From: saik.urien.svp <*saik.urien*>

Date: Mon, 21 Jul 2008 10:26:21 +0200

Mark, Leonid

I suspect that OMEGA values above 2 or 3 units are very doubtful. As =

Leonid pointed out, such variability levels does not tell us anything on =

priors. Another point to discuss about is the s.e. that are associated =

to these OMEGA estimates. What is their extent ?

Finally with such results I would have subjected the model to a =

bootstrap evaluation , to check the true confidence intervals of the =

model estimates.

Regards

Saïk

----- Original Message -----

From: Mark Sale - Next Level Solutions

Cc: nmusers

Sent: Sunday, July 20, 2008 3:52 AM

Subject: RE: [NMusers] algorithm limits

Thanks Leonid,

I believe what you tell me, and I understand that FOCE doesn't =

solve the problem with the approximation that FO makes, only reduces it =

(and possibly expands the range that the approximation is useful for?). =

Anyone out there with insight into what a practical limit is for FOCE =

and/or if there are any diagnostics that are helpful when you're close =

to it? Is it really 0.5 for FO?

Mark

Mark Sale MD

Next Level Solutions, LLC

www.NextLevelSolns.com

919-846-9185

-------- Original Message --------

Subject: Re: [NMusers] algorithm limits

From: Leonid Gibiansky <LGibiansky

Date: Sat, July 19, 2008 9:37 pm

To: Mark Sale - Next Level Solutions <mark

Cc: nmusers

Mark,

The description that you gave confirms that population model =

has limited

value unless four parameters (baseline, percent change, time =

to drop and

time to recovery) correlate somehow. If not, your data tells =

you that

the biomarker may start from very small or very large values, =

decrease

to zero or not decrease at all, and recover in a week or in a =

year.

Moreover, as I understood, there is no central tendency there: =

any

baseline, drop, time to decrease and time to recovery are =

independent

and equally-probable (otherwise, you would have reasonable =

OMEGAs with

the bell-shaped rather than flat distribution of random =

effects. Sparse

sampling will not work in this case, and if you have dense =

sampling, you

may just use two-stage to describe observed (uniform?) =

distribution of

individual parameters (and correlations if there are any).

Leonid

--------------------------------------

Leonid Gibiansky, Ph.D.

President, QuantPharm LLC

web: www.quantpharm.com

e-mail: LGibiansky at quantpharm.com

tel: (301) 767 5566

Mark Sale - Next Level Solutions wrote:

* >
*

* > Leonid,
*

* > This isn't PK, and the model show basically the right shape, =
*

and the

* > data suggest reasonable residual error (the biological =
*

marker falls from

* > a value between 5 and 310000, to somewhere between 0 and no =
*

change from

* > baseline, over a course of a couple of hours to a couple of =
*

weeks, then

* > recovers somewhere between a 100 hours and 9000 hours =
*

later.)

* > ie., it start at a highly variable level fall by some highly =
*

variable

* > fraction, over some variable lenghth of time and recovers =
*

somewhere

* > between about a week and about a year.
*

* > But, within those limits, it appears pretty well behaved.
*

* >
*

* >
*

* > Mark Sale MD
*

* > Next Level Solutions, LLC
*

* > www.NextLevelSolns.com <http://www.NextLevelSolns.com>
*

* > 919-846-9185
*

* >
*

* > -------- Original Message --------
*

* > Subject: Re: [NMusers] algorithm limits
*

* > From: Leonid Gibiansky <LGibiansky *

* > Date: Sat, July 19, 2008 5:36 pm
*

* > To: Mark Sale - Next Level Solutions =
*

<mark

* > Cc: nmusers *

* >
*

* > Hi Mark,
*

* >
*

* > If you really have 10,000 fold differences in, say, volume =
*

or

* > bioavailability, population model does not make any sense: =
*

individual

* > parameters have uninformative priors; they are defined by =
*

the

* > individual
*

* > data only, no meaningful predictions can be made for the =
*

next patient.

* > So, if you need data description, you can directly see =
*

whether the

* > method provides you with the correct line, but you cannot =
*

count on

* > prediction: they can be anywhere.
*

* >
*

* > For the estimation procedure, my understanding is that large =
*

OMEGAs

* > will
*

* > discount population model influence on the individual fit, =
*

and in this

* > respect, the method will give you the correct answer =
*

(individual

* > parameters controlled by the individual data only). This is =
*

how you

* > trick nonmem into the individual model fit: assign huge =
*

OMEGAs. Whether

* > your true OMEGA value is 50 or 150 is more or less =
*

irrelevant: both

* > values are huge and do not provide informative priors for =
*

the

* > individual
*

* > parameters.
*

* >
*

* > Sometimes you get huge OMEGAs if there is a strong =
*

correlation between

* > parameters, so that combination of ETAs is finite while each =
*

of them

* > individually can be anywhere. Removal of some random effects =
*

can

* > help in
*

* > this case. Sometimes large OMEGAs are indicative of =
*

multivariate

* > distributions (or strong categorical covariate effects): =
*

this will be

* > seen on ETA distributions histograms or ETAs vs covariates =
*

plots.

* >
*

* > Overall, I think you have problems with the model or data =
*

rather than

* > with the estimation method failure.
*

* >
*

* > Thanks
*

* > Leonid
*

* >
*

* > --------------------------------------
*

* > Leonid Gibiansky, Ph.D.
*

* > President, QuantPharm LLC
*

* > web: www.quantpharm.com <http://www.quantpharm.com>
*

* > e-mail: LGibiansky at quantpharm.com <http://quantpharm.com>
*

* > tel: (301) 767 5566
*

* >
*

* >
*

* >
*

* >
*

* > Mark Sale - Next Level Solutions wrote:
*

* > >
*

* > > General question:
*

* > > What are practical limits on the magnitude of OMEGA that =
*

is

* > compatible
*

* > > with the FO and FOCE/I method? I seem to recall Stuart at =
*

one time

* > > suggesting that a CV of 0.5 (exponential OMEGA of 0.5) was =
*

about the

* > > limit at which the Taylor expansion can be considered a =
*

reasonable

* > > approximation of the real distribution. What about FOCE-I?
*

* > > I'm asking because I have a model that has an OMEGA of 13,
*

* > exponential
*

* > > (and sometime 100) FOCE-I, and it seems to be very poorly =
*

behaved in

* > > spite of overall, reasoable looking data (i.e., the =
*

structural model

* > > traces a line that looks like the data, but some people =
*

are WAY

* > above
*

* > > the line and some are WAY below, and some rise MUCH =
*

faster, and some

* > > rise MUCH later, by way I mean >10,000 fold, but residual =
*

error

* > looks
*

* > > not too bad). Looking at the raw data, I believe that the =
*

the

* > > variability is at least this large. Can I beleive that =
*

NONMEM FOCE

* > > (FO?) will behave reasonably?
*

* > > thanks
*

* > > Mark
*

* > >
*

* >
*

Received on Mon Jul 21 2008 - 04:26:21 EDT

Date: Mon, 21 Jul 2008 10:26:21 +0200

Mark, Leonid

I suspect that OMEGA values above 2 or 3 units are very doubtful. As =

Leonid pointed out, such variability levels does not tell us anything on =

priors. Another point to discuss about is the s.e. that are associated =

to these OMEGA estimates. What is their extent ?

Finally with such results I would have subjected the model to a =

bootstrap evaluation , to check the true confidence intervals of the =

model estimates.

Regards

Saïk

----- Original Message -----

From: Mark Sale - Next Level Solutions

Cc: nmusers

Sent: Sunday, July 20, 2008 3:52 AM

Subject: RE: [NMusers] algorithm limits

Thanks Leonid,

I believe what you tell me, and I understand that FOCE doesn't =

solve the problem with the approximation that FO makes, only reduces it =

(and possibly expands the range that the approximation is useful for?). =

Anyone out there with insight into what a practical limit is for FOCE =

and/or if there are any diagnostics that are helpful when you're close =

to it? Is it really 0.5 for FO?

Mark

Mark Sale MD

Next Level Solutions, LLC

www.NextLevelSolns.com

919-846-9185

-------- Original Message --------

Subject: Re: [NMusers] algorithm limits

From: Leonid Gibiansky <LGibiansky

Date: Sat, July 19, 2008 9:37 pm

To: Mark Sale - Next Level Solutions <mark

Cc: nmusers

Mark,

The description that you gave confirms that population model =

has limited

value unless four parameters (baseline, percent change, time =

to drop and

time to recovery) correlate somehow. If not, your data tells =

you that

the biomarker may start from very small or very large values, =

decrease

to zero or not decrease at all, and recover in a week or in a =

year.

Moreover, as I understood, there is no central tendency there: =

any

baseline, drop, time to decrease and time to recovery are =

independent

and equally-probable (otherwise, you would have reasonable =

OMEGAs with

the bell-shaped rather than flat distribution of random =

effects. Sparse

sampling will not work in this case, and if you have dense =

sampling, you

may just use two-stage to describe observed (uniform?) =

distribution of

individual parameters (and correlations if there are any).

Leonid

--------------------------------------

Leonid Gibiansky, Ph.D.

President, QuantPharm LLC

web: www.quantpharm.com

e-mail: LGibiansky at quantpharm.com

tel: (301) 767 5566

Mark Sale - Next Level Solutions wrote:

and the

marker falls from

change from

weeks, then

later.)

variable

somewhere

<mark

or

individual

the

next patient.

whether the

count on

OMEGAs

and in this

(individual

how you

OMEGAs. Whether

irrelevant: both

the

correlation between

of them

can

multivariate

this will be

plots.

rather than

is

one time

about the

reasonable

behaved in

structural model

are WAY

faster, and some

error

the

NONMEM FOCE

(image/png attachment: left.letterhead_)