- On 8 Oct 2004 at 09:55:35, "Cory Langston" (langston.-at-.cvm.msstate.edu) sent the message

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I'm part of a project that's modeling historical (literature) data on

various antimicrobials used in food animals. One approach I'm using is

through Pharsight's Trial Simulation software and, through input of the

PK

variable mean and SD, predict population percentiles that reach certain

plasma concentrations.

On a PK parameter such as lambda-z with a log-normal distribution

(assumed; that's another issue) I have been allowing plus or minus 3 SD

as

the high and low bounds that the parameter is allowed to fall within for

the Monte Carlo simulation. This however often results in a negative

lower bound. The program runs, but it bothers me since negative numbers

are not physiologically possible. How have others handled setting the

bounds on allowed parameter variability when making population

predictions? Can someone refer me to a reference?

Thanks,

Cory

Cory Langston, DVM, PhD, DACVCP

College of Veterinary Medicine

Box 6100 (Spring Street for courier)

Miss. State, MS 39762-6100

phone 662-325-1265

fax 662-325-4011

email langston.at.cvm.msstate.edu - On 8 Oct 2004 at 12:03:39, "Wang, Yaning" (WangYA.-a-.cder.fda.gov) sent the message

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Cory:

I assume the SD you mentioned is referering to the log-transformed

scale.

Therefore, the negative lower bound should apply to the log-transformed

lambda-z. Once it is antilog-transformed back to its true scale, it will

always be positive. Log-normal distribution makes sure you always get

positive numbers unless it is approximated by a constant CV distribution

like in NONMEM. But that is not the case for trial simulator. You can

output

all the lambda-z in the simulation to confirm this.

Yaning Wang, PhD

Pharmacometrician

FDA

[I was assuming non transformed parameters and knowing some of that

data there are wide SD values commonly reported as non transformed

values. A lower bound of zero would be an answer, not great though.

Using log-transformed parameters as explained Dr Wang would be a better

answer. I've been playing with log-normal simulations in Boomer (but

may have it the wrong way round ;-) I would expect that the Pharsight

Simulator has that option. If you have the parameter values for the

individual subject you might recalculate the log-transformed parameter

mean and sd values - db] - On 8 Oct 2004 at 12:45:19, "Sam Liao" (sliao.aaa.pharmaxresearch.com) sent the message

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Hi Cory:

One possible explanation might be that in the lower and upper bound of

the parameter in Pharsight's drug model, you did not do the anti-log

transformation for the -3 and +3 SD. An example is shown below for a

lambda of 0.1, the 3rd column has the exp of -0.9 and 0.9, the 4th

column has the median times the ratio to obtain the lower and upper

bound. Hope this is helpful.

median 0.1

sd(lnx) 0.3

-3 SD -0.9 0.407 0.041

3 SD 0.9 2.460 0.246

Best regards,

Sam Liao, PharMax Research - On 9 Oct 2004 at 07:24:17, "Steve Duffull" (sduffull.-at-.pharmacy.uq.edu.au) sent the message

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Hi

Just a comment really. Yaning's idea of choosing a more appropriate

distribution for lambda-z is the most usual solution, but if you really

wanted to continue with the normal rather than the 'better' log normal

then you would have to truncate your normal distribution at an

appropriate lower bound (this does change the distributional assumption

of normality though).

Unfortunately simulating lambda's rather than CL's and V's runs the

risk of getting your lambdas out of order too (i.e. inadvertently

simulating lambda-1 < lambda-z on some occasions), so you would need to

check for this too - or simulate your lambda's from conditional

distributions.

A note about Yanings comment:

"Log-normal distribution makes sure you always get

positive numbers unless it is approximated by a constant CV distribution

like in NONMEM."

When simulating, NONMEM uses the exact model you choose - so if you

simulated lambda from LZ = THETA(1)*EXP(ETA(1)) then LZ will have a log

normal distribution and will not give you negative numbers. It is only

when NONMEM does estimation that the first-order expansion around the

random effects is used and hence the approximation occurs.

My overall feeling is that you should always simulate from biologically

meaningful parameters (CL, Q, V1, V2 ... etc) from appropriate

distributions (lognormal etc) in preference to other parameterizations

(even with this parameterization flip flop may occur if you are

simulating Ka as well - in which case the NMusers list has both a

thread on this at the moment and archives on what to do about this).

Regards

Steve

Stephen Duffull

School of Pharmacy

University of Queensland

Brisbane 4072

Australia

Tel +61 7 3365 8808

Fax +61 7 3365 1688

University Provider Number: 00025B

Email: sduffull.at.pharmacy.uq.edu.au

www: http://www.uq.edu.au/pharmacy/sduffull/duffull.htm

PFIM: http://www.uq.edu.au/pharmacy/sduffull/pfim.htm

MCMC PK example: http://www.uq.edu.au/pharmacy/sduffull/MCMC_eg.htm - On 9 Oct 2004 at 08:59:35, Nick Holford (n.holford.aaa.auckland.ac.nz) sent the message

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Yaning Wang, PhD, Pharmacometrician, FDA wrote:

> Log-normal distribution makes sure you always get

> positive numbers unless it is approximated by a constant CV

distribution

> like in NONMEM. But that is not the case for trial simulator.

I think this comment is misleading. NONMEM simulation is exactly the

same as Trial Simulator. If you specify EXP(eta) in NONMEM you will

simulate from a log-normal distribution. If you choose to use (1+eta)

in NONMEM (or the equivalent in TS) then it is possible to sample

negative values.

--

Nick Holford, Dept Pharmacology & Clinical Pharmacology

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

Zealand

email:n.holford.-a-.auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556

http://www.health.auckland.ac.nz/pharmacology/staff/nholford/ - On 9 Oct 2004 at 08:51:37, Nick Holford (n.holford.at.auckland.ac.nz) sent the message

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Cory Langston wrote:

>

> On a PK parameter such as lambda-z with a log-normal distribution

> (assumed; that's another issue) I have been allowing plus or minus 3

SD

> as

> the high and low bounds that the parameter is allowed to fall within

for

> the Monte Carlo simulation. This however often results in a negative

> lower bound. The program runs, but it bothers me since negative

numbers

> are not physiologically possible.

You must be doing something wrong in TS. It is impossible to sample

from a log normal distribution with a positive geometric mean and get

negative numbers.

TS has a rather unintuitive user interface for specifying distributions.

http://www.cognigencorp.com/nonmem/nm/98nov121999.html

How it is done varies depending on whether you use a single

distribution or a mulitvariate distribution. The multivariate

distribution is often preferable because it allows the specification of

covariance (see below).

When I use the multivariate distribution block I specify zero mean and

enter the variance-covariance matrix. I do not check the exp box. Then

I sample from the distribution, exponentiate it and multiply the result

by the geometric mean to get the parameter value.

e.g. with a log normally distributed variable with name PPV_CL

CL=CLmean*exp(PPV_CL) ; do this in a separate expression block

Constraints are specified as the deviation from zero e.g. if the

variance of PPV_CL is 0.01 then the SD of PPV_CL is 0.1. You enter a

lower bound of -0.2 and upper bound of 0.2 to get +/- 2 SDs.

> How have others handled setting the

> bounds on allowed parameter variability when making population

> predictions? Can someone refer me to a reference?

If you want to be physiological about your simulations I would suggest

you reparameterize your model in terms of clearances and volumes rather

than rate constants.

I alos suggest you include the covariance of parameters whenever you

can find estimates of them. This helps to avoid unrealistic

combinations.

--

Nick Holford, Dept Pharmacology & Clinical Pharmacology

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

Zealand

email:n.holford.-at-.auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556

http://www.health.auckland.ac.nz/pharmacology/staff/nholford/ - On 11 Oct 2004 at 12:58:35, "Hans Proost" (j.h.proost.-a-.farm.rug.nl) sent the message

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Dear Nick,

You wrote in answer to a question of Cory Langston:

> Constraints are specified as the deviation from zero e.g. if the

> variance of PPV_CL is 0.01 then the SD of PPV_CL is 0.1. You enter a

> lower bound of -0.2 and upper bound of 0.2 to get +/- 2 SDs.

The next question (my question) is: Why does one use bounds in Monte

Carlo

simulation? As stated by Steve Duffull, bounds change the distributional

assumption of normality. Of course, when using a normal distribution a

lower

bound of zero must be used for clearance, and at least some positive

value

for volume, but for the preferred (I totally agree) lognormal

distribution

this is not necessary. In my view bounds like +/- 2 or 3 SD are not in

agreement with real life. Of course some bound is necessary due to

computational limitions, but I do not see any reason to restrict this

to a

range narrower than, say +/- 5 SD. In any case, +/- 2 SD sounds

ridiculous

in my view, since it covers only 95% of the distribution.

> I alos suggest you include the covariance of parameters whenever you

> can find estimates of them. This helps to avoid unrealistic

> combinations.

I agree, but I would like to make some additional comments. In general

we

prefer models in which parameters are uncorrelated, or with low

correlation.

A low correlation is difficult to detect, and in most cases observed

'low

correlations' are not statistically significant. In addition, low

correlations hardly help to avoid unrealistic combinations.

In case of significant and relevant correlations, with a correlation

coefficient (absolute value) exceeding, say, 0.6, I fully agree with

you,

but usually I would try to reparametrize the model to reduce the

correlation, e.g. by addition of covariates like body weight.

Finally, what are 'unrealistic combinations'? A very low value of

parameter

1 and a very high value of parameter 2 is not necessarily unrealistic.

E.g.

an ICU patient may have a very low clearance due to liver and/or kidney

failure, but a high volume of distribution due to overhydration,

without a

correlation between the two parameters in the population.

Best regards,

Hans Proost

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 - On 11 Oct 2004 at 09:20:03, "Walt Woltosz" (walt.-at-.simulations-plus.com) sent the message

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Hans,

You bring up some interesting points.

In the Virtual Trials function in GastroPlus, we provide the ability to

sample a large number of parameters, each from their user-specified

distribution (normal, log-normal, or uniform), with a user-specified CV%

(for the log distribution, the CV of the log is used). We also provide

hard upper and lower limits that can be set as wide or narrow as the

user desires.

Why? Because we thought that assuming normal or log-normal shape for

most parameters is just that - an assumption - a mathematical

convenience that we use because the real distribution is unknowable.

Real data never seems to be either, but closer to one than the other.

Unfortunately, when we run thousands of virtual subjects in a trial,

there are those occasional extreme values that are generated. If the

user decides that volume of distribution has a mean of 10 L/kg, with a

CV of, say, 50%, then the smallest volumes could be very small. The user

must decide if this is realistic, or if they believe there is a

realistic lower limit that makes sense.

With enough subjects in the trial, these extremes should be overwhelmed

by the majority of more reasonable parameter values. But it seems that

to say that is to say that you could have thrown that one out without a

significant effect. If so, why not resample until all parameters are

within their specified limits and then run a more useful trial?

The type of trial is also important. For a true clinical virtual trial,

you're dealing with patients, who may have, as you noted, parameter

values that might be considered extreme in a healthy population. For a

virtual bioequivalence trial in healthy subjects, one would not expect

to see such extremes unless the drug has some unusual behavior.

Walt

Walt Woltosz

Chairman & CEO

Simulations Plus, Inc. (AMEX: SLP)

1220 W. Avenue J

Lancaster, CA 93534-2902

U.S.A.

http://www.simulations-plus.com

Phone: (661) 723-7723

FAX: (661) 723-5524

E-mail: walt.at.simulations-plus.com - On 11 Oct 2004 at 14:33:34, "Cory Langston" (langston.at.cvm.msstate.edu) sent the message

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Thanks to the several people who replied. Many of you pointed out that

one can not get a negative value for a log-normal distribution. What is

unclear to me at this point and, most likely due to my unfamiliarity

with

the software, is whether transformations or even additional blocks are

necessary to specify the bounds.

In other words, in the Block Properties dialog box for a parameter you

specify that you want a log-normal distribution. In that same dialog

box

you also enter the mean, SD, and upper and lower bounds. What I don't

know is whether the parameters are:

a) entered as untransformed numbers (hence you can put negative numbers

into the lower bound entry box to encompass -3SD) and then the program

makes the transformation for you because you specified a lognormal

distribution

b) you enter the values as natural logs of the parameters (seems

unlikely)

c) one has to make the log transformations, figure the upper and lower

bounds, and then take the antilog of these figure to back-transform it

for

entry into the program

or

d) a separate expression block, as Nick describes below, is necessary

BTW, these analyses are looking across historic (literature) analyses,

some of which are quite old. As such, they are not true population

models

and have no covariates. The intent of this Trial Sim modeling is to

take

the basic PK compartmental model and make predictions as to what

population percentiles achieve certain concentrations with differing

dosage regimens.

Thanks,

Cory

Cory Langston, DVM, PhD, DACVCP

College of Veterinary Medicine

Box 6100 (Spring Street for courier)

Miss. State, MS 39762-6100

phone 662-325-1265

fax 662-325-4011

email langston.-at-.cvm.msstate.edu - On 13 Oct 2004 at 04:41:44, Nick Holford (n.holford.-at-.auckland.ac.nz) sent the message

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Hans,

Hans wrote:

> The next question (my question) is: Why does one use bounds in Monte

> Carlo simulation?

I use bounds because otherwise there is nothing to stop one sampling

from a distribution and getting values that are 1000 time smaller or

larger than the population mean. I would consider such values

ridiculous in almost all imaginable situations. They would certainly be

extrapolations well beyond any observed values. My own interest in

Monte Carlo simulation is to explore plausible situations not

absurdities.

Hans wrote:

> As stated by Steve Duffull, bounds change the distributional

> assumption of normality. Of course, when using a normal distribution a

> lower bound of zero must be used for clearance, and at least some

positive

> value for volume, but for the preferred (I totally agree) lognormal

> distribution this is not necessary. In my view bounds like +/- 2 or 3

SD are not in

> agreement with real life. Of course some bound is necessary due to

computational

> limitions,but I do not see any reason to restrict this to a

> range narrower than, say +/- 5 SD. In any case, +/- 2 SD sounds

ridiculous

> in my view, since it covers only 95% of the distribution.

In my response to Cory I illustrated how to use bounds of +/- 2 SD

because that was the original question. The choice of bounds should be

determined by the person who is in intellectual charge of the project.

I don't think one can make general recommendations about appropriate

bounds without understanding the context.

One approach is to truncate the distribution to lie within the observed

range of parameter values that one has observed. The results of the

simulation would then be based on interpolation rather than

extrapolation.

Nick wrote:

> > I also suggest you include the covariance of parameters whenever

you

> > can find estimates of them. This helps to avoid unrealistic

combinations.

>

Hans wrote:

> I agree, but I would like to make some additional comments. In general

> we prefer models in which parameters are uncorrelated, or with low

> correlation.

I do not disagree in theory but in the real world the search for the

Holy Grail has not so far been successful for pharmacokineticists. It

is just impractical to propose that one can commonly (or even ever)

understand the fixed effects well enough to remove all parameter

covariance. For practical simulations this unexplained covariance

should not be ignored because otherwise one will simulate parameter

combinations that are extremely unlikely even though the individual

parameters are not especially unusual.

Nick

--

Nick Holford, Dept Pharmacology & Clinical Pharmacology

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

Zealand

email:n.holford.at.auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556

http://www.health.auckland.ac.nz/pharmacology/staff/nholford/ - On 12 Oct 2004 at 16:56:53, Roger Jelliffe (jelliffe.at.usc.edu) sent the message

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Dear Cory:

Why all this discussion about these parameter distributions and

what their shape should be? Why don't you first use a population

modeling

method that:

1. Makes no assumptions at all about what the distribution shape

should be

2. Its shape of the parameter distributions are determined only by

the

data itself, and the error model used

3. Is mathematically consistent - the more subjects you study, the

closer the results get to the truth. (The great majority of parametric

methods used today do not have this guarantee).

4. Is statistically efficient (has good precision in parameter

estimates).

5. The calculation of the likelihood is exact, not approximate.

Nonparametric population modeling methods have all these

properties. They make no assumptions about the shape of the parameter

distributions, they are consistent, and they are more efficient, with

more

precise parameter estimates, than methods that use either the FO or the

FOCE approximation to the likelihood function. Why does NONMEM not

report

the likelihood of its results in most of its studies? I look for it and

rarely find it. Why?

If you go to www.lapk.org and click on New Advances in

Population

Modeling, you will see Bob Leary's work comparing NPAG, with exact

likelihoods, with methods using the FO and FOCE approximations,

including

IT2B and NONMEM. Then decide which method you really would like to use.

Very best regards,

Roger Jelliffe

Roger W. Jelliffe, M.D. Professor of Medicine,

Division of Geriatric Medicine,

Laboratory of Applied Pharmacokinetics,

USC Keck School of Medicine

2250 Alcazar St, Los Angeles CA 90033, USA

Phone (323)442-1300, fax (323)442-1302, email= jelliffe.aaa.usc.edu

Our web site= http://www.lapk.org - On 13 Oct 2004 at 11:46:55, "Hans Proost" (j.h.proost.-at-.farm.rug.nl) sent the message

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Dear Nick,

Thank you for your well-considered reply. My question with respect to

the

use of bounds was somewhat provocative, to hear the arguments for it.

> My own interest in

> Monte Carlo simulation is to explore plausible situations not

> absurdities.

This is a convincing argument, and I agree. But Monte Carlo simulations

are

also used to explore the statistical properties of a procedure, e.g. in

population analysis or Bayesian estimations. In this case the use of

bounds

may influence the results; a reliable procedure should handle the

extremes

as well as 'normal' values, and this cannot be checked if (narrow)

bounds

are used. I agree that even in this case one would not need to worry if

'extremely extreme' values cause problems. So, 'reasonable' bounds may

be

the best thing to do. Besides, I use Monte Carlo simulations also for

checking the reliability and robustness of procedures and their

implementation in software. For this purpose the 'absurdities' are quite

useful.

> One approach is to truncate the distribution to lie within the

observed

> range of parameter values that one has observed. The results of the

> simulation would then be based on interpolation rather than

> extrapolation.

Again a convincing argument, although I would prefer at least some

extrapolation outside the range obtained from a limited number of

subjects,

parameters, or measurements. A value outside the observed range is not

necessarily an 'absurdity'.

> I do not disagree in theory but in the real world the search for the

> Holy Grail has not so far been successful for pharmacokineticists. It

> is just impractical to propose that one can commonly (or even ever)

> understand the fixed effects well enough to remove all parameter

> covariance. For practical simulations this unexplained covariance

> should not be ignored because otherwise one will simulate parameter

> combinations that are extremely unlikely even though the individual

> parameters are not especially unusual.

I agree. The variability of parameters is expressed in the entire

variance-covariance matrix, and not in the variances (diagonal) only, so

theoretically one should always use it in Monte Carlo simulations; for

low

correlations it makes hardly any difference, so it is neither relevant

to

include an observed, non-significant correlation, nor harmful to assume

zero

correlation.

Best regards,

Hans Proost

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.aaa.farm.rug.nl - On 13 Oct 2004 at 12:57:11, "Hans Proost" (j.h.proost.at.farm.rug.nl) sent the message

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Dear Walt,

Thank you for your well-considered reply. I agree with your arguments. A

problem is that bounds must be chosen, introducing an arbitrary choice.

It

is 'more objective' to use a normal or log-normal distribution based on

mean

and standard deviation obtained from experimental data. But I agree that

leaving out Nick's 'absurdities' is less problematic than the need to

choose

arbitrary bounds.

> With enough subjects in the trial, these extremes should be

overwhelmed

> by the majority of more reasonable parameter values. But it seems that

> to say that is to say that you could have thrown that one out without

a

> significant effect. If so, why not resample until all parameters are

> within their specified limits and then run a more useful trial?

If the bounds are chosen relatively narrow, 'throwing out' values

outside

the range may have a significant effect, since the actual SD will be

smaller

than the assumed SD.

> The type of trial is also important. For a true clinical virtual

trial,

> you're dealing with patients, who may have, as you noted, parameter

> values that might be considered extreme in a healthy population. For a

> virtual bioequivalence trial in healthy subjects, one would not expect

> to see such extremes unless the drug has some unusual behavior.

Thank you for this extension. I agree.

Best regards,

Hans Proost

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.at.farm.rug.nl - On 13 Oct 2004 at 19:13:14, "Walt Woltosz" (walt.-a-.simulations-plus.com) sent the message

Back to the Top

Hans,

Thanks for your reply - just a couple of comments:

Hans: "A problem is that bounds must be chosen, introducing an arbitrary

choice. It is 'more objective' to use a normal or log-normal

distribution based on Mean and standard deviation obtained from

experimental data. But I agree that leaving out Nick's 'absurdities' is

less problematic than the need to choose arbitrary bounds."

True that bounds are chosen, but they should not be arbitrary.

Rather, they should be chosen based on prior information by someone with

knowledge and experience (sort of a "heuristic Bayesian approach"). The

choice of distribution type and CVs is done with such prior information.

Hans: "If the bounds are chosen relatively narrow, 'throwing out' values

outside the range may have a significant effect, since the actual SD

will be smaller than the assumed SD."

We believe that only values that can be clearly identified as

extremely unlikely should be thrown out. This should not be done

carelessly or to excess, but should be done only enough to ensure that

absurdities are avoided.

Walt Woltosz

Chairman & CEO

Simulations Plus, Inc. (AMEX: SLP)

1220 W. Avenue J

Lancaster, CA 93534-2902

U.S.A.

http://www.simulations-plus.com

Phone: (661) 723-7723

FAX: (661) 723-5524

E-mail: walt.at.simulations-plus.com - On 14 Oct 2004 at 08:50:28, "J.H.Proost" (J.H.Proost.aaa.farm.rug.nl) sent the message

Back to the Top

Dear Walt,

Thank you for your reply. I fully agree with your

comments. Let me end with a final comment: I'm afraid that

bounds are not always chosen 'based on prior information

by someone with knowledge and experience'.

Best regards,

Hans

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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