From: Faelens, Ruben <*Ruben.Faelens*>

Date: Fri, 13 Apr 2018 17:40:57 +0000

Hi Tingjie,

I used Nelder-Mead because it is the default method in R optim(). No other reasoning.

With regards to OFIM: the inverse of the hessian of the likelihood at the optimum ETA is an estimate for the standard error of this ETA estimate. This is called the Observed Fisher Information Matrix.

If you will forgive me the childish language, this can be explained intuitively: the second derivative describes how 'pointy' the OFV is. It shows how much the objective function changes when you 'jiggle' around the ETA parameters.

A very pointy OFV means a high change in OFV for different estimates, and therefore high certainty and low residual error.

An almost flat OFV means different estimates give similar OFV (are equally likely), and therefore a low certainty and high residual error.

Subjects with no information will have ETA =0 as the maximum likelihood estimate (shrinkage), but the uncertainty will be equal to population IIV.

I forgot the exact formulas though, you can find it in literature discussing d-optimality.

In my view, taking uncertainty into account on posthoc estimates is an elegant solution to sparse profiles, but I have rarely seen it applied in practice. I am not entirely certain whether the asymptotic convergence of OFIM to the residual error applies for ETA estimates either, especially in the case of sparse sampling. Which is why I searched for feedback from the list.

Anyway, the above is largely an academic interest anyway. Good luck with your project!

Please excuse my brevity, this was sent from a mobile device

________________________________

From: Tingjie Guo <iam

Sent: Friday, April 13, 2018 5:20:40 PM

To: Jakob Ribbing

Cc: Faelens, Ruben (Belgium); nmusers

Subject: Re: [NMusers] ETAs & SIGMA in external validation

o raise an extended question: if the model contains one covariate, the values of which from external data make parameters negative, what would be the optimal solution for this?

Mead method instead of others in your software? And what do you mean OFIM?

Met vriendelijke groet

,

T

G

On Tue, Apr 10, 2018 at 3:19 PM, Jakob Ribbing <jakob.ribbing

Hi Ruben,

I think I misread Tingjies original posting as taking ABS(ETA), whereas his initial attempt was actually ABS(1+ETA), which is less problematic.

The latter would not bias simulations much if IIV is e.g. 30% CV, agreed.

However, as Tingjies is mainly interested in estimation, I believe that without the ABS-correction, no subject will have the EBE at ETA <= -1 for a parameter that could not be <=0.

Unless possibly in a subject which is a) uninformative on that parameter and b) where the eta is also part of an omega-block - a scenario which seems unlikely to me, but may occur in theory.

Implementing the ABS-korrection ETA=-1.2 would give the same solution (parameter value) as ETA=-0.8, but at a higher OFV for that subject.

It seems to me, if negative parameter values are only a problem in the eta search for the EBE, whereas the EBE for individual parameters are always positive, then it should be more straightforward to use FOCE, with the addition e.g.:

IF(PARA.LT.0.001) PARA=0.001

Probably, no subject will have such a low individual parameter value, when looking into the table output?

If there are any such subjects I would look for errors in the data set and nonmem code (as outlined in my initial reply).

The above concerns estimation.

In simulation (unless %CV is low), we may get a fraction of subject with PARA=0.001, which may be an unreasonably low parameter value.

Whether that is acceptable or not depends on the objectives and in this case there was no need for simulations even for model evaluation (?), so I will not elaborate further.

Cheers

Jakob

Information in this email and any attachments is confidential and intended solely for the use of the individual(s) to whom it is addressed or otherwise directed. Please note that any views or opinions presented in this email are solely those of the author and do not necessarily represent those of the Company. Finally, the recipient should check this email and any attachments for the presence of viruses. The Company accepts no liability for any damage caused by any virus transmitted by this email. All SGS services are rendered in accordance with the applicable SGS conditions of service available on request and accessible at http://www.sgs.com/en/Terms-and-Conditions.aspx

Received on Fri Apr 13 2018 - 13:40:57 EDT

Date: Fri, 13 Apr 2018 17:40:57 +0000

Hi Tingjie,

I used Nelder-Mead because it is the default method in R optim(). No other reasoning.

With regards to OFIM: the inverse of the hessian of the likelihood at the optimum ETA is an estimate for the standard error of this ETA estimate. This is called the Observed Fisher Information Matrix.

If you will forgive me the childish language, this can be explained intuitively: the second derivative describes how 'pointy' the OFV is. It shows how much the objective function changes when you 'jiggle' around the ETA parameters.

A very pointy OFV means a high change in OFV for different estimates, and therefore high certainty and low residual error.

An almost flat OFV means different estimates give similar OFV (are equally likely), and therefore a low certainty and high residual error.

Subjects with no information will have ETA =0 as the maximum likelihood estimate (shrinkage), but the uncertainty will be equal to population IIV.

I forgot the exact formulas though, you can find it in literature discussing d-optimality.

In my view, taking uncertainty into account on posthoc estimates is an elegant solution to sparse profiles, but I have rarely seen it applied in practice. I am not entirely certain whether the asymptotic convergence of OFIM to the residual error applies for ETA estimates either, especially in the case of sparse sampling. Which is why I searched for feedback from the list.

Anyway, the above is largely an academic interest anyway. Good luck with your project!

Please excuse my brevity, this was sent from a mobile device

________________________________

From: Tingjie Guo <iam

Sent: Friday, April 13, 2018 5:20:40 PM

To: Jakob Ribbing

Cc: Faelens, Ruben (Belgium); nmusers

Subject: Re: [NMusers] ETAs & SIGMA in external validation

o raise an extended question: if the model contains one covariate, the values of which from external data make parameters negative, what would be the optimal solution for this?

Mead method instead of others in your software? And what do you mean OFIM?

Met vriendelijke groet

,

T

G

On Tue, Apr 10, 2018 at 3:19 PM, Jakob Ribbing <jakob.ribbing

Hi Ruben,

I think I misread Tingjies original posting as taking ABS(ETA), whereas his initial attempt was actually ABS(1+ETA), which is less problematic.

The latter would not bias simulations much if IIV is e.g. 30% CV, agreed.

However, as Tingjies is mainly interested in estimation, I believe that without the ABS-correction, no subject will have the EBE at ETA <= -1 for a parameter that could not be <=0.

Unless possibly in a subject which is a) uninformative on that parameter and b) where the eta is also part of an omega-block - a scenario which seems unlikely to me, but may occur in theory.

Implementing the ABS-korrection ETA=-1.2 would give the same solution (parameter value) as ETA=-0.8, but at a higher OFV for that subject.

It seems to me, if negative parameter values are only a problem in the eta search for the EBE, whereas the EBE for individual parameters are always positive, then it should be more straightforward to use FOCE, with the addition e.g.:

IF(PARA.LT.0.001) PARA=0.001

Probably, no subject will have such a low individual parameter value, when looking into the table output?

If there are any such subjects I would look for errors in the data set and nonmem code (as outlined in my initial reply).

The above concerns estimation.

In simulation (unless %CV is low), we may get a fraction of subject with PARA=0.001, which may be an unreasonably low parameter value.

Whether that is acceptable or not depends on the objectives and in this case there was no need for simulations even for model evaluation (?), so I will not elaborate further.

Cheers

Jakob

Information in this email and any attachments is confidential and intended solely for the use of the individual(s) to whom it is addressed or otherwise directed. Please note that any views or opinions presented in this email are solely those of the author and do not necessarily represent those of the Company. Finally, the recipient should check this email and any attachments for the presence of viruses. The Company accepts no liability for any damage caused by any virus transmitted by this email. All SGS services are rendered in accordance with the applicable SGS conditions of service available on request and accessible at http://www.sgs.com/en/Terms-and-Conditions.aspx

Received on Fri Apr 13 2018 - 13:40:57 EDT