- On 7 Feb 2013 at 10:16:05, Bernard Murray (Bernard.Murray.-a-.gilead.com) sent the message

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Hello there,

I have been mentoring one of my colleagues on the principles of

noncompartmental analysis. They have training in statistics so, for

better or worse, I skipped the usual MRT = AUMC/AUC approach and instead

showed them that the concentration-time curve could be converted to a

probability curve by dividing each concentration by the AUC and then

replotting. They were then comfortable that classical statistical

moment theory could be applied to calculate the mean of the distribution

(MRT) straight from the raw first moment curve.

During the conversation, one of their questions made me hesitate, so I

wanted to check with you to make sure I wasn't misleading them.

"What is the meaning of the probability curve, calculated from the PK

curve?"

My answer was that it was that each point represented the probability of

finding drug in plasma at that particular time.

Does that sound right?

As statisticians they were disappointed that we didn't have much use for

higher statistical moments (for variance, skewness and kurtosis) in PK,

but when I pointed out the potential errors resulting in multiplying a

24-hr concentration by 24^4, and the huge area extrapolations that would

likely be needed for the higher moments, they could see the practical

limitations.

All the very best,

Bernard

Bernard Murray, Ph.D.

Senior Research Scientist, Drug Metabolism

Gilead Sciences

[Reminds me an applied math course I helped to teach many years ago. In

one example the

mathematics instructor turned the PK equation into stochastic events - db] - On 7 Feb 2013 at 18:12:01, Roger Jelliffe (jelliffe.at.usc.edu) sent the message

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The following message was posted to: PharmPK

Dear Bernard:

I don't understand. What good does noncompartmental modeling do for

you that real compartmental modeling does not do better, especially

nonparametric population modeling? How do you plan to use these models?

How

do you use them, for example, to develop dosage regimens of drugs for

maximally precise dosage regimens as with nonparametric models and

multiple

model dosage design? Can you help me?

Some references

1. Jelliffe R, Schumitzky A, Bayard D, Milman M, Van Guilder M, Wang

X,

Jiang F, Barbaut X, and Maire P: Model-Based, Goal-Oriented,

Individualized

Drug Therapy: Linkage of Population Modeling, New "Multiple Model"

Dosage

Design, Bayesian Feedback, and Individualized Target Goals. Clin.

Pharmacokinet. 34: 57-77, 1998.

2. Jelliffe R: Goal-Oriented, Model-Based Drug Regimens: Setting

Individualized Goals for each Patient. Therap. Drug Monit. 22: 325-329,

2000.

3. Jelliffe R, Bayard D, Milman M, Van Guilder M, and Schumitzky A:

Achieving Target Goals most Precisely using Nonparametric Compartmental

Models and "Multiple Model" Design of Dosage Regimens. Therap. Drug

Monit.

22: 346-353, 2000.

4. Leary, R., Jelliffe R., Schumitzky, A., and Van Guilder, M An

adaptive grid non-parametric approach to pharmacokinetic and

dynamic(PK/PD)

population models, 14-th IEEE Symposium on Computer Based Medical

Systems,

389-394, 2001.

5. Jelliffe R: Estimation of Creatinine Clearance in Patients with

Unstable Renal Function, without a Urine Specimen. Am. J. Nephrology,

22:

320-324, 2002.

6. Bayard D, and Jelliffe R: A Bayesian Approach to Tracking Patients

having Changing Pharmacokinetic Parameters. J. Pharmacokin. Pharmacodyn.

31

(1): 75-107, 2004.

7. Bustad A, Terziivanov D, Leary R, Port R, Schumitzky A, and Jelliffe

R: Parametric and Nonparametric Population Methods: Their Comparative

Performance in Analysing a Clinical Data Set and Two Monte Carlo

Simulation

Studies. Clin. Pharmacokinet., 45: 365-383, 2006.

8. Macdonald I, Staatz C, Jelliffe R, and Thomson A: Evaluation and

Comparison of Simple Multiple Model, Richer Data Multiple Model, and

Sequential Interacting Multiple Model (IMM) Bayesian Analyses of

Gentamicin

and Vancomycin Data Collected From Patients Undergoing Cardiothoracic

Surgery. Ther. Drug Monit. 30:67-74, 2008.

9. Jelliffe R, Schumitzky A, Bayard D, Leary R, Botnen A, Van Guilder

M, Bustad A, and Neely M: Human Genetic variation, Population

Pharmacokinetic - Dynamic Models, Bayesian feedback control, and

Maximally

precise Individualized drug dosage regimens. Current Pharmacogenomics

and

Personalized Medicine, 7: 249-262, 2009.

10. Neely M, van Guilder M, Yamada W, Schumitzky A, and Jelliffe R:

Accurate Detection of Outliers and Subpopulations with Pmetrics, a

Nonparametric and Parametric Pharmacometric Modeling and Simulation

Package

for R. Therap. Drug Monit. 34: 467-476, 2012.

11. Tatarinova T, Neely M, Bartroff J, van Guilder M, Walter Yamada W,

Bayard D, Jelliffe R, Leary R, Chubatiuk A, and Schumitzky A: Two

General

Methods for Population Pharmacokinetic Modeling: Non-Parametric Adaptive

Grid and Non-Parametric Bayesian. J. Pharmacokin. Pharmacodyn, in press.

Very best regards,

Roger Jelliffe

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

Professor of Medicine,

Founder and Co-Director, Laboratory of Applied Pharmacokinetics

www.lapk.org

USC Keck School of Medicine

2250 Alcazar St, Room 134-B

Los Angeles CA 90033 - On 8 Feb 2013 at 03:46:06, "Wang, Yaning" (Yaning.Wang.-at-.fda.hhs.gov) sent the message

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Hi, Bernard:

AUC normalized concentration curve (Ct/AUC) can be described as follows

(assuming F=1 for simplicity):

Ct/AUC=Ct/(Dose/CL)=Ct/(Dose/(V*K))=(Ct*V/Dose)*K

Ct*V/Dose is the fraction of drug molecules remaining (alive) in the

body at time t. This is the same as survival function in statistics,

S(t), proportion of people still alive at time t. K is approximately the

fraction of drug (relative to the drug amount at time t) eliminated from

the body within a small time interval (I like this way of interpreting K

because K can always be converted to a <1 number by scaling time to a

very small unit, such as min, sec, to make K intuitively meaningful.

E.g. K=1/hr can be expressed as 0.0167/min, meaning approximately 1.67%

of remaining drug molecules is eliminated within 1 min). In survival

statistics, K is the same as hazard or conditional failure rate (h), the

fraction of people (relative to the people alive at time t) dying within

a small time interval. Then (Ct*V/Dose)*K is the fraction of drug

molecules (relative to the total dose) eliminated at time t (within a

small time interval around time t). To make it more consistent with the

statistical description, (Ct*V/Dose)*K is the fraction of drug molecules

(relative to the total dose) that has a residence time (survival in the

body) of t because this fraction of drug molecules are not eliminated

(die) until time t. This is the same as the density function or

unconditional failure rate, f(t), in survival statistics. And it is well

known f(t)=S(t)*h. So at each t, Ct/AUC is just like a histogram summary

(expressed as proportion) of drug molecules with different residence

times. E.g. at Ct/AUC=0.1 at 2 hours means that 10% of drug molecules

survived up to 2 hours (residence time=2). Ct/AUC=0.2 at 10 hours means

that 20% of drug molecules survived up to 10 hours (residence time=10).

Therefore, the raw Ct/AUC can be used to calculate the mean residence

time. I hope this will help your colleagues to understand this PK

concept better. There is a close link between PK and survival

statistics. PK is basically a description of the drug molecules

surviving in the body.

David:

Any first order process can be described as a random walk process. The

rate constant can be interpreted as the probability of moving to another

state (compartment) and 1-rate constant is the probability of staying at

the current state (compartment). Of course, the rate constant needs to

be converted to a <1 number as described above to make this

interpretation meaningful.

Thanks

Yaning

Yaning Wang, Ph.D.

Associate Director for Science

Division of Pharmacometrics

Office of Clinical Pharmacology

Office of Translational Science

Center for Drug Evaluation and Research

U.S. Food and Drug Administration

"The contents of this message are mine personally and do not necessarily

reflect any position of the Government or the Food and Drug

Administration." - On 8 Feb 2013 at 09:46:45, Bernard Murray (Bernard.Murray.-at-.gilead.com) sent the message

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The following message was posted to: PharmPK

Hello Roger,

I understand your concern about inappropriate use of NCA, but in this

case it is being applied to nonclinical studies, either to early

discovery pharmacokinetics or to toxicokinetics. The aim is only to

have simple, objective measures of exposure (AUC, Cmax etc.) and

persistence (MRT). My colleague's question was largely triggered by

curiosity as to how MRT calculations were performed. There are some

nice papers on the use of higher statistical moments in pharmacokinetics

(e.g. Weiss & Pang, J Pharmacokin Biopharm, 20: 253-278 [1992]) but, for

reasons I mentioned before, they are not routinely applicable.

I can assure you that we switch to compartmental modeling for

development candidate molecules, or for those used in nonclinical

pharmacodynamic models. It is unfortunate that we don't have time to

develop and validate more sophisticated models for some of our more

"interesting" compounds.

Thank you very much for the literature review. I'll pass that to my

colleague and I am sure that there will be future mentoring sessions on

that topic.

All the very best,

Bernard

Bernard Murray, Ph.D.

Senior Research Scientist, Drug Metabolism

Gilead Sciences - On 12 Feb 2013 at 18:12:14, (Angusmdmclean.at.aol.com) sent the message

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Yaning: Thank you for your informative and thought provoking commentary

concerning the significance of the AUC normalized concentration curve Ct/AUC.

Could I ask you to enlarge upon it a little to include the significance

of

Cmax/AUC inf quotient.

Thanks

Angus McLean Ph.D. - On 14 Feb 2013 at 03:45:12, "Wang, Yaning" (Yaning.Wang.at.fda.hhs.gov) sent the message

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The following message was posted to: PharmPK

Angus:

Following "Ct/AUC is just like a histogram summary (expressed as proportion) of

drug molecules with different residence times", Cmax(observed)/AUC is the peak

of this histogram, representing the largest fraction of drug molecules with a

specific residence time: Tmax (observed).

Thanks

Yaning

Yaning Wang, Ph.D.

Associate Director for Science

Division of Pharmacometrics

Office of Clinical Pharmacology

Office of Translational Science

Center for Drug Evaluation and Research

U.S. Food and Drug Administration - On 14 Feb 2013 at 08:51:32, (Angusmdmclean.-a-.aol.com) sent the message

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Yaning: As you are aware Ct/AUC has the dimension of time. Therefore

could I say that Cmax(observed)/AUC is the peak of the Ct/AUC histogram

and represents the time of occurrence of the largest fraction of drug

molecules with a specific residence time (Tmax (observed).

Do you agree with this way of putting it?

Angus McLean

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