From: Ethan Wu <*ethan.wu75*>

Date: Wed, 25 Feb 2009 09:49:19 -0800 (PST)

Hi Bob, I don't have enough math to understand difference of those matrix, =

but, the final matrix output from nonmem was positive definite in my=

case ________________________________ From: Bob Leary <ble=

ary

25, 2009 8:33:53 AM Subject: RE: [NMusers] var-cov matrix issue? If=

S is singular, then the 'covariance' matrix Rinv * S * Rinv is also singul=

ar, as is the 'inverse coveriance matrix' R*Spseudoinv*R (the eigenval=

ues of Spseudoinv for the usual Moore Penrose pseudoinverse are the inve=

rse of the eigenvalues of S, except where the S has a zero eigenvalue, in w=

hich case the corresponding eigenvalue of Spseudoinv is also zero. The e=

igenvectors are the same for S and Spseudoinv). Thus none of these quant=

ities is really directly suitable for use in simulation if positive defin=

iteness is a requirement. Robert H. Leary, PhD Fellow Pha=

rsight - A Certara(tm) Company 5625 Dillard Dr., Suite 205 Cary, NC 275=

11 Phone/Voice Mail: (919) 852-4625, Fax: (919) 859-6871 Email: b=

leary

s for the sole use of the intended recipient and may contain confidential=

and proprietary information. Any disclosure or distribution to third=

parties that is not specifically authorized by the sender is prohibited.=

If you are not the intended recipient, please contact the sender by rep=

ly email and destroy all copies of the original message. -----O=

riginal Message----- From: owner-nmusers

musers

ry 24, 2009 15:59 PM To: Bachman, William Cc: Ethan Wu; justin.wilkins

novartis.com; nmusers

x issue? According to the manual, covariance matrix IS calculated b=

y the default method (Rinv S Rinv) even when S is singular but the inver=

se covariance matrix (R Sinv R) cannot be computed as usual since S is s=

ingular (see below). From the same manual "An error message stating that=

the S matrix is singular indicates strong overparameterization". If som=

e of your OMEGAs are estimated with large error, I would try to remove t=

hose ETAs from the model. Scatter plot matrix of ETAs vs ETAs could be h=

elpful: if some of your ETAs are redundant, you could see strong correla=

tion of the ETAs estimates. -- The inverse variance-covaria=

nce matrix R*Sinv*R is also output (labeled as the =

Inverse Covariance Matrix), where Sinv is the inverse of the S matrix=

.. If S is judged to be singular, a pseudo-inverse of S is used,=

and since a pseudo-inverse is not unique, the inverse=

the inverse variance-covariance matrix can be used to develop a j=

oint con- fidence region for the complete set of population parameter=

s. As we usually develop a confidence region for a very limi=

ted set of popula- tion parameters, this use of the inverse variance-=

covariance matrix is somewhat limited. -- --------------------=

------------------ Leonid Gibiansky, Ph.D. President, QuantPharm LLC =

web: www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel=

: (301) 767 5566 Bachman, William wrote: > As a clar=

ification, this is not an error. It is an indication of a > numerical=

condition generated by the matrix algebra. it says that the > covari=

ance could not be calculated by the default method (possibly due > to il=

l conditioning) so it was calculated by an alternative method. You > =

could generate standard errors by an alternative method, e.g. bootstrap, =

------------------------------------------ > *From:* owner-nmusers

axnm.com > [mailto:owner-nmusers

vartis.com > *Cc:* nmusers

r-cov matrix issue? > > Hi Justin, only ETA was estimated with high SE=

f > such error message appears > > --------------------------------=

---------------------------------------- > *From:* "justin.wilkins

is.com" <justin.wilkins

ent:* Tuesday, February 24, 2009 1:19:17 PM > *Subject:* Fw: [NMusers] va=

r-cov matrix issue? > > > Dear Ethan, > > Algorithmically sing=

ular matrices are often a sign that that your model > is ill-conditioned=

in some way; I would be careful in how I used the > variance-covariance=

matrix in this scenario, and especially for > simulation. Are there any=

parameters that are being estimated with > particularly high standard e=

rrors? This might suggest overparamaterization. > > Not sure how helpf=

ul this is! > > Best > Justin > *Justin Wilkins > Senior Modeler=

** > Modeling & Simulation (Pharmacology)* > CHBS, WSJ-027.6.076 > No=

vartis Pharma AG > Lichtstrasse 35 > CH-4056 Basel > Switzerland > =

Phone: +41 61 324 6549 > Fax: +41 61 324 3039 > Cell: +41 76 561 0949=

com> > > > > ----- Forwarded by Justin Wilkins/PH/Novartis on 20=

09/02/24 07:15 PM ----- > *Ethan Wu <ethan.wu75

owner-nmusers

> To > nmusers

Subject > [NMusers] var-cov matrix issue? > > > =

> > > > > > Dear all, > I recently encounter thi=

s error message (below). My objective was to > use nonmem var-cov output=

for approximation of distribution of > parameters for performing a s=

imulation. > if such error message occur, is the var-cov matrix sti=

ll OK to use? > -- I know that better way to figure out distribution of p=

arameters is to > do bootstrap, but given limited time I have..... >=

> thanks > > "0MINIMIZATION SUCCESSFUL > NO. OF FUNCTION E=

VALUATIONS USED: 331 > NO. OF SIG. DIGITS IN FINAL EST.: 3.3 > =

ETABAR IS THE ARITHMETIC MEAN OF THE ETA-ESTIMATES, > AND THE P-VALUE IS=

GIVEN FOR THE NULL HYPOTHESIS THAT THE TRUE MEAN IS 0. > ETABAR: 0=

..11E-02 > SE: 0.23E-01 > P VAL.: 0.96E+00 > 0S MATRI=

X ALGORITHMICALLY SINGULAR > 0S MATRIX IS OUTPUT > 0INVERSE COVARIANCE =

MATRIX SET TO RS*R, WHERE S* IS A PSEUDO INVERSE OF S > 1 > " > > =

ICON plc made the following annotations. > ------------------------------=

------------------------------------------------ > This e-mail transmissi=

on may contain confidential or legally privileged information > that is i=

ntended only for the individual or entity named in the e-mail address. If y=

ou > are not the intended recipient, you are hereby notified that any dis=

closure, copying, > distribution, or reliance upon the contents of this e=

-mail is strictly prohibited. If > you have received this e-mail transmis=

sion in error, please reply to the sender, so that > ICON plc can arrange=

for proper delivery, and then please delete the message. > Thank You, =

*> ICON plc
> South County Business Park
> Leopardstown
> Dublin 18
=
*

*> Ireland
> Registered number: 145835
>
>
*

Received on Wed Feb 25 2009 - 12:49:19 EST

Date: Wed, 25 Feb 2009 09:49:19 -0800 (PST)

Hi Bob, I don't have enough math to understand difference of those matrix, =

but, the final matrix output from nonmem was positive definite in my=

case ________________________________ From: Bob Leary <ble=

ary

25, 2009 8:33:53 AM Subject: RE: [NMusers] var-cov matrix issue? If=

S is singular, then the 'covariance' matrix Rinv * S * Rinv is also singul=

ar, as is the 'inverse coveriance matrix' R*Spseudoinv*R (the eigenval=

ues of Spseudoinv for the usual Moore Penrose pseudoinverse are the inve=

rse of the eigenvalues of S, except where the S has a zero eigenvalue, in w=

hich case the corresponding eigenvalue of Spseudoinv is also zero. The e=

igenvectors are the same for S and Spseudoinv). Thus none of these quant=

ities is really directly suitable for use in simulation if positive defin=

iteness is a requirement. Robert H. Leary, PhD Fellow Pha=

rsight - A Certara(tm) Company 5625 Dillard Dr., Suite 205 Cary, NC 275=

11 Phone/Voice Mail: (919) 852-4625, Fax: (919) 859-6871 Email: b=

leary

s for the sole use of the intended recipient and may contain confidential=

and proprietary information. Any disclosure or distribution to third=

parties that is not specifically authorized by the sender is prohibited.=

If you are not the intended recipient, please contact the sender by rep=

ly email and destroy all copies of the original message. -----O=

riginal Message----- From: owner-nmusers

musers

ry 24, 2009 15:59 PM To: Bachman, William Cc: Ethan Wu; justin.wilkins

novartis.com; nmusers

x issue? According to the manual, covariance matrix IS calculated b=

y the default method (Rinv S Rinv) even when S is singular but the inver=

se covariance matrix (R Sinv R) cannot be computed as usual since S is s=

ingular (see below). From the same manual "An error message stating that=

the S matrix is singular indicates strong overparameterization". If som=

e of your OMEGAs are estimated with large error, I would try to remove t=

hose ETAs from the model. Scatter plot matrix of ETAs vs ETAs could be h=

elpful: if some of your ETAs are redundant, you could see strong correla=

tion of the ETAs estimates. -- The inverse variance-covaria=

nce matrix R*Sinv*R is also output (labeled as the =

Inverse Covariance Matrix), where Sinv is the inverse of the S matrix=

.. If S is judged to be singular, a pseudo-inverse of S is used,=

and since a pseudo-inverse is not unique, the inverse=

the inverse variance-covariance matrix can be used to develop a j=

oint con- fidence region for the complete set of population parameter=

s. As we usually develop a confidence region for a very limi=

ted set of popula- tion parameters, this use of the inverse variance-=

covariance matrix is somewhat limited. -- --------------------=

------------------ Leonid Gibiansky, Ph.D. President, QuantPharm LLC =

web: www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel=

: (301) 767 5566 Bachman, William wrote: > As a clar=

ification, this is not an error. It is an indication of a > numerical=

condition generated by the matrix algebra. it says that the > covari=

ance could not be calculated by the default method (possibly due > to il=

l conditioning) so it was calculated by an alternative method. You > =

could generate standard errors by an alternative method, e.g. bootstrap, =

------------------------------------------ > *From:* owner-nmusers

axnm.com > [mailto:owner-nmusers

vartis.com > *Cc:* nmusers

r-cov matrix issue? > > Hi Justin, only ETA was estimated with high SE=

f > such error message appears > > --------------------------------=

---------------------------------------- > *From:* "justin.wilkins

is.com" <justin.wilkins

ent:* Tuesday, February 24, 2009 1:19:17 PM > *Subject:* Fw: [NMusers] va=

r-cov matrix issue? > > > Dear Ethan, > > Algorithmically sing=

ular matrices are often a sign that that your model > is ill-conditioned=

in some way; I would be careful in how I used the > variance-covariance=

matrix in this scenario, and especially for > simulation. Are there any=

parameters that are being estimated with > particularly high standard e=

rrors? This might suggest overparamaterization. > > Not sure how helpf=

ul this is! > > Best > Justin > *Justin Wilkins > Senior Modeler=

** > Modeling & Simulation (Pharmacology)* > CHBS, WSJ-027.6.076 > No=

vartis Pharma AG > Lichtstrasse 35 > CH-4056 Basel > Switzerland > =

Phone: +41 61 324 6549 > Fax: +41 61 324 3039 > Cell: +41 76 561 0949=

com> > > > > ----- Forwarded by Justin Wilkins/PH/Novartis on 20=

09/02/24 07:15 PM ----- > *Ethan Wu <ethan.wu75

owner-nmusers

> To > nmusers

Subject > [NMusers] var-cov matrix issue? > > > =

> > > > > > Dear all, > I recently encounter thi=

s error message (below). My objective was to > use nonmem var-cov output=

for approximation of distribution of > parameters for performing a s=

imulation. > if such error message occur, is the var-cov matrix sti=

ll OK to use? > -- I know that better way to figure out distribution of p=

arameters is to > do bootstrap, but given limited time I have..... >=

> thanks > > "0MINIMIZATION SUCCESSFUL > NO. OF FUNCTION E=

VALUATIONS USED: 331 > NO. OF SIG. DIGITS IN FINAL EST.: 3.3 > =

ETABAR IS THE ARITHMETIC MEAN OF THE ETA-ESTIMATES, > AND THE P-VALUE IS=

GIVEN FOR THE NULL HYPOTHESIS THAT THE TRUE MEAN IS 0. > ETABAR: 0=

..11E-02 > SE: 0.23E-01 > P VAL.: 0.96E+00 > 0S MATRI=

X ALGORITHMICALLY SINGULAR > 0S MATRIX IS OUTPUT > 0INVERSE COVARIANCE =

MATRIX SET TO RS*R, WHERE S* IS A PSEUDO INVERSE OF S > 1 > " > > =

ICON plc made the following annotations. > ------------------------------=

------------------------------------------------ > This e-mail transmissi=

on may contain confidential or legally privileged information > that is i=

ntended only for the individual or entity named in the e-mail address. If y=

ou > are not the intended recipient, you are hereby notified that any dis=

closure, copying, > distribution, or reliance upon the contents of this e=

-mail is strictly prohibited. If > you have received this e-mail transmis=

sion in error, please reply to the sender, so that > ICON plc can arrange=

for proper delivery, and then please delete the message. > Thank You, =

Received on Wed Feb 25 2009 - 12:49:19 EST