From: peter.bonate@quintiles.com

Date: Thu, 16 Aug 2001 08:52:12 -0500

Vladmir responded that using Matrix=S in a $COV statement may be

misleading. How so? The default in NONMEM is something like R^(-1)*S*R.

This is the heteroscedastic consistent estimator. Many books on nonlinear

regression report that inversion of S alone is also valid and should be

approximately the same as the other estimator. Why not so with nonlinear

On to another question, I know this is minutia, but I am giving a talk on

random number generators in simulation at an AAPS meeting in September and

I am pretty certain that someone will ask this: what is the random number

generator used by NONMEM for performing simulations? Does someone have a

From: "Piotrovskij, Vladimir [JanBe]" <VPIOTROV@janbe.jnj.com>

Subject: RE: S-matrix and RNGs

Date: Thu, 16 Aug 2001 16:48:28 +0200

It may be so, and may be not. The question is how good is "approximately".

At least there should be reasons for selecting R^(-1)*S*R as the default in

From: "Perez Ruixo, Juan Jose [JanBe]" <JPEREZRU@janbe.jnj.com>

Subject: RE: S-matrix and RNGs

Date: Fri, 17 Aug 2001 14:24:15 +0200

I made some exercise in order to compare the default option in

covariance step with MATRIX=S (see below). I fitted the two-compartmental

model with sequential zero and first order absorption to data. As you can

see there are substantial differences between two options in the magnitude

of SE they prodiced. Moreover, the run time with MATRIX=S option was 3 times

shorter. I think for large datasets and complex model the MATRIX=S option

could be a good alternative during the model development in order to avoid

delays. But for the final model, the default option should be used in order

to compute confidence intervals and made inferences, otherwise conclusions

Global Pharmacokinetics and Clinical Pharmacology Dpt.

NO. OF FUNCTION EVALUATIONS USED: 2233

NO. OF SIG. DIGITS IN FINAL EST.: 6.3

THETAs TH1 TH2 TH3 TH4 TH5 TH6 TH7

34.300 88.000 6.110 35.100 1.060 0.432 0.410

- Default option 3.0900 6.4800 1.3900 5.3900 0.2880 0.0670 0.0908

- Matrix S 2.6600 6.9000 0.6100 3.4800 0.1280 0.0280 0.2460

ETA4 0.0000 0.0000 0.0000 1.0400

ETA5 0.0000 0.0000 0.0000 0.0000 0.5780

ETA6 0.0000 0.0000 0.0000 0.0000 0.0000 0.3640

ETA7 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.1900

ETA8 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.2900

ETA4 0.0000 0.0000 0.0000 0.7900

ETA5 0.0000 0.0000 0.0000 0.0000 0.2070

ETA6 0.0000 0.0000 0.0000 0.0000 0.0000 0.1200

ETA7 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.7980

ETA8 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.4350

SE of OMEGAs (Matrix=S option)

ETA4 0.0000 0.0000 0.0000 0.3870

ETA5 0.0000 0.0000 0.0000 0.0000 0.2260

ETA6 0.0000 0.0000 0.0000 0.0000 0.0000 0.1210

ETA7 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.4230

ETA8 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.4970

Date: Mon, 20 Aug 2001 11:25:07 -0700 (PDT)

I am giving a talk on random number generators in simulation at an AAPS

meeting in September and I am pretty certain that someone will ask this:

what is the random number generator used by NONMEM for performing

simulations? Does someone have a reference for it?

Pete, here is a reference, but I frankly do not quite see why this should

be a burning question for anyone involved with *PK simulations*.

In my opinion, the level with which randomness is truly obtained with such

simulations need not be great.

Uniform random numbers are obtained via the Lewis-Goodman-Miller

Lewis, P.A.W., Goodman, A.S., Miller J.M (1969). "A pseudo-random

number generator for the system/360." IBM System Journal 8, 136-146.

modified to be independent of machine architecture ala

Schrage, L (1979). "A more portable Fortran random number generator."

ACM Transaction on Mathematical Software, 5, 132-138.

Normal random numbers are obtained via the Box-Muller algorithm:

Box, G., Muller, M. (1958). "A note on the generation of random normal

deviates." Annals of Mathematical Statistics, 29, 610-611.

From: Nick Holford <n.holford@auckland.ac.nz>

Subject: Re: NONMEM random number generator

Date: Tue, 21 Aug 2001 09:17:34 +1200

I wonder if you would please expand on 2 things you raise here:

1. Why do you think that RNG issues are not important for *PK simulations*? I suspect the question was more than just PK models but in connection with clinical trial simulations which may have a PK model as just one of components with a stochastic element requiring a RNG.

2. What is the criterion you use for judging the "level with which randomness is truly obtained" and thus deciding whether the RNG properties are adequate for the task?

Nick Holford, Divn Pharmacology & Clinical Pharmacology

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

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