Re: OFV from different algorithms
Colleagues,
I believe that the ODE solutions may be different both in the predictions
and the gradients (which are computed and added for focei). Hence the
difference that Dennis saw.
Leonid is right that this can be done in NONMEM by adding an additional
estimation step, but I'm unsure if you can change the ODE solver in the
extra step and I'm unsure if it will estimate the ETAs when calculating the
objective function (like a POSTHOC step). If it re-estimates the ETAs,
then the objective function does not necessarily reflect the true solution
of the other method (FOCEi is conditioned on the individual estimates so
changing the ETAs will change the objective function).
Another way to compare and compare across software as Immanuel suggested
is by using nlmixr's objective function.
If you recast the model in nlmixr you can use the nlmixr ODE solver to
compare the NONMEM estimation methods with pre-specifying the ETAs (which
can be fixed) and then set maximum outer and inner evaluations to zero
However, this still requires the nlmixr ODE solving method to give the same
solutions as NONMEM (ie ADVAN6 or ADVAN13 may be different).
However, if you linearize the system and recast the linearized system in
nlmixr, you can use the NONMEM predictions coupled with nlmixr's objective
to get a FOCEi objective function based on any software's solutions.
Automatic linearization in nlmixr is not yet supported, though.
Matt.
Quoted reply history
On Thu, Sep 24, 2020 at 1:07 AM Immanuel Freedman <
[email protected]> wrote:
> Colleagues,
>
> In principle, the log likelihood can be used for such comparisons, however
> an L2 or peak Signal to Noise ratio or cross entropy is widely used in the
> signal processing literature for such comparisons.
>
> In NONNEM, the problem relates to numerical stability and accuracy of the
> approximations by which the OFV is estimated. The closed form exact
> derivative often results in far less numerical noise. This is also true
> for ADVAN6 when analytic derivatives (not numerical) are utilized.
>
> The signal processing and machine learning fields have evolved methods to
> handle this and these questions of comparing structures and covariance
> matrix have good practical solutions.
>
> It would be interesting to make the same comparisons in e.g., torsten,
> nlmixr or Pumas.
>
> Regards,
>
> Immanuel
>
> On September 23, 2020 8:49 PM Steven L Shafer <[email protected]>
> wrote:
>
>
> Dear Dennis:
>
>
>
> Gosh, that is super interesting. I would guess it was the differences in
> the first derivative between the methods. ADVAN4 will be closed form, and
> ADVAN6 will be (I believe) numerically calculated.
>
>
>
> Steve
>
>
>
> *From:* [email protected] <[email protected]> *On
> Behalf Of *Dennis Fisher
> *Sent:* Wednesday, September 23, 2020 5:36 PM
> *To:* Mark Tepeck <[email protected]>
> *Cc:* [email protected]
> *Subject:* Re: [NMusers] OFV from different algorithms
>
>
> Mark
>
>
> I posed a variant of this question to Stu Beal (Sheiner's statistician) >
> 20 years ago. He answered that one cannot compare ADVAN's, e.g., between
> ADVAN4 and ADVAN6 for the identical model.
>
> I verified this today when I ran a model with those two ADVAN's -- both
> converged, they yielded quite similar parameter estimates, but the OF
> differed by 60 units.
>
>
> I will be interested to hear Bob Bauer's reply to this issue.
>
>
> Dennis
>
>
> Dennis Fisher MD
> P < (The "P Less Than" Company)
> Phone / Fax: 1-866-PLessThan (1-866-753-7784)
> www.PLessThan.com http://www.plessthan.com/
>
>
>
>
>
>
> On Sep 23, 2020, at 5:09 PM, Mark Tepeck <[email protected]> wrote:
>
>
> Hi NMusers,
>
> I believe below is a very common question, but I could not find a
> clear answer in literature.
>
> Sometimes, we want to find out which algorithm offers the better model
> fitting for a given dataset.
>
> Is it possible to use the objective function value (OFV) to compare
> the model fitting computed by various algorithms (e.g. FOCE, IMP, and
> SAEM) ? Put it into another way, the same input dataset with the same
> fitted model/estimates will lead to similar OFVs among FOCE, IMP, and
> SAEM?
>
>
> Thanks,
>
>
> Mark
>
>
>