Back to the Top
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
Back to the Top
[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
PharmPK Discussion List Archive Index page
Copyright 1995-2010 David W. A. Bourne (david@boomer.org)