[Population Modeling] Parameter estimation for population models

[Hunt, C. Anthony]

I like Jacob’s concept of a spectrum of parameter estimation techniques.
In our work, we may be outside that spectrum.  So, I suggest expanding the
concept.  I’ll explain how and why.

For convenience of use and historical reasons, most population-focused
mathematical models purposefully conflate two fundamentally different
model types. They conflate a pattern-generating model with a
model-output-to-referent mapping model.

Accepting or rejecting that model conflation concept has profound
implications for how the models can and should be used scientifically.

Preferring conflation causes the parameterized model to become relatively
inflexible. The parameterized model is grounded tightly to a particular
conceptual model AND to a particular target reality (wet-lab or clinical
trial). To accomplish our requirements, we must keep those model types
uncoupled.  

The importance of keeping those model types uncoupled can be illustrated
by considering animal-to-human allometric scaling. The animal experiments
(the phenomena-generating [pattern-generating] model) are completely
separate from the task of discovering an appropriate allometric scaling
model [1][2], which is the mapping model. The same is true when attempting
to map measurements made on integrated organ-on-chip models to available
or expected measurements in humans: phenomena generation and the task of
mapping those measurements to human targets are separate activities.

We argue that mappings from [measurements of phenomena generated by
computational] models to wet-lab (or clinical) counterpart measurements
are analogous.  

Consider time. Parameterized mathematical model typically map to (ground
to) clock time. Might there be other, possibly even more biomimetic
alternatives? Maybe model time should map to some number of heartbeats or
some other measure of physiologic time [3][4]. By conflating clock time
into the mathematical model we may avoid even thinking about a physiologic
time based explanation because doing so may require reengineering the
model.  Physiologic (or biologic) time in two different experimental
conditions may not advance at precisely the same pace, yet the same model
could explain observations made in those different experiments by using
two different model-to-referent mapping models.

Physiologic (or biologic) time in two different experimental conditions
may not advance at precisely the same pace, yet the same model could
explain observations made in those different experiments by using two
different model-to-referent mapping models.

Many assumptions go into any phenomena generating model.  Often many more
assumptions go into the mapping-to-referent model. By keeping the models
and the processes separated, the weakest assumptions for both become clear
(which increases credibility).  However, when they are conflated (for a
modestly complicated model) it is impracticable (if not infeasible) for
someone outside the originating group to untangle mushed together
assumptions, and that increases the risks of reuse.

1. 
http://informahealthcare.com/doi/abs/10.1517/17425255.2014.934671?journalCo
de=emt
2. 
http://informahealthcare.com/doi/abs/10.3109/00498254.2015.1007112?journalC
ode=xen
3. http://aac.asm.org/content/27/6/887.full.pdf
4. http://ajpregu.physiology.org/content/245/6/R768



On 10/1/15, 2:05 AM, "popmodwkgrpimag-news-bounces at simtk.org on behalf of
popmodwkgrpimag-news-request at simtk.org"
<popmodwkgrpimag-news-bounces at simtk.org on behalf of
popmodwkgrpimag-news-request at simtk.org> wrote:

>Send PopModWkGrpIMAG-news mailing list submissions to
>	popmodwkgrpimag-news at simtk.org
>
>To subscribe or unsubscribe via the World Wide Web, visit
>	https://simtk.org/mailman/listinfo/popmodwkgrpimag-news
>or, via email, send a message with subject or body 'help' to
>	popmodwkgrpimag-news-request at simtk.org
>
>You can reach the person managing the list at
>	popmodwkgrpimag-news-owner at simtk.org
>
>When replying, please edit your Subject line so it is more specific
>than "Re: Contents of PopModWkGrpIMAG-news digest..."
>
>
>Today's Topics:
>
>   1. Re: Parameter estimation for population models (Jacob Barhak)
>
>
>----------------------------------------------------------------------
>
>Message: 1
>Date: Wed, 30 Sep 2015 17:52:34 -0500
>From: Jacob Barhak <jacob.barhak at gmail.com>
>To: Matthias Chung <mcchung at vt.edu>
>Cc: "IMAG \(popmodwkgrpimag-news at simtk.org\)"
>	<popmodwkgrpimag-news at simtk.org>
>Subject: Re: [Population Modeling] Parameter estimation for population
>	models
>Message-ID:
>	<CAM_y+3QXjthdodTJ-UTBaQ=JRpBoJTxRQVzo0O5cWR4p49kFxg at mail.gmail.com>
>Content-Type: text/plain; charset="utf-8"
>
>Thanks Mattias,
>
>Estimation of model parameters is an important topic. You will find that
>most of us in the list, had to deal with such issues.
>
>It is commendable that you decided to share code - model reproducibility
>is
>important. You may want to follow the discussion on the data and model
>sharing group they have interesting ways of coding differential equation
>models that help sharing those. This may be helpful in the future,
>
>Glancing at the paper, I see you took an approach of simplifying the
>problem to allow solution. Many of us use assumptions. In fact,  the model
>structure we use is an assumption as well. So there is a level of human
>judgment embedded in the estimation method. Although in your case it is
>small.
>
>I am curious how other people in the list estimate model parameters. I
>encountered several approaches in the past that build a spectrum of
>estimation techniques that can be characterized by amount of human
>decision
>making.
>
>One interesting end of the spectrum was reported by Steve Leff, where
>human
>experts go thorough a controlled process to determine parameters. Steve
>may
>want to elaborate on this technique. And I also know he used other
>techniques in the past as well from other sides of this estimation
>spectrum.
>
>In the middle of the spectrum some modelers just picking numbers reported
>in the literature to drive models.
>
>On the other extreme spectrum end, there are robust mathematical
>estimation
>techniques that rely on computation once the model is defined. The paper
>Matthias attached falls near this end of the spectrum.
>
>Where do modelers in this group find themselves? Do you rely more on human
>judgment for estimation? Or do you find yourself on the end of relying on
>numerical techniques?
>
>I hope people choose to share experiences and insights.
>
>                Jacob
>
>
>On Wed, Sep 30, 2015 at 9:42 AM, Matthias Chung <mcchung at vt.edu> wrote:
>
>> Hi everyone,
>>
>> Some of you might be interested in parameter estimation in population
>> dynamic models. We developed a new efficient and robust estimation code
>>in
>> Matlab to ?match? data with a differential equation model. We provide
>>the
>> code here:
>>
>> http://www.math.vt.edu/people/mcchung/resources/Continuous_Shooting.zip.
>>
>> The associated preprint can be found here:
>> http://arxiv.org/abs/1509.06926
>>
>> Thanks,
>>
>> Matthias Chung