- On 29 May 2005 at 09:53:01, Daniel Byrd (byrdd.at.cox.net) sent the message

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The following message was posted to: PharmPK

TO: PharmPK

On May 19, 2005, I asked Nick Holford (Department of Pharmacology &

Clinical Pharmacology at the University of Auckland in New Zealand) and

Hans Proost (Department of Pharmacokinetics and Drug Delivery at the

University Centre for Pharmacy in the Netherlands) what they meant by a

"standard two-stage" (STS) model? I appreciated their efforts in

sharing information with viewers of PharmPK, but they started a

discussion that I could not follow, in part because of nomenclature.

"STS" in a risk assessment context (more my field), implies the use of a

filtered Poisson model (e.g., Suresh Moolgavkar's "two-stage" model).

However, their comments suggested that my inference was incorrect.

They kindly replied individually with messages, which I edited and will

share with the note group as follows:

(A) Nick Holford:

If you search with Google for "standard two stage pharmacokinetic" gives

many hits illustrating its wide spread use in the PK field. I believe

this name was first proposed here Rowland M, Sheiner LB, Steimer JL.

Variability in drug therapy: description, estimation, and control. New

York: Raven Press; 1985.

The two stage method is:

1. Estimate parameters from each individual, e.g., Clearance (CL) and

volume (V)

2. Calculate the average and standard deviation for each parameter

across the sample of individuals.

The average is an estimate of the population mean CL and the standard

deviation is an estimate of the population parameter variability (PPV)

(both between and within subject).

The standard two stage method stops at this point. The estimates of the

means are expected to be OK, but the PPV is upwardly biased because it

includes the (wanted) between and within subject variability and the

(unwanted) uncertainty arising from the imprecision of the individual

estimates.

Details of this and other methods can be found here: Racine-Poon A,

Wakefield J. Statistical methods for population pharmacokinetic

modeling. Stat Methods Med Res 1998;7(1):63-84.

http://www.ingentaconnect.com/content/arn/sm/1998/00000007/00000001/art00006

(B) Hans Proost:

The PharmPK group often uses terms and abbreviations without explaining

what is meant. This is quite practical and efficient as long as

everybody understands the same. Of course this is not always the case,

and a question like yours may be helpful to be more clear.

In my view, the 'standard two-stage' (STS) approach (or method; not

'model') in population analysis (or shortly 'STS analysis') is the

following. We have data (in PK: drug concentration measurements) from a

number of individuals, and we want to make a description of the

pharmacokinetic behavior of a drug in this 'population', i.e., to derive

'typical' values (usually mean values) for the parameters of a

pharmacokinetic (mathematical) model describing (in PK) the time course

of drug concentration in plasma, and their interindividual standard

deviation. In addition, correlation between parameters and influence of

patient covariate (weight, age, gender etcetera) can be investigated.

STS works as follows:

Step 1: Analyse the data for each individual separately, and estimate

(calculate, fit) the parameters of the model for each individual without

taking into account the data from other individuals.

Step 2: Calculate 'typical' values (usually mean values; or geometric

mean in case a lognormal distribution is assumed), standard deviations,

correlations, etcetera from the set of individual parameters obtained in

step 1.

STS is what one would do without any knowledge of 'population analysis',

and this was indeed the way population analysis was done until around

1980, when mixed effect modeling was introduced by Sheiner and Beal. In

the same period also more refined two-stage methods were derived,

including the Iterative Two-Stage Bayesian approach (Steimer JL, Mallet

A, Golmard JL, Boisvieux JF. Alternative approaches to estimation of

population pharmacokinetic parameters: comparison with the nonlinear

mixed-effect model. Drug Metab. Rev. 1984; 15:265-292).

So, my use of the term STS refers to population pharmacokinetics (and

pharmacodynamics).

---

Daniel M. Byrd III, Ph.D., D.A.B.T.

Deputy Director

Life Sciences Research Office

9650 Rockville Pike

Bethesda, MD 20814-3998

(301)634-7034 phone

(301)634-7876 fax

byrdd.-at-.lsro.org email

at home:

8370 Greensboro Drive

McLean, VA 22102-3500

(703)848-0100

byrdd.-at-.cox.net - On 29 May 2005 at 16:36:23, Nick Holford (n.holford.-at-.auckland.ac.nz) sent the message

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The following message was posted to: PharmPK

Daniel,

It seems that Hans and I share the same view of what STS means in the

field of PK.

Would you like to inform us about your statement:

"STS" in a risk assessment context (more my field), implies the use of a

filtered Poisson model (e.g., Suresh Moolgavkar's "two-stage" model)."

What do you mean by:

1. Risk assessment

2. Poisson model

3. Filtered Poisson model

4. Suresh Moolgavkar's "two-stage" model

5. So, my use of the term STS refers to population pharmacokinetics (and

pharmacodynamics).

?

Statement 5 is particularly puzzling because STS (as defined by Hans and

me) can be applied in any field so what is the point of saying it refers

to population PK and PD?

Nick

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