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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
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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
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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
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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
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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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Copyright 1995-2010 David W. A. Bourne (david@boomer.org)