From: pascal.girard

Date: Wed, 11 Feb 2015 17:29:45 +0000

Dear Aziz,

NM does not return the asymptotic SE of THETA(1) in model 1 on the log-scal=

e. So I would use model 2.

With best regards / Mit freundlichen Grüßen / Cordialement

Pascal

From: owner-nmusers

Behalf Of Chaouch Aziz

Sent: 11 February 2015 17:22

To: nmusers

Subject: [NMusers] Standard errors of estimates for strictly positive param=

eters

Hi,

I'm interested in generating samples from the asymptotic sampling distribut=

ion of population parameter estimates from a published PKPOP model fitted w=

ith NONMEM. By definition, parameter estimates are asymptotically (multivar=

iate) normally distributed (unconstrained optimization) with mean M and cov=

ariance C, where M is the vector of parameter estimates and C is the covari=

ance matrix of estimates (returned by $COV and available in the lst file).

Consider the 2 models below:

Model 1:

TVCL = THETA(1)

CL = TVCL*EXP(ETA(1))

Model 2:

TVCL = EXP(THETA(1))

CL = TVCL*EXP(ETA(1))

It is clear that model 1 and model 2 will provide exactly the same fit. How=

ever, although in both cases the standard error of estimates (SE) will refe=

r to THETA(1), the asymptotic sampling distribution of TVCL will be normal =

in model 1 while it will be lognormal in model 2. Therefore if one is inter=

ested in generating random samples from the asymptotic distribution of TVCL=

, some of these samples might be negative in model 1 while they'll remain n=

icely positive in model 2. The same would happen with bounds of (asymptotic=

) confidence intervals: in model 1 the lower bound of a 95% confidence inte=

rval for TVCL might be negative (unrealistic) while it would remain positiv=

e in model 2.

This has obviously no impact for point estimates or even confidence interva=

ls constructed via non-parametric bootstrap since boundary constraints can =

be placed on parameters in NONMEM. But what if one is interested in the asy=

mptotic covariance matrix of estimates returned by $COV? The asymptotic sam=

pling distribution of parameter estimates is (multivariate) normal only if =

the optimization is unconstrained! Doesn't this then speak in favour of mod=

el 2 over model 1? Or does NONMEM take care of it and returns the asymptoti=

c SE of THETA(1) in model 1 on the log-scale (when boundary constraints are=

placed on the parameter)?

Thanks,

Aziz Chaouch

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anish and Portuguese versions of this disclaimer.

Received on Wed Feb 11 2015 - 12:29:45 EST

Date: Wed, 11 Feb 2015 17:29:45 +0000

Dear Aziz,

NM does not return the asymptotic SE of THETA(1) in model 1 on the log-scal=

e. So I would use model 2.

With best regards / Mit freundlichen Grüßen / Cordialement

Pascal

From: owner-nmusers

Behalf Of Chaouch Aziz

Sent: 11 February 2015 17:22

To: nmusers

Subject: [NMusers] Standard errors of estimates for strictly positive param=

eters

Hi,

I'm interested in generating samples from the asymptotic sampling distribut=

ion of population parameter estimates from a published PKPOP model fitted w=

ith NONMEM. By definition, parameter estimates are asymptotically (multivar=

iate) normally distributed (unconstrained optimization) with mean M and cov=

ariance C, where M is the vector of parameter estimates and C is the covari=

ance matrix of estimates (returned by $COV and available in the lst file).

Consider the 2 models below:

Model 1:

TVCL = THETA(1)

CL = TVCL*EXP(ETA(1))

Model 2:

TVCL = EXP(THETA(1))

CL = TVCL*EXP(ETA(1))

It is clear that model 1 and model 2 will provide exactly the same fit. How=

ever, although in both cases the standard error of estimates (SE) will refe=

r to THETA(1), the asymptotic sampling distribution of TVCL will be normal =

in model 1 while it will be lognormal in model 2. Therefore if one is inter=

ested in generating random samples from the asymptotic distribution of TVCL=

, some of these samples might be negative in model 1 while they'll remain n=

icely positive in model 2. The same would happen with bounds of (asymptotic=

) confidence intervals: in model 1 the lower bound of a 95% confidence inte=

rval for TVCL might be negative (unrealistic) while it would remain positiv=

e in model 2.

This has obviously no impact for point estimates or even confidence interva=

ls constructed via non-parametric bootstrap since boundary constraints can =

be placed on parameters in NONMEM. But what if one is interested in the asy=

mptotic covariance matrix of estimates returned by $COV? The asymptotic sam=

pling distribution of parameter estimates is (multivariate) normal only if =

the optimization is unconstrained! Doesn't this then speak in favour of mod=

el 2 over model 1? Or does NONMEM take care of it and returns the asymptoti=

c SE of THETA(1) in model 1 on the log-scale (when boundary constraints are=

placed on the parameter)?

Thanks,

Aziz Chaouch

This message and any attachment are confidential and may be privileged or o=

therwise protected from disclosure. If you are not the intended recipient, =

you must not copy this message or attachment or disclose the contents to an=

y other person. If you have received this transmission in error, please not=

ify the sender immediately and delete the message and any attachment from y=

our system. Merck KGaA, Darmstadt, Germany and any of its subsidiaries do n=

ot accept liability for any omissions or errors in this message which may a=

rise as a result of E-Mail-transmission or for damages resulting from any u=

nauthorized changes of the content of this message and any attachment there=

to. Merck KGaA, Darmstadt, Germany and any of its subsidiaries do not guara=

ntee that this message is free of viruses and does not accept liability for=

any damages caused by any virus transmitted therewith.

Click http://www.merckgroup.com/disclaimer to access the German, French, Sp=

anish and Portuguese versions of this disclaimer.

Received on Wed Feb 11 2015 - 12:29:45 EST