From: "Doshi, Sameer" sdoshi@amgen.com
Subject: [NMusers] Effect of FOCE vs FOCE INTER on success of covariance step within a model with additive error
Date: Thu, 9 Mar 2006 18:19:10 -0800 

Hello,
I am trying to fit a model with additive error; Y=EFF+ERR(1) using FOCE
which converges successfully but ends with the following error:
0R MATRIX ALGORITHMICALLY NON-POSITIVE-SEMIDEFINITE
 BUT NONSINGULAR
0COVARIANCE STEP ABORTED

I tried running the same model with FOCE INTER without making any other
changes to the control stream.  When running the model with FOCE INTER, the
model converged (with the same results and objective function) and with a
successful covariance step.

Could the group please offer some insight as to why using FOCE INTER
resulted in a successful covarariance step when FOCE did not?

Thanks for your help,
Sameer


Sameer Doshi
Pharmacokinetics and Drug Metabolism, Amgen Inc.
(805) 447-6941

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From: Takuya Okagaki okagaki@tanabe.co.jp
Subject: Re: [NMusers] Effect of FOCE vs FOCE INTER on success of covariance step within a model with additive error
Date: Fri, 10 Mar 2006 15:29:49 +0900

Dear Sameer

When we simulated the datasets which followed a normal distribution,
the estimates which resulted from good convergence using FOCE 
corresponds with those using FOCE INTER.
(Dr Beal told us that the estimates using FOCE and FOCE INTER should be equal
if the data followed a normal distribuion.)

However, some datasets showed not convergence using both methods,
some other datasets showed not convergence using FOCE but FOCE INTER,
and conversely, some other datasets showed not convergence using FOCE INTER but FOCE.

When many outlying values existed (but they follow a normal distribution strictly),
the FOCE and FOCE INTER methods cound not converge.
For datasets on a thin line between convergence or not convergence, results
to converge using FOCE might not be consist with those using FOCE INTER. 

INTER option requires many calculations for matrix, so there might be 
a delicate difference of a convergent result between FOCE INTER and FOCE methods.

Takuya Okagaki

Statistical Analysis Section
Clinical Research Planning & Coordination Department
Clinical Research Division
Tanabe Seiyaku Co., Ltd.
e-mail: okagaki@tanabe.co.jp
tel: +81-6-6205-5835  fax: +81-6-6205-5223
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From:  Xu Xu xu.xu@bms.com
Subject: Re: [NMusers] Effect of FOCE vs FOCE INTER on success of covariance step within a model with additive error
Date: Fri, 10 Mar 2006 09:43:08 -0500

Hi,

When I get this error massage, I usually set MATRIX=S in $COV and then the covariance
step would run successfully. But this doesn't work for "R MATRIX SINGULAR". Could
someone explain what is the reason for this? What is the difference
between R and S matrices?

Thanks a lot!

Xu 
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From:  "Gastonguay, Marc" marcg@metrumrg.com
Subject:  Re: [NMusers] Effect of FOCE vs FOCE INTER on success of covariance step within a model with additive error
Date:  Fri, 10 Mar 2006 10:31:57 -0500

Hi, Sameer. These results are a bit puzzling, but I'll offer a possible explanation below. The NONMEM documentation for
INTERACTION states: "The dependence on etas of the model for  intra-individual  random error  is preserved in the
computation of the objective function".  In your case there is no ETA-EPS interaction because the individual prediction
is not involved in the calculation of the residual variance, but INTERACTION may still play a small role.

I did investigate a couple of additive residual model examples, and although the starting OFV, min OFV and parameters
were identical (up to the precision reported) under FOCE vs FOCE INT, I did observe that some of the RES and WRES were
different in the 4th decimal place and some parameter gradients near the minimum were different in the second (or higher)
digit when comparing FOCE and FOCE INT. Did you observe similar differences? This could result in the difference you've
seen in the successful calculation of the VAR-COV matrix of the estimates during $COV.

Here's one possible explanation: The residuals in a NONMEM population model are weighted by the square root of the total
variance (inter-individual and intra-individual and inter-occasion,  etc.), which is represented by the Individual
Covariance Matrix (C[i]).  C[i] is a function of all variability terms; something like

C[i] = G*OMEGA*transpose(G) + H*SIGMA*transpose(H);

where G is the partial derivative matrix w.r.t. ETAs and H is the partial deriv matrix w.r.t. EPS.
Although the intra-individual variance is additive and ETA does not play a role in that portion of C[i], it may be
that INTERACTION imposes a difference in the way that the G matrix is calculated (evaluated at individual ETA, rather than ETA=0).
This discrepancy between FOCE and FOCE INT with additive residual var. is probably most evident when OMEGA is large, relative
to SIGMA. The NONMEM documentation is not clear on this topic, and I'll leave it up to someone with more intimate knowledge
of NONMEM internals to confirm my explanation.

The kind of behavior you've described could also be indicative of differences due to NONMEM bug fixes, hardware/OS, compiler
type, version and/or optimization settings. Were all of these identical in your 2 runs?

Marc 

Marc R. Gastonguay, Ph.D.
www.metrumrg.com 
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