- On 3 Aug 2000 at 22:54:19, Korbtham Sathirakul (pyksk.-at-.mahidol.ac.th) sent the message

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Dear All

I am now suprising that there are still be quite a few people estimate the

AUC by using the linear trepazoid. According to Gabrielsson textbook for

PK and PD data analysis, their group strongly suggested the log/linear

trepazoid. I myself teach my students to do the log/linear trepazoid.

However, i found that in pharm industry, quite a few of people still used

the linear one. Could anybody please contribute to comment on using linear

or log/linear trepazoid. Thank you very much.

Best regards

Asoc. Prof. Dr. Korbtham Sathirkaul

Faculty of Pharmacy

Mahidol University

Bangkok, Thailand. - On 4 Aug 2000 at 11:29:20, "Derrick J (Rick) Bates" (DJ.Rick.Bates.-at-.pnl.gov) sent the message

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My own preference is to dispense with either of the two methods below

(which I label AUTs - Area Under the Trapezoids) that were originally

developed as a quick and dirty approximations to the real

AUC - Area under the Curve.

I prefer to use the real Area under the Curve from the fitted model.

For example, in the simple exponential model, this is easily estimated

as Co/ke, where Co is the estimated concentration at time 0

and ke is the estimated elimination coefficient. - On 4 Aug 2000 at 14:29:51, Roger Jelliffe (jelliffe.-a-.usc.edu) sent the message

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Dear Dr. Sathirakul:

About AUC's. Why not make a model of the behavior of the

drug, and then simulate with the model and compute the AUC that way?

You could use a Bayesian approach based first on a population model

and then on whatever serum data you obtain from an individual

patient. You would also capture the relationships between the doses,

the concentrations found, and the AUC, and it would be easy to

compute the regimen to achieve a desired concentration for a desired

time, or a desired profile until a desired AUC is reached? Any

comments, anyone?

Roger Jelliffe

Roger W. Jelliffe, M.D. Professor of Medicine, USC

USC Laboratory of Applied Pharmacokinetics

2250 Alcazar St, Los Angeles CA 90033, USA

Phone (323)442-1300, fax (323)442-1302, email= jelliffe.aaa.hsc.usc.edu

Our web site= http://www.usc.edu/hsc/lab_apk

**** - On 4 Aug 2000 at 14:30:25, "Paul B. Laub" (plaub.-a-.incyte.com) sent the message

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Here are several useful papers on the AUC / noncompartmental analysis topic --

Robert Purves

"Optimum Numerical Integration Methods for Estimation of Area-Under-the-Curve

(AUC) and Area-Under-the-Moment-Curve (AUMC)" in JPB 20: 211-226 (1992).

KC Yeh and KC Kwan, "A Comparison of Numerical Integrating Algorithms by

Trapezoidal, Lagrange, and Spline Approximation" Journal of

Pharmacokinetics and

Biopharmaceutics (JPB) 6: 79-98 (1978).

ML Rocci, Jr and WJ Jusko, "LAGRAN program for area and moments in

pharmacokinetic analysis" Computer Programs in Biomedicine 16: 203-216 (1983)

P.B. Laub and J.M. Gallo

"NCOMP - A Windows-based Computer Program for

Noncompartmental Analysis of Pharmacokinetic Data"

J. Pharm. Sci. 85: 393-395 (1996)

Paul

--

-- 30 -- 30 -- 30 --

Mr. Paul B. Laub Expression Bioinformatics (650) 845-5411 (voice)

Incyte Genomics (650) 855-0572 (fax)

3160 Porter Dr. Palo Alto, CA 94304 plaub.-a-.incyte.com - On 6 Aug 2000 at 22:17:07, Stephen Day (shday.aaa.yahoo.com) sent the message

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I find this post needs some comment.

>

> My own preference is to dispense with either of the

> two methods below

> (which I label AUTs - Area Under the Trapezoids)

> that were originally

> developed as a quick and dirty approximations to

> the real

> AUC - Area under the Curve.

Really? This method is used in every other field of

science to calculate the area under a curve. I can

assure you it was not developed as a quick and dirty

approximation - it was just good mathematics (and

still is).

If the rate of change of concentration is first-order

with respect to concentration, the Log-linear method

gives the *exact* area between two data points. No

quick and dirty here.

>

> I prefer to use the real Area under the Curve from

> the fitted model.

Models are never perfect, therefore you will still

only find an estimate of the "real" AUC in this way.

Why rely on the accuracy of any model when you can use

one of the trapezoid methods?

=====

Stephen Day

Merck-Frosst Centre for Therapeutic Research

Kirkland, QC CANADA - On 6 Aug 2000 at 22:17:25, "Lakritz, Jeffrey" (LakritzJ.at.missouri.edu) sent the message

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Dear Drs. Jelliffe, Sathirakul, et al,

While we are on the subject of AUC's. I analyzed some data on a 3rd

generation cephalosporin after IV, IM and subcutaneous administration in

animals. The AUC after IM and sub Q came out significantly higher than

after IV, so bioavailability is >100%. I determined the AUC using the

trapezoidal approximations. Since I am going to have to go back and try to

determine how this happened, could anyone suggest why? I suppose, that

after IV the drug is more rapidly cleared via the kidney than after IM/SQ.

Any thoughts for a beginner?

Jeff Lakritz DVM, PhD. - On 7 Aug 2000 at 11:25:47, David_Bourne (david.aaa.boomer.org) sent the message

Back to the Top

[A few replies from over the weekend - db]

Sender: PharmPK.aaa.boomer.org

Reply-To: Nick Holford

MIME-Version: 1.0

From: Nick Holford

Date: Sat, 05 Aug 2000 08:46:49 +1200

To: david.-at-.boomer.org

Subject: Re: PharmPK Re: Log-linear or linear trapezoid

The following message was posted to: PharmPK

"Derrick J (Rick) Bates (by way of David_Bourne)" wrote:

> My own preference is to dispense with either of the two methods below

> (which I label AUTs - Area Under the Trapezoids) that were originally

> developed as a quick and dirty approximations to the real

> AUC - Area under the Curve.

The "AUT"s (0-inf or over SS Dosing Interval) are themselves only of

any real PK value as initial estimates of Clearance/F.

> I prefer to use the real Area under the Curve from the fitted model.

> For example, in the simple exponential model, this is

>easily estimated

> as Co/ke, where Co is the estimated concentration at time 0

> and ke is the estimated elimination coefficient.---

More generally (any number of compartments) "real" AUC can be

computed from Dose*F/CL. Any (linear) PK model should be

parameterizable in terms of CL/F so you only need to know one

parameter (CL/F) (rather than two, C0,ke, as Derrick suggests).

But if I have an estimate of CL/F why would I have any

pharmacokinetic reason to bother calculating AUC? Perhaps the only

reason is to satisfy regulatory bioequivalance guidelines -- but in

this context any pharmacokinetic science (e.g. compartmental models)

is typically too hard for the regulators and one must resort to

empirical AUC, Tmax, Cmax statistics developed at the Walt Disney

School of Pharmacokinetics.

AUC (derived from Dose*F/CL) has some use as an empirical "exposure"

quantity in pharmacodynamics. But because information about time is

necessarily lost by integration of C wrt t learning about schedule

dependence is very hard. I believe the AUC approach to

pharmacodynamics was also developed at the Walt Disney School of

Pharmacokinetics. Many graduates of WDSP seem to be working in the

anti-cancer field which is perhaps a reflection of why it is

difficult to find examples that demonstrate that AUC is any better

than dose as a predictor of drug response in this area.

--

Nick Holford, Dept Pharmacology & Clinical Pharmacology

University of Auckland, Private Bag 92019, Auckland, New Zealand

email:n.holford.-a-.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556

http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm

---

Sender: PharmPK.aaa.boomer.org

Reply-To: "J.G. Wright"

MIME-Version: 1.0

From: "J.G. Wright"

Date: Mon, 7 Aug 2000 12:07:42 +0100 (GMT)

To: david.at.boomer.org

Subject: Re: PharmPK Re: Log-linear or linear trapezoid

The following message was posted to: PharmPK

Dear Stephen,

Let say I give a bolus dose, and then take a couple of samples. In all

but a few cases (eg enterohepatic recycling), concentration will decrease

with time. So if I put my

first point at time zero, concentration zero, I will miss a big chunk

of the AUC and obtain

correspondingly biased estimates of clearances. If you back-extrapolate

in some way, then you are modelling and you may a well do it in a

statistical manner, acknowledging uncertainty.

Join-the-dots pharmacokinetics (whatever good mathematics it calls upon)

ignores two fundamental factors - the dosing history and the existence of

error. You say that the loglinear trapezoidal gives an exact area between

two points - this would only be true if the samples are error-less. They

are measured with error and it probably will not be the same at both

points.

There is a common misconception that noncompartmental methods are

model-independent. This is not the case, they are simply based on

assumptions which are somewhat physiologically strange (straight lines

join the dots,

on some scale) and hence unstated. As the use of

AUC to calculate clearance depends on many of the assumptions required for

a simple compartmental model, speed and perhap simplicity are all that is

gained.

In a pharmacological context, there is a lot to understand. Join-the-dots

pharmacokinetics doesn't acknowledge its assumptions and furthermore

provides no diagnostics for when they are violated. A method cannot be

divorced from its context - trapezoidal AUCs are quick and very dirty.

On the other hand,

timing error won't make much difference...

Regards,

James Wright

---

Sender: PharmPK.-a-.boomer.org

Reply-To: "Bhatti, Masood"

MIME-Version: 1.0

From: "Bhatti, Masood"

Date: Mon, 7 Aug 2000 09:22:52 -0400

To: david.-a-.boomer.org

Subject: RE: PharmPK Re: Log-linear or linear trapezoid

The following message was posted to: PharmPK

Dear Jeff,

Is it possible that your drug is undergoing first pass lung metabolism after

I.V. administration?

Masood Bhatti

Section Leader

Purdue Pharma

---

Sender: PharmPK.-a-.boomer.org

Reply-To: zhao wang

Mime-Version: 1.0

From: zhao wang

Date: Mon, 07 Aug 2000 09:05:01 -0500

To: david.at.boomer.org

Subject: Re: PharmPK Re: Log-linear or linear trapezoid

The following message was posted to: PharmPK

I think:

1) IV does not make kidney clearance "more rapidly"and this the one

of the assumptions that is made to estimate BA;

2) Try normalize the dose by body weight for each subject being studied;

3) Try use the same subject for different administration;

4) Simultaneously IV, oral and sub Q modeling to estimate BA will be

more accuracy but you need a software like SAAM II.

5) If each study (different dose administration ) is from different

subject, there will be some variation of Vd and Cle from either

inter-or intra individuals and therefore, if the variation of BA

estimation is within this range, it should be acceptable, 105% of BA

does not mean BA > 100%, but the variation of estimation.

Just some thoughts.

Zhao Wang, M.D.

Northwestern University Medical School

Anesthesia Research

---

Sender: PharmPK.aaa.boomer.org

Reply-To: "David S. Farrier"

Mime-Version: 1.0

From: "David S. Farrier"

Date: Mon, 07 Aug 2000 10:35:49 -0400

To: david.-at-.boomer.org

Subject: Re: PharmPK Re: Log-linear or linear trapezoid

The following message was posted to: PharmPK

A group from Phoenix International's PK Department presented a poster in

1996 at the AAPS annual meeting. They ran simulations comparing the results

of calculating AUC using trapezoid, log-trapezod, and spline smoothing

methods. Their conclusion was: given the normal variability of plasma level

data, the log-trapezoid and spline methods did not give a statistically

better estimate of the AUC than the standard trapezoid rule.

We built and tested a module for PK Solutions that produced a side-by-side

comparison of AUC values (partials and cumulative) calculated by both the

standard trapezoid and log-trapezoid methods. The overall results were

statistically so similar, except with rare and unlikely plasma profiles,

that we decided to only use the standard trapezoid method for our software.

Not that log-trapezoid is any more difficult or sophisticated, but why make

things more esoteric when the simpler approach is adequate and justified.

David

David S. Farrier, Ph.D.

Summit Research Services

1374 Hillcrest Drive

Ashland, OH 44805 USA

Tel/Fax: (419)-289-9207

Email: DFarrier.aaa.SummitPK.com

Web Site: www.SummitPK.com

[I seem to remember a paper by Kwan (some time back) that came to a

similar conclusion...I had a graduate student do some (limited)

simulations once and we came to same conclusion. However, Purves

paper and suggestion convinced to add a one after the other

comparison in Boomer output. Linear trapezoid and Purves' linear /

log-linear method - db] - On 8 Aug 2000 at 10:29:56, ml11439.aaa.goodnet.com sent the message

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Dr.Lakritz,

The reason why bioavailability(F)= AUCoral/AUCiv is that

the first order absorption equation Cp= [KaFd/Vd(Ka-Ke)][e-Ket- e-Kat]

when integrated from infinity->0 reduces to:

AUCoral= FD/VdKe

When compared to AUCiv= D/VdKe

AUCoral= (F)*AUCiv

Since an F value greater than one is not possible, the possibility

of a decreased Ke when given by the IV route is one of the most likely

possibilities. At any rate, some factor is affecting the determination

of the Ke value when given by different routes.

Mike Leibold, PharmD, RPh

ML11439.aaa.goodnet.com - On 8 Aug 2000 at 11:07:27, "stefans" (stefans.-at-.moag.gov.il) sent the message

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Dear Friends,

I've been following your interesting discussion concerning the AUC

determination. I'd like to add one more aspect to the discussion

that, in my understanding, nobody has addressed yet.

The analytical error at the end of a concentration vs. time curve

increases (especially when the concentrations are analyzed to the

limit of the method). There appears to be a possibility that only

data points that fall on the "positive" side of the LOQ will be

recorded while those on the "negative" side would fall in the

category of non-quantifiable. This seems to be a possibility

especially with shallow curves.

My question is: What is the effect of the analytical error at or

close to the LOQ on the determination of AUC by curve fitting

especially when weighting is used?

With best regaards,

Stefan Soback, DVM, PhD

Kimron Veterinary Institute

Beit Dagan

Israel - On 8 Aug 2000 at 21:20:09, Nick Holford (n.holford.aaa.auckland.ac.nz) sent the message

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by way of David_Bourne wrote:

>

> The reason why bioavailability(F)= AUCoral/AUCiv is that

> the first order absorption equation Cp= [KaFd/Vd(Ka-Ke)][e-Ket- e-Kat]

> when integrated from infinity->0 reduces to:

>

> AUCoral= FD/VdKe

> Since an F value greater than one is not possible, the possibility

> of a decreased Ke when given by the IV route is one of the most likely

> possibilities. At any rate, some factor is affecting the determination

> of the Ke value when given by different routes.

Algebra CL=Vd x Ke

Biology Ke=CL / Vd

From a biological perspective clearance and volume of distribution are

quite distinct. Ignoring random variation one can consider them to be

"constant". The elimination rate "constant" is only a constant if CL and

Vd do not change. A change in either CL or Vd will alter Ke.

However, ONLY a change in CL will change AUC. A change in Vd cannot

change AUC (for a drug wihe linear kinetics integrated from 0-inf for a

single dose or over a dosing interval at steady state).

The asssumption of linear kinetics is easily violated when oral doses

are given. Rate dependent extent of absorption can occur easily because

portal vein concs can be high enough to cause the mixed order

elimination during first pass. Inspection of plasma conc profiles may

only support first order elimination.

A higher AUCoral than AUCiv can occur if the oral absorption rate is

rapid. This can lead to erroneous conclusions. One of the most infamous

examples is the widely cited but erroneous assertion that the stomach is

a major source of first pass metabolism of ethanol. Frezza M. di Padova

C. Pozzato G. Terpin M. Baraona E. Lieber CS. High blood alcohol levels

in women. The role of decreased gastric alcohol dehydrogenase activity

and first-pass metabolism [published errata appear in N Engl J Med 1990

May 24;322(21):1540 and 1990 Aug 23;323(8):553] New England Journal of

Medicine. 322(2):95-9, 1990 Jan 11. These authors completely ignored the

mixed order elimination of ethanol and interpreted the ratio of

AUCoral/AUViv as a measure of extent of absorption. The NEJM is not an

authoratative source for PK issues!

--

Nick Holford, Division of Pharmacology & Clinical Pharmacology

University of Auckland, Private Bag 92019, 85 Park Road, Auckland, NZ

email: n.holford.at.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556

http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm - On 8 Aug 2000 at 21:21:20, Nick Holford (n.holford.-at-.auckland.ac.nz) sent the message

Back to the Top

"stefans (by way of David_Bourne)" wrote:

>

> The analytical error at the end of a concentration vs. time curve

> increases (especially when the concentrations are analyzed to the

> limit of the method). There appears to be a possibility that only

> data points that fall on the "positive" side of the LOQ will be

> recorded while those on the "negative" side would fall in the

> category of non-quantifiable. This seems to be a possibility

> especially with shallow curves.

>

> My question is: What is the effect of the analytical error at or

> close to the LOQ on the determination of AUC by curve fitting

> especially when weighting is used?

The role of analytical error (and other sources of random variation) can

be recognized by using a model based approach and bypassing the Walt

Disney AUC step all together.

--

Nick Holford, Division of Pharmacology & Clinical Pharmacology

University of Auckland, Private Bag 92019, 85 Park Road, Auckland, NZ

email: n.holford.-a-.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556

http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm - On 9 Aug 2000 at 10:07:07, prashant bodhe (prashnvb.-at-.dr.com) sent the message

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Dear Members

My opinion on the issue is as follows

1. In case of biological research field especially like PK, we can closely

approximate the facts and not determine them exactly. And I feel it

impossible and un-necessary as well to have 100% accuracy. (one of the

factors is cost involved).

With the accuracy and precision levels currently prevailing, the purpose of

studying the PK of drugs is generally seved.

2. The impact of the values close to LOQ on AUC can be ignored. Because the

contribution of the corresponding AUC(Tm to Tn) to the total AUC is

generally small.

3. In very few cases it may not be so. Then the analytical method needs

'upgradation' - On 9 Aug 2000 at 10:08:12, "David S. Farrier" (DFarrier.aaa.SummitPK.com) sent the message

Back to the Top

>The role of analytical error (and other sources of random variation) can

>be recognized by using a model based approach and bypassing the Walt

>Disney AUC step all together.

>

>--

>Nick Holford, Division of Pharmacology & Clinical Pharmacology

True Nick, except FDA only accepts the Disney-like, model-independent

approach for bioequivalence studies.

David S. Farrier, Ph.D.

Summit Research Services

1374 Hillcrest Drive

Ashland, OH 44805 USA

Tel/Fax: (419)-289-9207

Email: DFarrier.-a-.SummitPK.com

Web Site: www.SummitPK.com - On 10 Aug 2000 at 23:27:09, Roger Jelliffe (jelliffe.-a-.usc.edu) sent the message

Back to the Top

Dear Members:

About accuracy and precision. They ARE important. At least

for potentially toxic drugs, we are not playing with data, we are

modeling it so we can act on it OPTIMALLY, that is, to develop dosage

regimens to achieve desired target goals with maximal precision.

The issue of LOQ is also important here. I hate to belabor

this point, but when we have no other info about the specimen except

the measured value itself, then there most certainly IS a LOQ.

However, when we do most PK work, that is not the case. We know, with

reasonable precision, when the doses were given and when the samples

were obtained. So we know the drug is really present. Even simple

linear models show us that the last molecule is never excreted. So,

instead of having to ask, as we must in toxicological work, if the

drug is PRESENT OR NOT, and having therefore to develop a LOQ, we

know the drug is present. The question being asked is not the same as

in toxicology. It is instead - HOW MUCH drug is present?

Now comes the question of weighting the data optimally. Most

people agree that weighting data by its Fisher information is

appropriate - the reciprocal of the variance of the data point. It

works quite well. The point is that when you determine the assay

error and express it as a polynomial function of the concentration,

that important relationship continues over the entire range of the

assay, down to and including the blank, if you set it up correctly.

This point is discussed in more detail in an article in Therap Drug

Monit 15:380-393, 1993, especially the section on Evaluating the

Credibility of Population Parameter Values and Serum Level Data, pp.

386-391.

Best regards,

Roger Jelliffe

Roger W. Jelliffe, M.D. Professor of Medicine, USC

USC Laboratory of Applied Pharmacokinetics

2250 Alcazar St, Los Angeles CA 90033, USA

Phone (323)442-1300, fax (323)442-1302, email= jelliffe.-a-.hsc.usc.edu

Our web site= http://www.usc.edu/hsc/lab_apk

******* - On 11 Aug 2000 at 13:04:24, "Derrick J (Rick) Bates" (DJ.Rick.Bates.aaa.pnl.gov) sent the message

Back to the Top

> I've been following your interesting discussion concerning the AUC

> determination. I'd like to add one more aspect to the discussion

> that, in my understanding, nobody has addressed yet.

>

> The analytical error at the end of a concentration vs. time curve

> increases (especially when the concentrations are analyzed to the

> limit of the method).

First, a digression from your main point below.

Well, it is true that the analytical error/precision at the end of

a concentration vs. time curve typically increases in a RELATIVE

sense, i.e, the analytical error relative to the result increases.

It is also true that the analytical error/precision at the end of

a concentration vs. time curve generally decreases in an ABSOLUTE

sense, i.e. the analytical error/precision itself gets smaller and

smaller towards the end of the concentration vs. time curve

(basically the low end of the calibration curve).

> There appears to be a possibility that only

> data points that fall on the "positive" side of the LOQ will be

> recorded while those on the "negative" side would fall in the

> category of non-quantifiable. This seems to be a possibility

> especially with shallow curves.

>

Happens all the time in the data I see.

But this is a topic that I will avoid getting mired in here.

Oops, now a second digression just occurred to me.

Another reason I prefer to use AUCs (Area Under Curve)

instead of AUTs (Area under Trapezoids)

is because of the ability to generate uncertainty estimates

(measures of quality) for AUCs whereas I seem to have to accept

AUTs with no concept of uncertainty or quality measure for them.

> My question is: What is the effect of the analytical error at or

> close to the LOQ on the determination of AUC by curve fitting

> especially when weighting is used?

>

Since the model fitting programs I am aware of try to minimize

the ABSOLUTE errors instead of the RELATIVE errors then

analytical error at the end of the curve should have minimal

effect on the determination of the AUC.

Having said that, it must of course be caveated when weighting

is used. The end effect of weighting is minimize what become

"relative" errors.

My personal experience has been that LOQ and weighting seem to

have minimal effect on the AUC estimates except in those cases

where the terminal elimination becomes very flat and gets

extrapolated to infinity. It is this extrapolation to infinity

that is the source of the problem. The same problem would exist

for the AUT if it was extrapolated to infinity by the terminal

elimination estimate. - On 16 Aug 2000 at 16:07:03, Roger Jelliffe (jelliffe.at.usc.edu) sent the message

Back to the Top

Dear Derrick:

Good for you! You are right - the absolute error, not the

relative error, is the important thing. The SD and the variance, not

the CV%, are what is important in determining the credibility of a

data point by its Fisher information

Best regards,

Roger Jelliffe

Roger W. Jelliffe, M.D. Professor of Medicine, USC

USC Laboratory of Applied Pharmacokinetics

2250 Alcazar St, Los Angeles CA 90033, USA

Phone (323)442-1300, fax (323)442-1302, email= jelliffe.aaa.hsc.usc.edu

Our web site= http://www.usc.edu/hsc/lab_apk

*****

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