Dear Sumeet, Actually please ignore my last remark, and thanks to Jonathan French for pointing out to me that, the ratio of two log-Normals is indeed log-Normal. I should have deferred to statistical theory rather than fuzzy memory of Normal/Normal being Cauchy so must somehow extend to log-Normals and trying to make silly plots that did not properly display the density due to my code/parameter choice:
https://stats.stackexchange.com/questions/21735/what-are-the-mean-and-variance-of-the-ratio-of-two-lognormal-variables/21740 Corrected R-code to properly plot the density when the mean is closer to zero: # Simulate some realistic PK for a water soluble renally cleared drug vd <- 40 * exp(rnorm(10000, sd = 0.5)) cl <- 6 * exp(rnorm(10000, sd = 0.5)) k <- cl / vd # Visualise the histograms and use fitdistr function to # fit a log-Normal require(MASS) # Volume: hist(vd, freq = FALSE) fit <- fitdistr(vd, "log-normal")$estimate lines(dlnorm(0:max(vd), fit[1], fit[2]), lwd = 3) # ...yes # # Clearance: hist(cl, freq = FALSE) fit <- fitdistr(cl, "log-normal")$estimate lines(dlnorm(0:max(cl), fit[1], fit[2]), lwd = 3) # ...yes # # K hist(k, freq = FALSE) fit <- fitdistr(k, "log-normal")$estimate lines(seq(0,max(k),length=200),dlnorm(seq(0,max(k),length=200), fit[1], fit[2]), lwd = 3) # ...YES! Lucky no-one who taught me statistics follows NMUsers! BW, Joe Joseph F Standing MRC Fellow, UCL Institute of Child Health Antimicrobial Pharmacist, Great Ormond Street Hospital Honorary Senior Lecturer, St George's University of London Tel: +44(0)207 905 2370 Mobile: +44(0)7970 572435 ________________________________________ From: [email protected] [[email protected]] on behalf of STANDING, Joseph (GREAT ORMOND STREET HOSPITAL FOR CHILDREN NHS FOUNDATION TRUST) [[email protected]] Sent: 05 February 2019 10:53 To: [email protected]; 'Leonid Gibiansky'; 'Singla, Sumeet K' Cc: [email protected] Subject: RE: [NMusers] Why should we avoid using micro rate constants? --- This message was sent from an email address external to NHSmail but gives the appearance of being from an NHSmail (@nhs.net) address. The recipient should verify the sender and content before acting upon information contained within. --- Dear Sumeet, If you are assuming a distribution for your parameters (e.g. log-Normal p = theta * exp(eta)) then it might matter if you use rate constants versus clearances and volumes. In general, if you want to make the log-Normal assumption you should use clearances and volumes as there is reasonable biological prior knowledge to show these generally follow a log-Normal distribution (do some reading on the occurrence of log-Normal distributions in biology). The rate constant is a ratio of two (usually) log-Normally distributed variables (e.g. k = CL/V) and hence may not necessarily be a shape that can itself be described as a log-Normal. Here is some R-code that highlights this: # Simulate some realistic PK for a water soluble renally cleared drug vd <- 40 * exp(rnorm(10000, sd = 0.5)) cl <- 6 * exp(rnorm(10000, sd = 0.5)) k <- cl / vd # Visualise the histograms and use fitdistr function to # fit a log-Normal require(MASS) # Volume: hist(vd, freq = FALSE) fit <- fitdistr(vd, "log-normal")$estimate lines(dlnorm(0:max(vd), fit[1], fit[2]), lwd = 3) # ...yes # # Clearance: hist(cl, freq = FALSE) fit <- fitdistr(cl, "log-normal")$estimate lines(dlnorm(0:max(cl), fit[1], fit[2]), lwd = 3) # ...yes # # K hist(k, freq = FALSE) fit <- fitdistr(k, "log-normal")$estimate lines(dlnorm(0:max(k), fit[1], fit[2]), lwd = 3) # ...no People who do not like to make assumptions on distributions of parameters use a nonparametric approach, and in this case it does not matter whether you use rate constants or clearances and volumes. However, unless you collect rich informative data (to get good individual parameter estimates) and lots of it (to get a true idea of the distribution of parameters in the population) it is usually advised to make a distributional assumption, and the log-Normal is often sensible. BW, Joe Joseph F Standing MRC Fellow, UCL Institute of Child Health Antimicrobial Pharmacist, Great Ormond Street Hospital Honorary Senior Lecturer, St George's University of London Tel: +44(0)207 905 2370 Mobile: +44(0)7970 572435 ________________________________________ From: [email protected] [[email protected]] on behalf of [email protected] [[email protected]] Sent: 05 February 2019 06:51 To: 'Leonid Gibiansky'; 'Singla, Sumeet K' Cc: [email protected] Subject: RE: [NMusers] Why should we avoid using micro rate constants? Hi All, It could also be the statistical model. If you are estimating 4 parameters then different parameterisations should be fairly equivalent if a BLOCK(4) structure is used for both parameterisations. If only the diagonal option is used, then this could be why different results/minimisations are obtained for different parameterisations. Kind regards, Janet Janet R Wade, PhD Occams Senior Consultant From: [email protected] <[email protected]> On Behalf Of Leonid Gibiansky Sent: 04 February 2019 07:30 To: Singla, Sumeet K <[email protected]> Cc: [email protected] Subject: Re: [NMusers] Why should we avoid using micro rate constants? It could be just coding error, could you show the control stream? Thanks Leonid On Feb 3, 2019, at 12:44 PM, Singla, Sumeet K <[email protected]<mailto:[email protected]>> wrote: Hello everyone! I have a question. I was trying to build a 2-compartment PK model for marijuana use in occasional and chronic smokers. Initially, I was using providing rate constants K12 and K21 in PK block and it resulted in poor fitting. Then, I later changed to CL,V1, V2 , Q and it resulted in proper fitting. I was perplexed as to why I couldn’t get a proper fit by providing rate constants? I tried to look online but couldn’t find any proper explanation about when (or not) we should use micro constants in PK block to define our model in NONMEM? Does anyone has any useful insights into this? Regards, Sumeet Singla Graduate Student Dpt. of Pharmaceutics & Translational Therapeutics College of Pharmacy- University of Iowa ******************************************************************************************************************** This message may contain confidential information. If you are not the intended recipient please inform the sender that you have received the message in error before deleting it. 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