- On 26 Feb 2003 at 10:01:34, Virginia Fajt (fajt.-at-.iastate.edu) sent the message

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List Members,

What is the distribution of serum concentration values (of most drugs)

usually assumed to be? I have seen several references to normal and

log-normal, and I wonder what evidence there is for any of these. I

also

just read a paper suggesting a gamma or log Cauchy distribution might be

more appropriate. We are dealing with small numbers of animals and

often

have insufficient data to test our assumptions, so any comments would be

appreciated.

Thanks,

vf

Virginia Fajt, DVM, PhD

Pueblo, Colorado

fajt.-at-.iastate.edu - On 26 Feb 2003 at 15:11:24, RPop.-at-.pharmamedica.com sent the message

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Hi Virginia,

The commonly accepted statistical distribution for drug levels is the

log-normal distribution.

The possible values for the drug concentration in blood/serum/plasma

are limited on the lower-value side by the LOQ of the analytical

method, while the high-value end is open. Therefore, the actual

distribution is not symmetrical.

It was said that this kind of distributions become "normal" after

log-transformation (the compression of the scale at the high-value end).

For this reason the extensive pharmacokinetic parameters (AUC, Cmax)

are analyzed statistically under the normal distribution assumption

after the log-transformation.

I hope this help,

radu

Radu D. Pop

Director Biopharmaceutics

Pharma Medica Research Inc.

966 Pantera Drive

Mississauga, Ontario

Canada, L4W 2S1 - On 27 Feb 2003 at 10:29:09, Nick Holford (n.holford.at.auckland.ac.nz) sent the message

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RPop.-at-.pharmamedica.com wrote:

>

> PharmPK - Discussions about Pharmacokinetics

> Pharmacodynamics and related topics

>

> Hi Virginia,

> The commonly accepted statistical distribution for drug levels is the

> log-normal distribution.

The simple log-normal distribution may is probably only commonly

accepted by pharmacokineticists who do not use PK residual error

models. More plausible (and empirically verifiable) models for the

residual error in concentrations typically have a proportional

component (similar to log normal distribution) and a concentration

independent (normal distribution) additive component. The proportional

component is usually used by analytical chemists to describe their

assay as "%CV" of replicate measurements. The additive component is a

measure of "background noise" and reflects the reality that a simple

constant CV error model is not appropriate at concentrations which

challenge the assay sensitivity.

> The possible values for the drug concentration in blood/serum/plasma

> are limited on the lower-value side by the LOQ of the analytical

> method, while the high-value end is open. Therefore, the actual

> distribution is not symmetrical.

> It was said that this kind of distributions become "normal" after

> log-transformation (the compression of the scale at the high-value

> end).

The additive component helps to protect somewhat against the

difficulties caused by analytical chemists arbitrarily truncating their

measurements by the use of LOQ (discussed many times on this list

before).

> For this reason the extensive pharmacokinetic parameters (AUC, Cmax)

> are analyzed statistically under the normal distribution assumption

> after the log-transformation.

The distributions of AUC and Cmax have a different justification. Their

are two sources of random variability in these values. The first and

typically minor component is due to the measurement error (decribable

by the residual error models discussed above). The second, and

quantitatively much larger, component is due to the between

subject/between occasion variability. These random effects have

typically been modelled under the assumption of a log-normal

distribution because 1) all AUC and Cmax values must be non-negative

and the normal assumption does not enforce this assumption 2) the

distribution of estimates of AUC and Cmax in reasonable sample sizes

are often right skewed which is compatible with a log-normal

distribution.

Nick

Nick Holford, Divn Pharmacology & Clinical Pharmacology

University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New

Zealand

email:n.holford.-at-.auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556

http://www.health.auckland.ac.nz/pharmacology/staff/nholford/ - On 27 Feb 2003 at 08:56:22, "Eliane Fuseau" (eliane.-at-.emf-consulting.com) sent the message

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Nick and others,

Different problem, but somewhat related: have you ever been in the

situation of analysing a phase IIa dose ranging study, with parallel

design and geometric progression of doses, people sampled at trough

steady-state?

High doses and/or concentrations (not clear whether a priori or not)

were assayed after multiple dilutions, while low doses groups use the

"normal" calibration curve. This was an LC-MS/MS assay validated from 10

to 10,000ng/mL, going up to 100,000ng/mL after dilutions at 2, 5, 10 or

20 ratios.

We have great difficulties with multiple combined additive +

multiplicative error models, each for different ranges of concentrations

determined by dose range...

Thanks for any new idea!

Eliane

Eliane Fuseau, PhD, CEO

EMF Consulting

BP 2

13545 Aix en Provence cedex 4

tel +33 442 908 102

fax +33 442 908 101

mobile +33 622 040 516

eliane.aaa.emf-consulting.com - On 28 Feb 2003 at 09:01:02, Nick Holford (n.holford.-at-.auckland.ac.nz) sent the message

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The following message was posted to: PharmPK

Elaine,

Eliane Fuseau wrote:

> Different problem, but somewhat related: have you ever been in the

> situation of analysing a phase IIa dose ranging study, with parallel

> design and geometric progression of doses, people sampled at trough

> steady-state?

> High doses and/or concentrations (not clear whether a priori or not)

> were assayed after multiple dilutions, while low doses groups use the

> "normal" calibration curve. This was an LC-MS/MS assay validated from

> 10

> to 10,000ng/mL, going up to 100,000ng/mL after dilutions at 2, 5, 10 or

> 20 ratios.

> We have great difficulties with multiple combined additive +

> multiplicative error models, each for different ranges of

> concentrations

> determined by dose range...

Hard to answer your question without you being more explicit about the

"great difficulties". I assume you are attempting a NONMEM analysis of

the PK data with different residual error models for each dose range.

One approach would be to estimate the parameters of a variance model

for the assay error from replicate known concs measured using each

calibration curve. Then use these model parameters as fixed SIGMAs for

each calibration curve range and use an extra one or two SIGMAs to

estimate the model misspecification component of the residual error.

You could then focus on the PK part of the model (the signal) instead

of the residual error (the noise).

e.g.

Assume replicate measurements of standard concs for calibration curve i

have this model:

var(i) = int(i) + slope(i)*stdconc(j)

then in your NM-TRAN control stream you might do this:

$SIGMA int(1) FIX ; ERR1 Additive part of calib curve 1

$SIGMA slope(1) FIX ; ERR2 Proportional part of calib curve 1

.... etc for each calib curve

$SIGMA misspec ; ERR3 Model misspecification variance

$ERROR

; provide a data item CURV that indicates which calibration curve was

used for each DV

IF (CURV.EQ.1) THEN

ASSERR=ERR(1) + ERR(2)*F ; random effect due to assay error

ENDIF

MDLERR=ERR(3) ; random effect due to model misspecification

Y = F + ASSERR + MLDERR

If you want you could include the replicate concs as DVs and estimate

int(i) and slope(i) jointly with the PK model parameters.

Bonne chance!

Nick

Nick Holford, Divn Pharmacology & Clinical Pharmacology

University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New

Zealand

email:n.holford.-at-.auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556

http://www.health.auckland.ac.nz/pharmacology/staff/nholford/

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