intended recipient. > If you are not the intended recipient, disclosure, copying, use or > distribution of the information included in this message is prohibited > --- Please immediately and permanently delete. > ------------------------------------------------------------------------ This message and any attachment are confidential and may be privileged or otherwise protected from disclosure. If you are not the intended recipient, you must not copy this message or attachment or disclose the contents to any other person. If you have received this transmission in error, please notify the sender immediately and delete the message and any attachment from your system. 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