- On 14 Oct 2001 at 12:05:49, "atul" (bvatul.aaa.ufl.edu) sent the message

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Hello All

Could everybody share their views on this?

I am using a regression program called SCIENTIST for analysis of PKPD

data set. The software has interestingly six different integrator

options:

1. Euler

2. Simple runge kutta

3. Error controlled runge-kutta

4. Burlisch-Stoer

5. Episode (Adams)

6. Episode (Stiff)

For a simple data set (Pharmacokinetics etc) the Eulers method works

fine. But when I am analysing a PKPD model which is relatively

complicated (disease progression/disease reversal) with effect of

drug and indirect response model. I find that Eulers method is not

working well. The estimates touch values as low as E-16 or as high as

E+05. The simplex procedure works but the Least Squares Estimation

which I suppose is based on these methods is behaving strangely with

Eulers method. There is no problem with a simple PKPD model or a

simple indirect response model with Eulers method but inclusion of a

disease progression makes it behave strangely. I then tried the

Simple runge Kutta option and it is working very well. The estimates

make much meaning and although it is very slow it still converges. If

I use a episode (stiff) the starting values do not change at all and

the program terminates.

Can I use the runge kutta method? How can I decide if the estimates

by this method are reliable in comparison to Eulers? I wish now to

transfer my model to NONMEM. How can NONMEM be different here?

Thanks in advance for your time

Atul - On 15 Oct 2001 at 17:39:47, David Bourne (david.aaa.boomer.org) sent the message

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[A few replies - db]

From: Anna Georgieva

Date: Sun, 14 Oct 2001 23:39:37 -0400

To: david.-at-.boomer.org

Subject: Re: PharmPK Integrator options

The following message was posted to: PharmPK

Hello, usually Runge-Kutta is a 4 order method in comparison with 1st for

Euler so you have improvement

anna

---

From: alex.macdonald.aaa.pharma.novartis.com

Date: Mon, 15 Oct 2001 08:50:58 +0200

To: david.-at-.boomer.org

Subject: Re: PharmPK Integrator options

The following message was posted to: PharmPK

Hello Atul,

I'm not familiar with the Scientist software program, but from your email

it sounds like your confusing non-linear regression and numerical

integration. Non-linear regression techniques, such as Gauss-Newton and the

Simplex methods, are used for obtaining parameter estimates of non-linear

models. Numerical integration methods, such as the six you've listed, are

for solving ordinary differential equations, i.e solving or simulating the

model over time once you've obtained reasonable parameter estimates. With

respect to numerical integration, the Euler method is the simplest and most

limited numerical method. We were always advised to only use Euler as a

check on other methods. Runge Kutta methods are widely used and can be

accurate for many applications. Problems with accuracy and inefficiency can

arise when the models or system of differential equations are particularly

stiff, i.e. there are both very short and very long time constants within

the model. An example of such a system would be a multi-compartment PBPK

model where compartments representing the highly perfused organs can

equilibrate in the order of minutes whereas the drug in fat can take days

or weeks to equilibrate. Stiff solvers, such as backward differentiation

formulas (Gear's method) or the more efficient numerical differentiation

formulas can be used.

One reference for numerical integration methods is Shampine, L.F. Numerical

Solution of Ordinary Differential Equations, Chapman & Hill, 1994.

Best Regards

Alex

Dr. A.J.MacDonald

Drug Metabolism and Pharmacokinetics

Novartis Pharma AG.

WKL-135.1.67

Klybeckstrasse

CH-4057 Basel

Switzerland

Tel. + 41 61 69 67 798

Fax + 41 61 69 66 992

email alex.macdonald.aaa.pharma.novartis.com

---

From: "Hans Proost"

Date: Mon, 15 Oct 2001 08:58:46 MET

To: david.-at-.boomer.org

Subject: Re: PharmPK Integrator options

The following message was posted to: PharmPK

Dear Dr. Atul,

I am not familiar with the program SCIENTIST, but I have quite

some experience with numerical integration procedures. The

problem is the choice of the stepsize, which may preset and fixed

or may be adapted by the program. The latter is a prerequisite for a

flexible application in PK and PKPD.

> 1. Euler

This method should never be used. It is either very inaccurate (if

the stepsize is not very small) or extremely slow.

> 2. Simple runge kutta

If you mean a 'fourth-order Runge-Kutta' (the best known variant of

Runge-Kutta), this method works fine in many cases, but a fixed

stepsize may result in inaccurate results (if chosen too large) or

long runs (if chosen much too small).

When solving differential equations, there is a simple rule of thumb

for the stepsize. The stepsize should never exceed 1/kmax where

kmax is the maximum value of all rate constants in the model. In

case of more than one rate constant from one compartment, kmax

is the sum of these rate constants. In my experience, this works

very well in fourth-order Runge-Kutta.

> 3. Error controlled runge-kutta

> 4. Burlisch-Stoer

> 5. Episode (Adams)

> 6. Episode (Stiff)

If implemented well, with a stepsize adapted to a preset accuracy,

these methods work well. The best choice depends on the

particular problem. If a method does not work properly, there may

be, e.g., a problem in the initial setting of the stepsize. It also may

be a bug in the software (this is not unusual, as we all know).

Best regards,

Johannes H. Proost

Dept. of Pharmacokinetics and Drug Delivery

University Centre for Pharmacy

Antonius Deusinglaan 1

9713 AV Groningen, The Netherlands

tel. 31-50 363 3292

fax 31-50 363 3247

Email: j.h.proost.-a-.farm.rug.nl

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