From: stuart@c255.ucsf.edu
Date: Mon, 20 Aug 2001 11:25:07 -0700 (PDT)
Peter Bonate writes:
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
algorithm:
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.
Stuart Beal
S-matrix and RNGs
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
Hi everyone,
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
may be wrong.
Regards!
Juan Jose Perez Ruixo
Senior Scientist
Global Pharmacokinetics and Clinical Pharmacology Dpt.
Janssen Research Foundation
Turnhoutseweg, 30
B-2340 Beerse
Belgium
Tel: (+32) 14 60 75 08
Email: jperezru@janbe.jnj.com
MINIMIZATION SUCCESSFUL
NO. OF FUNCTION EVALUATIONS USED: 2233
NO. OF SIG. DIGITS IN FINAL EST.: 6.3
MOF 11538.69
THETAs TH1 TH2 TH3 TH4 TH5 TH6 TH7
TH8
34.300 88.000 6.110 35.100 1.060 0.432 0.410
1.870
SE of THETAs
- Default option 3.0900 6.4800 1.3900 5.3900 0.2880 0.0670 0.0908
0.6270
- Matrix S 2.6600 6.9000 0.6100 3.4800 0.1280 0.0280 0.2460
0.2930
OMEGAs
ETA1 0.3520
ETA2 0.0000 0.0265
ETA3 0.0000 0.0000 0.3680
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
SE of OMEGAs (Default option)
ETA1 0.1880
ETA2 0.0000 0.0202
ETA3 0.0000 0.0000 0.5480
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)
ETA1 0.1220
ETA2 0.0000 0.0342
ETA3 0.0000 0.0000 0.3420
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
SIGMAs 0.0675
SE of SIGMAs
- Default option 0.0135
- Matrix S 0.0139
From: Nick Holford <n.holford@auckland.ac.nz>
Subject: Re: NONMEM random number generator
Date: Tue, 21 Aug 2001 09:17:34 +1200
Stuart,
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?
Thanks,
Nick
--
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
http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm