From: James G Wright <*james*>

Date: Tue, 22 Jul 2008 18:49:36 +0100

Hi Mark,

This is a good question. I am not aware of any public domain simulation

work in extreme variability scenarios, so my comments are based on the

theory.

The fundamental problem with the standard NONMEM algorithm, where the

fixed effect and random effects are estimated simultaneously by joint

maximum likelihood, is that the size of the variance parameters can bias

the mean, sometimes substantially (and hence generalized least squares

remains the standard algorithm in the statistical community). If the

variance model is even slightly misspecified (which it nearly always

is), this can be very damaging to your population mean estimate. Often

this leads to overestimates of the mean (so the variance can be smaller)

but in some circumstances you can get an excessively high CV% because

the mean is underestimated. The other common cause is that you have

parameter values close to zero in a subset of subjects, which on a

log-scale is minus infinity. Given that you are getting such a high CV%

the lognormal may not be the best approach. Switching to additive

intersubject variability would remove this dependence between mean and

variance, and I would definitely give this a try as an exploratory step.

In WinBugs or a nonparametric package, you could explore other

distributions - in NONMEM, your only option is subsetting the data

manually or using a mixture model, each of which bring new problems.

Linearization is a slightly different issue, as this effects how the

random effects impact the fit. FOCE linearization will probably give

you good individual fits if your individual data contain information

about all parameters (ie you could almost get away with a two-stage

approach), but this is not the same question as having reliable

population parameter estimates. From your description of the model it

sounds like you have variability parallel to the time axis, and this is

the toughest to linearize - this pushes you away from classic NONMEM as

a software choice if the problem lies in a parameter that shifts the

predicted curve horizontally in time (like a lag-time does).

As a rule of thumb, I would definitely be cynical about a CV over 300%,

and would be extremely cautious to use such a model for prediction. My

eyebrows start to raise at around 130%. If you decide to simulate, good

luck, and I would love to know your findings. Best regards,

James G Wright PhD

Scientist

Wright Dose Ltd

Tel: 44 (0) 772 5636914

-----Original Message-----

From: owner-nmusers

On Behalf Of Mark Sale - Next Level Solutions

Sent: 19 July 2008 21:13

Cc: nmusers

Subject: [NMusers] algorithm limits

General question:

What are practical limits on the magnitude of OMEGA that is compatible

with the FO and FOCE/I method? I seem to recall Stuart at one time

suggesting that a CV of 0.5 (exponential OMEGA of 0.5) was about the

limit at which the Taylor expansion can be considered a reasonable

approximation of the real distribution. What about FOCE-I?

I'm asking because I have a model that has an OMEGA of 13, exponential

(and sometime 100) FOCE-I, and it seems to be very poorly behaved in

spite of overall, reasoable looking data (i.e., the structural model

traces a line that looks like the data, but some people are WAY above

the line and some are WAY below, and some rise MUCH faster, and some

rise MUCH later, by way I mean >10,000 fold, but residual error looks

not too bad). Looking at the raw data, I believe that the the

variability is at least this large. Can I beleive that NONMEM FOCE

(FO?) will behave reasonably?

thanks

Mark

Received on Tue Jul 22 2008 - 13:49:36 EDT

Date: Tue, 22 Jul 2008 18:49:36 +0100

Hi Mark,

This is a good question. I am not aware of any public domain simulation

work in extreme variability scenarios, so my comments are based on the

theory.

The fundamental problem with the standard NONMEM algorithm, where the

fixed effect and random effects are estimated simultaneously by joint

maximum likelihood, is that the size of the variance parameters can bias

the mean, sometimes substantially (and hence generalized least squares

remains the standard algorithm in the statistical community). If the

variance model is even slightly misspecified (which it nearly always

is), this can be very damaging to your population mean estimate. Often

this leads to overestimates of the mean (so the variance can be smaller)

but in some circumstances you can get an excessively high CV% because

the mean is underestimated. The other common cause is that you have

parameter values close to zero in a subset of subjects, which on a

log-scale is minus infinity. Given that you are getting such a high CV%

the lognormal may not be the best approach. Switching to additive

intersubject variability would remove this dependence between mean and

variance, and I would definitely give this a try as an exploratory step.

In WinBugs or a nonparametric package, you could explore other

distributions - in NONMEM, your only option is subsetting the data

manually or using a mixture model, each of which bring new problems.

Linearization is a slightly different issue, as this effects how the

random effects impact the fit. FOCE linearization will probably give

you good individual fits if your individual data contain information

about all parameters (ie you could almost get away with a two-stage

approach), but this is not the same question as having reliable

population parameter estimates. From your description of the model it

sounds like you have variability parallel to the time axis, and this is

the toughest to linearize - this pushes you away from classic NONMEM as

a software choice if the problem lies in a parameter that shifts the

predicted curve horizontally in time (like a lag-time does).

As a rule of thumb, I would definitely be cynical about a CV over 300%,

and would be extremely cautious to use such a model for prediction. My

eyebrows start to raise at around 130%. If you decide to simulate, good

luck, and I would love to know your findings. Best regards,

James G Wright PhD

Scientist

Wright Dose Ltd

Tel: 44 (0) 772 5636914

-----Original Message-----

From: owner-nmusers

On Behalf Of Mark Sale - Next Level Solutions

Sent: 19 July 2008 21:13

Cc: nmusers

Subject: [NMusers] algorithm limits

General question:

What are practical limits on the magnitude of OMEGA that is compatible

with the FO and FOCE/I method? I seem to recall Stuart at one time

suggesting that a CV of 0.5 (exponential OMEGA of 0.5) was about the

limit at which the Taylor expansion can be considered a reasonable

approximation of the real distribution. What about FOCE-I?

I'm asking because I have a model that has an OMEGA of 13, exponential

(and sometime 100) FOCE-I, and it seems to be very poorly behaved in

spite of overall, reasoable looking data (i.e., the structural model

traces a line that looks like the data, but some people are WAY above

the line and some are WAY below, and some rise MUCH faster, and some

rise MUCH later, by way I mean >10,000 fold, but residual error looks

not too bad). Looking at the raw data, I believe that the the

variability is at least this large. Can I beleive that NONMEM FOCE

(FO?) will behave reasonably?

thanks

Mark

Received on Tue Jul 22 2008 - 13:49:36 EDT