From: "Fuseau, Eliane" <ef16065@glaxowellcome.co.uk>

Subject: Simulation

Date: Fri, 12 Nov 1999 18:45:59 -0000

Dear users, HELP!

We tried to use a NONMEM model (parameters and pop estimates) to perform simulations in Pharsight, and found something we did not explain. Please have a look at the attached note and let us know what you think and/or what you know !

Merci

Eliane

<<NMusers.pdf>>

My address for the remaining of the year:

Eliane Fuseau

Clinical Pharmacology

GlaxoWellcome Research and Development

Greenford road

GREENFORD, UB6 0HE, UK

tel +44 181 966 4278

fax +44 181 966 2123

From: michael_looby@sandwich.pfizer.com

Subject: RE: Pharsight Simulations

Date: Mon, 15 Nov 1999 12:30:03 -0000

Dear Users

I am not sure what problem Eliane has encountered, but I have had an irritating problem with simulation in the Pharsight product. In the Pharshight trial designer, the log normal distribution simulation option expects you (for some strange reason) to enter the arithmetic mean rather than the geometric mean of your (log normal) distribution (In the manual it just says enter the mean of the log normal distribution!!). This does not make much sense since the geometric mean is the natural location parameter of this distribution and is in contrast to most other simulation packages. While incorrectly entering the geometric mean in the Pharsight package, I only noticed the problem when I was simulating parameters with large variability where the arithmetic and geometric mean start to differ significantly. It subsequently took me considerable time and effort to source the problem. This is perhaps a nice illustration of what can go wrong in simulation studies, particularly when you are unfamiliar with the software.

Regards

Michael Looby PhD

Clinical Project Manager

Pfizer Central Research, Sandwich

Kent CT13 9NJ, UK

Tel: +44 1304 648978

Fax: +44 1304 658159

Email: michael_looby@sandwich.pfizer.com

From: "HUTMACHER, MATTHEW" <MATTHEW.HUTMACHER@chi.monsanto.com>

Subject: RE: Simulations

Date: Mon, 15 Nov 1999 09:50:26 -0600

Elaine,

I am a little confused after reading your comparison of the NONMEM and Pharsight softwares on how you modeled the variability in NONMEM. On page 2 you sate "The variability in Ka, CL/F and V/F between subjects was modeled as proportional to the parameter and reported as a coefficient of variation (CV).". I translate this to mean you modeled, e.g. CL as CL=TVCLx(1+ETA(1)). Yet on page 5 in Table I, the table of PK parameter estimates, you report the model as "xexp(ETA(1))". These two models are not the same in terms of simulation. Estimation is a different matter. It is true under the first-order (FO) estimation scheme that these two models are equivalent in that the estimates of OMEGA for the two models should be within round-off error. If one uses the first-order conditional estimation method (FOCE), then these models will yield different estimates of OMEGA, especially for large intersubject variability.

If you are interested in assessing the difference in simulated individual PK parameters by the two software packages, a more direct comparison can be made using a Q-Q plot. To construct a Q-Q plot, one could output the simulated individual parameters to a file. Then for each parameter, e.g. CL, one could sort the simulated CLs in ascending order (to obtain the order statistics) for both software types. The two sets of CLs could then be paired by their order statistics and plotted, e.g. Pharsight's on the x-axis and NONMEM's on the y-axis. If the method of simulation between the two softwares is the same, the distribution of points should lie very close to the line of identity (y=x). If the points deviate from this line, how they deviate should provide information as to the nature of the discrepancy.

Hopefully this helps.

Matt

Date: Tue, 16 Nov 1999 11:41:20 -0800

From: Jeff Wald <jwald@pharsight.com>

Subject: Re: FW: Pharsight Simulations

With regards to Elianne's original posting, I have requested to see her Pharsight Trial Designer (PTD) model so I can provide an unequivocal resolution for the readers of this list.

In response to Mick, there are two options in for handling lognormal distributions in PTD. One is as you correctly point out, a log normal component based on the arithmetic mean and standard deviation of the distribution. The other option is to use an exponentiated normal distribution.

Reviewing common statistical packages demonstrates the following.

The user interface in S-PLUS is:

rlnorm(n, meanlog=0, sdlog=1),

where meanlog and sdlog denote mean and standard deviation of the distribution of the log of the random variable (E.g., the "arithmetic mean" and std of the "underlining normal distribution")

I am not aware of a function in SAS to directly generate pseudo log-normal deviates. Accordingly, one can generate normal deviates first and exponentiate them. If you are aware of other possibilities, please let us know.

As you see, the exponentiated normal option in PTD is consistent with standard stat packages. The log-normal option is an added feature which is particularly useful when one is working with reported statistics and does not have access to raw values.

I hope this helps to clear the air of any misunderstandings.

Regards, Jeff Wald

Pharsight Corporation

Date: Fri, 19 Nov 1999 10:10:51 -0800

From: Jeff Wald <jwald@pharsight.com>

Subject: Re: [Fwd: Simulations]

We have not noticed any differences between NONMEM and Pharsight Trial Designer (PTD) of the nature described in Eliane's e-mail. However, there are misconceptions that at times will lead to discrepant results. I have been given the opportunity to review the NONMEM and PTD models refrenced in Eliane's manuscript and have noticed 2 major differences between the two approaches.

1.) NONMEM always reports the variance of a normally-distributed eta. When using a parameter model of the form p=theta*exp(eta), then Var(eta) is APPROXIMATELY (CV(p))**2. That approximation is pretty good for small CV's. For example when sqrt(Var(eta)) = 0.1 then CV = 0.10025. However, when sqrt(Var(eta)) gets large the approximation isn't so good. This is illustrated here using the values from Eliane's manuscript:

Parameter sqrt(Var(eta)) CV

CL 0.56 0.607

V 0.604 0.664

ka 0.991 1.29

2.) The same model structure as NONMEM could have been used with normal distributions for log(p) and then translated to p. This approach is succinct in PTD through use of the exponentiated normal distribtion component.

Alternately, a parameter modeled as p=theta*exp(eta) in NONMEM would be:

mean(p) = theta*exp(Var(eta)/2)

sd(p) = mean(p)*sqrt(exp(Var(eta))-1)

In conclusion, NONMEM and PTD provide equivalent simulation results. If there are any questions as to formatting of population models in PTD, please send a note to support@pharsight.com.

Regards, Jeff Wald

Pharsight Corporation

Date: Mon, 22 Nov 1999 15:26:26 -0800 (PST)

From: ABoeckmann <alison@c255.ucsf.edu>

Subject: Re: [Fwd: Simulations]

Comment from Stuart Beal...

As a habit, I do not read NM-Users mail, and therefore have not read any mail described as "Eliane's e-mail". The following comments are simply meant as follow ups to some pointed comments recently made by Jeff Wald.

>1.) NONMEM always reports the variance of a normally-distributed eta. When

> using a parameter model of the form p=theta*exp(eta), then

> Var(eta) is APPROXIMATELY (CV(p))**2. That

> approximation is pretty good for small CV's. For example when

> sqrt(Var(eta)) = 0.1 then CV = 0.10025. However, when sqrt(Var(eta)) gets

> large the approximation isn't so good. This is illustrated here using the

> values from Eliane's manuscript:

>

>Parameter sqrt(Var(eta)) CV

>CL 0.56 0.607

>V 0.604 0.664

>ka 0.991 1.29

The approximation has nothing to do with normality, nor, really, does that which NONMEM reports. It is the so-called exact value (given in Jeff's table, but not given in NONMEM output) which depends on a normally distributed eta. For more information about the approximation (and the exact value), see my memos to NM-Users entitled "Computation of CV's from OMEGA" dated September 26,27, 1997, which may be found in the NM-Users Archive (http://www.cognigencorp.com/nonmem/nm/index.html).

>2.) The same model structure as NONMEM could have been used with normal

> distributions for log(p) and then translated to p. This approach is

> succinct in PTD through use of the exponentiated normal distribtion

> component. Alternately, a parameter modeled as p=theta*exp(eta) in

> NONMEM would be:

>

>mean(p) = theta*exp(Var(eta)/2)

>sd(p) = mean(p)*sqrt(exp(Var(eta))-1)

It is not clear to me what is being asserted here. Perhaps, it is being asserted that a technique might be used that involves computing the mean and sd of a parameter given be p=theta*exp(eta) using the two above formulas. I think this would be a bad idea. These formulas do rely on normality, and should not be generally trusted in population data analysis.

Stu Beal

Date: Wed, 24 Nov 1999 16:14:43 -0800

From: Jeff Wald <jwald@pharsight.com>

Subject: Pharsight to NONMEM, simulations and modeling

There has been discussion over the past week regarding Pharsight Trial Designer (PTD) and NONMEM. In a previous message I addressed the question regarding whether the two packages provide similar results. However, I failed to clear up confusion regarding the translation between the two formats. In the following note I will give examples of equivalent NONMEM and WinNonMix models and the corresponding PTD model.

The model is a simple case that was used as part of our internal testing of WinNonMix. I will provide a summary below. I have also included a summary of NONMEM and WinNonMix results when both programs were used to analyze simulated results.

The model (PTD.mdl):

One Compartment model with First Order Absorption

Exponential error on structural model parameters

Proportional residual error variance model

Simulate 100 replicates of trial using PTD

Each trial has 100 subjects

Each subject has 6 PK samples collected

No error in sampling times

Simulated parameter values are provided in the attached table.

NONMEM: (control.txt)

WinNonMix: WNM.txt

(Please note, the easiest way to present the WinNonMix model to the general audience was to show a summary ASCII file. However, the inputs to WinNonMix are made through the program's graphical user interface.)

Summary: (N0.pdf)

This file contains a table that shows input parameter values for the model and the average values obtained by different methods (First order and conditional first order estimation) in NONMEM and WinNonMix for 100 replicate simulations. I have eliminated much of the granularity regarding the process, but if parties are interested in the testing of WinNonMix please contact me directly or send a note to support@pharsight.com.

Regards, Jeff

Date: Mon, 29 Nov 1999 11:03:28 -0800 (PST)

From: "S.Beal" <stuart@c255.ucsf.edu>

Subject: Re: [Fwd: Simulations]

NM-Users:

Last week, Alison Boeckmann forwarded to NM-Users a few remarks I made concerning an approximation used for the computation of CV's from OMEGA. In these remarks I referred to an earlier memo I sent to NM-Users, stored in the NM-Users Archive. I gave the title of this memo, and thus implicitly suggested that one might find it by searching for this title: Computation of CV's from OMEGA.

Unfortunately, due to a problem with the NM-Users Archive, a search for the memo by searching for the phrase e.g. Computation of CV's, did not bring up this memo. This problem has now been corrected. One can now successfully use the advanced search engine available with the archive to search for the memo by the above phrase.

Stu Beal