- On 27 Oct 2006 at 07:46:29, sunil mishra (mishrasunil7.aaa.yahoo.com) sent the message

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Hi,

While fitting a model to a plasma conc.-time data, model parametes

are calculated by the software programs and parameter values are

given alongwith SE or %CV. While calculating the parameter values

the software varies the values of parameters to minimize the

objective function. Then, it should be a point estimate of the

parameter values at which the objective function will have minimum

value. I am not able to understand, where SE or % CV of the

parameter estimates come from? we should only get a point estimate

of parameter values without SE or %CV. I will be greatful if any of

you guys can make me understand it.

Mishra Sunil

University of Delhi

[SE/CV%'s are a reflection of the goodness of fit, not the population

estimate of the SE/CV%'s of the parameters. They are derived from the

shape of the WSS surface at the minimum. Step slope, small SE/CV%. - db]

But, SE = SD of the sample/Square root of n

CV% = SD/mean of values

Keeping that in mind, How do I interpret these terms in relation to

parameter estimates. I understand these reflect goodness of fit or in

other words how precise is the estimation of parameters, right.

For example, If we say SE of a parameter estimate is 0.020 or if we

say CV% of a parameter is 15%. How these values are calculated

keeping in mind the formulas of SE and CV% given above.

Thanks

Amit - On 27 Oct 2006 at 11:31:09, "Serge Guzy" (GUZY.at.xoma.com) sent the message

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The following message was posted to: PharmPK

When you are fitting a model to the data you never know the true

underlying population distribution. You have noise in the data, you have

only a sample from the population and each individual have only a

certain number of observations. Therefore, when you minimize the

objective function, you obtain one estimate of the population,

variance(s) and noise as you mention but you want to estimate the

uncertainty associated with your estimates. That is where the se are

coming from.

You can either bootstrap your data set or use Inverse Hessian approach.

The result is a se (or%cv) associated with all your population

estimates.

The intuitive approach to understand se of population estimates is to

consider the following scenario:

Simulate from a known population many data sets, let say 100.

Fit the underlying model to these 100 data sets

You get 100 individual estimated for all the population parameters.

Those are different one from the other although all come from the same

population.

Calculate the standard deviation of these 100 estimates

Average them

This will give you and estimate of the average standard error you should

get if you would estimate the standard error from the 100 data sets.

The same concept is used in Statistics all the time (estimate the mean

of a sample for example).

Here we just have a more complex system.

Serge Guzy

President POP-PHARM - On 30 Oct 2006 at 07:24:28, jose-antonio.allue.aaa.ipsen.com sent the message

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The following message was posted to: PharmPK

The %CV comes from the variance-covariance matrix (matrix of derivatives

of the function with respect to the parameters, in which the diagonal

term is the standard error of the parameters and the non-diagonal

terms are the covariances amongst them).

Hope this helps.

Jose Antonio Allue Ph.D.

Mass Spectrometry Laboratory

Drug Metabolism, Pharmacokinetics and Immunology Service

Research & Development Department

IPSEN-PHARMA S.A. Laboratories

Ipsen Group

Ctra. Laurea Miro 395

Sant Feliu de Llobregat, Barcelona, Spain

Telf.: 936858100

e-mail:jose-antonio.allue.aaa.ipsen.com - On 31 Oct 2006 at 07:29:58, jose-antonio.allue.-at-.ipsen.com sent the message

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Sorry but the diagonal elements are the variances of the parameters, so

the calculation of the standard error is straightforward.

(In my previous mail I wrote that the diagonal term elements are the

satnadard errors -deviations-)

Jose Antonio Allue Ph.D.

Mass Spectrometry Laboratory

Drug Metabolism, Pharmacokinetics and Immunology Service

Research & Development Department

IPSEN-PHARMA S.A. Laboratories

Ipsen Group

Ctra. Laurea Miro 395

Sant Feliu de Llobregat, Barcelona, Spain

Telf.: 936858100

e-mail:jose-antonio.allue.-at-.ipsen.com - On 31 Oct 2006 at 07:04:52, "Clerk Maxwell" (clerkmaxwell.at.hotmail.com) sent the message

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The following message was posted to: PharmPK

Please see the article by Boxenbaum, Riegelman et al in J Pharmacokin

Biopharm -- do a pubmed search to obtain the full reference. It came

out about 1974.

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