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 <i...@tingjie.name>
Sent: Friday, April 13, 2018 5:20:40 PM
To: Jakob Ribbing
Cc: Faelens, Ruben (Belgium); nmusers@globomaxnm.com
Subject: Re: [NMusers] ETAs & SIGMA in external validation

@Ruben@Jakob Very worthwhile discusstion! I would like to 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?

@Ruben Out of curiosity, why did you use Nelder-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.ribb...@pharmetheus.com<mailto:jakob.ribb...@pharmetheus.com>> wrote:
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



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