From: Chaouch Aziz <*Aziz.Chaouch*>

Date: Wed, 11 Feb 2015 16:21:56 +0000

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

Received on Wed Feb 11 2015 - 11:21:56 EST

Date: Wed, 11 Feb 2015 16:21:56 +0000

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

Received on Wed Feb 11 2015 - 11:21:56 EST