# PharmPK Discussion - Parameter estimate CV%

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• On 27 Oct 2006 at 07:46:29, sunil mishra (mishrasunil7.aaa.yahoo.com) sent the message
`Hi,While fitting a model to a plasma conc.-time data, model parametesare calculated by the software programs and parameter values aregiven alongwith SE or %CV. While calculating the parameter valuesthe software varies the values of parameters to minimize theobjective function. Then, it should be a point estimate of theparameter values at which the objective function will have minimumvalue. I am not able to understand, where SE or % CV of theparameter estimates come from? we should only get a point estimateof parameter values without SE or %CV. I will be greatful if any ofyou guys can make me understand it.Mishra SunilUniversity of Delhi[SE/CV%'s are a reflection of the goodness of fit, not the populationestimate of the SE/CV%'s of the parameters. They are derived from theshape of the WSS surface at the minimum. Step slope, small SE/CV%. - db]But, SE = SD of the sample/Square root of nCV% = SD/mean of valuesKeeping that in mind, How do I interpret these terms in relation toparameter estimates. I understand these reflect goodness of fit or inother words how precise is the estimation of parameters, right.For example, If we say SE of a parameter estimate is 0.020 or if wesay CV% of a parameter is 15%. How these values are calculatedkeeping in mind the formulas of SE and CV% given above.ThanksAmit`
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• On 27 Oct 2006 at 11:31:09, "Serge Guzy" (GUZY.at.xoma.com) sent the message
`The following message was posted to: PharmPKWhen you are fitting a model to the data you never know the trueunderlying population distribution. You have noise in the data, you haveonly a sample from the population and each individual have only acertain number of observations. Therefore, when you minimize theobjective function, you obtain one estimate of the population,variance(s) and noise as you mention but you want to estimate theuncertainty associated with your estimates. That is where the se arecoming from.You can either bootstrap your data set or use Inverse Hessian approach.The result is a se (or%cv) associated with all your populationestimates.The intuitive approach to understand se of population estimates is toconsider the following scenario:Simulate from a known population many data sets, let say 100.Fit the underlying model to these 100 data setsYou get 100 individual estimated for all the population parameters.Those are different one from the other although all come from the samepopulation.Calculate the standard deviation of these 100 estimatesAverage themThis will give you and estimate of the average standard error you shouldget if you would estimate the standard error from the 100 data sets.The same concept is used in Statistics all the time (estimate the meanof a sample for example).Here we just have a more complex system.Serge GuzyPresident POP-PHARM`
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• On 30 Oct 2006 at 07:24:28, jose-antonio.allue.aaa.ipsen.com sent the message
`The following message was posted to: PharmPKThe %CV comes from the variance-covariance matrix (matrix of derivativesof the function with respect to the parameters, in which the diagonalterm is the standard error of the parameters and the non-diagonalterms are the covariances amongst them).Hope this helps.Jose Antonio Allue Ph.D.Mass Spectrometry LaboratoryDrug Metabolism, Pharmacokinetics and Immunology ServiceResearch & Development DepartmentIPSEN-PHARMA S.A. LaboratoriesIpsen GroupCtra. Laurea Miro 395Sant Feliu de Llobregat, Barcelona, SpainTelf.: 936858100e-mail:jose-antonio.allue.aaa.ipsen.com`
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• On 31 Oct 2006 at 07:29:58, jose-antonio.allue.-at-.ipsen.com sent the message
`Sorry but the diagonal elements are the variances of the parameters, sothe calculation of the standard error is straightforward.(In my previous mail I wrote that the diagonal term elements are thesatnadard errors -deviations-)Jose Antonio Allue Ph.D.Mass Spectrometry LaboratoryDrug Metabolism, Pharmacokinetics and Immunology ServiceResearch & Development DepartmentIPSEN-PHARMA S.A. LaboratoriesIpsen GroupCtra. Laurea Miro 395Sant Feliu de Llobregat, Barcelona, SpainTelf.: 936858100e-mail:jose-antonio.allue.-at-.ipsen.com`
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• On 31 Oct 2006 at 07:04:52, "Clerk Maxwell" (clerkmaxwell.at.hotmail.com) sent the message
`The following message was posted to: PharmPKPlease see the article by Boxenbaum, Riegelman et al in J PharmacokinBiopharm -- do a pubmed search to obtain the full reference.  It cameout about 1974.`
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