# Re: algorithm limits

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
> 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 =
> > 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
> >
>