- On 16 Dec 2013 at 09:08:06, gary-gu.at.outlook.com sent the message

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Dear all,

I never saw anyone recommends or uses weighting in the terminal phase estimation when doing

non-compartment analysis (NCA) in any textbook or literature before.Recently, I saw one of our

collaborator using 1/Y^2 (Y: observed values) in the terminal phase estimation when he did the NCA

by Phoenix WinNonlin. The reason he gave is listed below:

"The plasma concentration at the end of elimination phase is subject to the noise and inherently

carries higher variation than the study samples in the PK profile. The bioanalysis typically

applies weighted linear regression (1/x or 1/x^2) to overcome this variation. In the estimation of

the elimination rate constant, we applied the same strategy in using weighted linear regression (1/x

or 1/x2). This approach will minimize the impact of the high concentration samples on the

regression. This issue is more prominent in the compartment analysis, and often we will not see a

random distribution of the residue."

I know weighting by the reciprocal the predicted values (1/yhat or 1/yhat^2) is generally

recommended in compartment analysis, however I suspect whether it is necessary for NCA. In my humble

opinion, for NCA, as less as the modeling assumption should be made. But how is this applied to

terminal phase estimation?

I appreciate any comment or literature recommendation on this issue.

Thanks

Gary - On 16 Dec 2013 at 11:29:28, Angusmdmclean.at.aol.com sent the message

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Gary: weighted linear regression can be useful for any regression analysis. It depends on the

points you have. In the specific case you cite you would have to look at the goodness of fit of the

regression line first using ordinary least squares regression and then compare with the weighted

option to see what is the best fit. That comparison will tell you whether the weighting is helping

your fit to the line better or not. If "yes" if not the use the ordinary least regression. See the

work below for some background. This technique comes from engineering and it can be very useful.

Application of a variance-stabilizing transformation approach to linear regression of calibration

lines

Angus M. McLean, Donald A. Ruggirello, Christopher Banfield, Mario A. Gonzalez, Meir Bialer. Article

first published online: 18 SEP 2006, DOI: 10.1002/jps.2600791112

Journal of Pharmaceutical Sciences, Volume 79, Issue 11, pages 1005–1008, November 1990

Hope this helps,

Angus McLean - On 16 Dec 2013 at 16:22:53, Peter Bonate (peter.bonate.-at-.gmail.com) sent the message

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Gary

Your collaborator is wrong. There is no need to weight the data in the terminal phase when doing an

NCA analysis. The heteroscedasticity in the data is controlled for by using log-linear regression.

Think of it this way. If

Observed Concentration = True Concentration*Exp(random noise)

then the variability of the observed data would appear log-normal. Variability would increase with

increasing concentration.

During the termination phase when you take the log-transform

Ln(observed) = Ln(true) + noise

Hence, by taking the log-transform the noise becomes a constant and so there is no need to weight

the data. You can simply use OLS. I hope this helps clarify things.

Pete Bonate - On 16 Dec 2013 at 21:17:47, Roger Jelliffe (jelliffe.at.usc.edu) sent the message

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Dear Gary and Peter:

Why use weighting? Because there are real errors involved. One wants to give weight to data

according to its credibility. If the lab assay data is Gaussian, and it usually is, Then the proper

measure of precision is the reciprocal of the assay variance at any result. This is well known

[1]. It represents measurement noise. Then, if you fit the data, there is another source of noise,

and that is process noise, due to the uncertainties in the differential equations themselves. People

are beginning to describe this correctly, but nothing is widely published on this as yet. Instead,

one currently can estimate this other noise source as if it were an additive source of measurement

noise. Not correct, but better than nothing.

Fitting data is not an art. One does not mess with mother nature. One should not explore

weighting schemes simply to get a better fit. If one assumes a constant assay variance, as many do

in fitting logs of serum concentrations, as Dr. Bonate suggests, then you run into the problem of

BLQ, and his assumption becomes no longer true, as you encounter the region of machine noise. Better

to fit a polynomial to the assay data, so you can also know the machine noise. You might see

Jelliffe RW, Schumitzky A, Van Guilder M, Liu M, Hu L, Maire P, Gomis P, Barbaut X, and Tahani B:

Individualizing Drug Dosage Regimens: Roles of Population Pharmacokinetic and Dynamic Models,

Bayesian Fitting, and Adaptive Control. Therapeutic Drug Monitoring, 15: 380-393, 1993.

This issue has been around for so long.

All the best for the Holidays,

Roger Jelliffe

Roger W. Jelliffe, M.D., F.C.P., F.A.A.P.S.

Professor of Medicine Emeritus

Founder and Director Emeritus, Laboratory of Applied Pharmacokinetics

www.lapk.org

USC Keck School of Medicine

Children's Hospital of Los Angeles

MC#51

4650 Sunset Blvd

Los Angeles CA 90027

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