# PharmPK Discussion - How to calculate intrasubject variability - Population PK

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• On 15 Mar 2002 at 14:44:59, Nick Holford (n.holford.at.auckland.ac.nz) sent the message
`The following message was posted to: PharmPK"anand iyer (by way of David Bourne)" wrote:>I am fresher who is just learning population PK. And this is somethingwhich has been bothering me a for some time. When we use population Pkapproach we consider the issue of inter as well as intra subjectvariability. And it is often said that using population Pk approach wecan calculate intra as well as inter subject variability. My question iswhen we use destructive sampling or even in clinical scenario if we ableto get just one sample for each time point from each subject how are weable to calculate intra-subject variability? The basic logic being thatyou need at least 2 samples from the same subject/animal for the sametime point to calculate intra subject variability. I understand the factby putting in various co-variaties like body weight, age etc we candetermine inter-subject variability. But can we estimate intra subjectvariability using these?This an excellent question. First of all let me caution you about theuse of the term "intra-individual variability". I think"intra-individual" is quite misleading. What is estimated is bettercalled residual unidentified variability (RUV). It is residual becauseit is what is left over after all the other sources have been accountedfor. It is unidentified because it is attributable to a variety ofconfounded sources including 1) model misspecification -- in many casesI suspect this is the biggest component. 2) measurement error -- thisincludes both the dependent variable e.g. concentration, and independentvariables such at time,dose, weight etc. 3) some true within subjectparameter variability (WSV) (although this is really modelmisspecification).You are quite correct in pointing out that that there areidentifiability problems with the destructive sampling (one sample persubject) design. Imagine the simplest PK experiment of a constant rateinput that is know to have reached steady state. With one concentrationmeasurement it is impossible to distinguish between variability arisingfrom differences in clearance from subject to subject (populationparameter variability; PPV) and RUV. One approach to solving thisproblem is to assume a value for RUV -- say 20% of the predictedconcentration. With this assumption the variability in concs can then beassigned to PPV.The use of covariates to identify predictable differences betweensubjects e.g. by using weight to assign higher clearances in heavierpeople, can help in reducing the size of PPV. Indeed, if you considerthe PPV without weight in the model this can be thought of as being thesum of predictable (PPVP) varibility and apparently random (PPVR)variability. As each covariate is added to the model its influence is tomove variability from PPVR to PPVP but the total PPV does not change andthere should be no effect on RUV (except via model misspecificationwhich may be decreased with an appropriate covariate model). Note thatPPVR includes variability from true between subject variability inparameters (BSV) and true within subject variability in parameters(WSV). These components can be identified by the use of anothercovariate (occasion) if it is possible to estimate the parameter on morethan one occasion within the same subject.In summary, covariates cannot help to estimate RUV except via decreasingmodel misspecification and if you misspecify the covariate model you canincrease RUV.Destructive sampling designs are a priori unidentifiable with respect todistinguishing PPV from RUV.The following reference illustrates some of the approaches to thisproblem: Is Mixed Effects Modeling or Na•ve Pooled Data AnalysisPreferred for the Interpretation of Single Sample per SubjectToxicokinetic Data? Hing J.P.; Woolfrey S.G.; Greenslade D.; WrightP.M.C. Journal of Pharmacokinetics and Pharmacodynamics, April 2001,28(2):193-210Nick--Nick Holford, Divn Pharmacology & Clinical Pharmacology University ofAuckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealandemail:n.holford.-at-.auckland.ac.nzhttp://www.health.auckland.ac.nz/pharmacology/staff/nholford/`
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