RE: [NMusers] Reporting Modeling Results

I guess I missed one point with a quick glance. The SE estimate for =
covariate coefficient may change but the SE for the CL should not change =
significantly, if the data is informative and representative and the =
model is stable and number of bootstrapping is large enough and....

Alan

-----Original Message-----
From: owner-nmusers_at_globomaxnm.com
[mailto:owner-nmusers_at_globomaxnm.com]On Behalf Of Xiao, Alan
Sent: Friday, October 26, 2007 8:45 AM
To: Leonid Gibiansky; Elassaiss - Schaap, J. (Jeroen)
Cc: John Mondick; nmusers_at_globomaxnm.com
Subject: RE: [NMusers] Reporting Modeling Results


I would imagine that when scaling is different, the absolute magnitude =
of the estimate of the coefficient for a covariate would be different =
and therefore its standard error (SE) would be different accordingly, =
although the SEM% (SE/Mean*100) might not be.

Alan


-----Original Message-----
From: owner-nmusers_at_globomaxnm.com
[mailto:owner-nmusers_at_globomaxnm.com]On Behalf Of Leonid Gibiansky
Sent: Thursday, October 25, 2007 11:27 PM
To: Elassaiss - Schaap, J. (Jeroen)
Cc: John Mondick; nmusers_at_globomaxnm.com
Subject: Re: [NMusers] Reporting Modeling Results


Hi Jeroen,
I cannot see any extra covariance introduced by scaling by a fixed
numbers. Moreover, I even not sure that the term "centered" is
applicable to this model. It came from the linear model where the model

Y=ax+b
was called centered if presented in the form
Y=a1*(x-meanX)+b1
(here and below a and b are parameters, THETAs, while x is random)
Indeed, it is more stable in the second, centered form. If you assume
that a1 and b1 are normally distributed without correlation, then

a = a1 and
b = b1-a1*meanX

are correlated, and correlation is higher for large meanX.

In this regard, the model that consist of several equations of the type
Y=b*x^0.75
is equivalent to the model with
Y=b'*(x/10)^0.75,
no extra correlations added.

However, the model

Y=b*x^a

is more like the linear model because it can be presented in the log
scale as
log(Y)=a*log(x) + log(b)
and then it is better be centered:
log(Y)= a1*(log(x)-mean(log(x))) + log(b1)
or equivalently
Y=b1*(x/x0)^a1
where x0 is geometric mean of x.

Thus, these two (examples only!) models need to be centered:

CL=THETA()+(WT-70)*THETA()

or

CL=THETA()*(WT/70)^THETA()

but this one can be used in any shape and form

CL=THETA()*(WT/10)^0.75 = (THETA()/10^0.75) WT^0.75 =~ THETA() =
WT^0.75

This is just a scheme, not exact derivation/proof, but the bottom line
is that scaling by a constant should not influence the standard errors,
there should be another reason (may be, just insufficient sample size of =

the bootstrap process? or bounds on the parameters?) for the
discrepancy. May be we need to stratify it into more than two age
groups, to guarantee sufficient coverage of the entire age range of
interest in each and every bootstrap set.

Leonid




Elassaiss - Schaap, J. (Jeroen) wrote:
> Hi Leonid,
>
> The aspect of the results that John describes as being dependent on
> scaling are the (bootstrap) confidence intervals, not the parameter
> estimates. I actually agree with John's original statements about not
> being surprised by the inflated standard errors when the model is not
> centered. Removal of normalization induces covariance in the =
estimation
> of affected parameters. This covariance naturally leeds to inflated
> standard errors (w/o bootstrapping). And as we all know, high
> correlation between parameters can result in matrix singularity and
> consequently failing covariance steps, consistent with John's
> statements.
>
> Best regards,
> Jeroen
>
> J. Elassaiss-Schaap
> Scientist PK/PD
> Organon NV
> PO Box 20, 5340 BH Oss, Netherlands
> Phone: + 31 412 66 9320
> Fax: + 31 412 66 2506
> e-mail: jeroen.elassaiss_at_organon.com
>
> -----Original Message-----
> From: owner-nmusers_at_globomaxnm.com =
[mailto:owner-nmusers_at_globomaxnm.com]
> On Behalf Of Leonid Gibiansky
> Sent: Thursday, 25 October, 2007 23:30
> To: John Mondick
> Cc: nmusers_at_globomaxnm.com
> Subject: Re: [NMusers] Reporting Modeling Results
>
> Hi John,
> The code seems to be good, and the results, in my opinion, should not
> depend on scaling. One idea: if you started both sets of problems =
(with
> and without scaling) from the same initial conditions (while the
> solutions differ by factor 5 or so), nonmem could have difficulties
> finding the correct minimum when started far from optimum. If your
> initial conditions were coming from 10.4 kg-normalized solution, then =
it
>
> could explain wider CI for the non-normalized problem: some of those
> runs did not converged or converged to a local minima. If this is =
true,
> you may want to repeat the non-normalized set with the initial
> conditions closer to the solution (if you choose to use non-normalized =

> problem as the final model).
> Leonid
>
> --------------------------------------
> Leonid Gibiansky, Ph.D.
> President, QuantPharm LLC
> web: www.quantpharm.com
> e-mail: LGibiansky at quantpharm.com
> tel: (301) 767 5566
>
>
>
>
> John Mondick wrote:
>>
>> $PK
>>
>> TVCL = THETA(1)*(WT/10.4)**0.75
>> BETA = THETA(5)
>> TCL = THETA(6)
>> FCL = 1-BETA*EXP(-(AGE-1)*0.693/TCL)
>> TVCL2 = TVCL*FCL
>> CL = TVCL2*EXP(ETA(1))
>>
>> TVV1 = THETA(2)*(WT/10.4)
>> V1 = TVV1*EXP(ETA(2))
>>
>> TVV2 = THETA(3)*(WT/10.4)
>> V2 = TVV2*EXP(ETA(3))
>>
>> TVQ = THETA(4)*(WT/10.4)**0.75
>> Q = TVQ
>>
>
>
> This message, including the attachments, is confidential and may be =
privileged. If you are not an intended recipient, please notify the =
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Received on Fri Oct 26 2007 - 08:59:08 EDT