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<h1 data-toc-skip>Testing hierarchical pathway kinetics with
residue data on dimethenamid and dimethenamid-P</h1>
<h4 data-toc-skip class="author">Johannes
Ranke</h4>
<h4 data-toc-skip class="date">Last change on 20 April 2023,
last compiled on 19 Mai 2023</h4>
<small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/prebuilt/2022_dmta_pathway.rmd" class="external-link"><code>vignettes/prebuilt/2022_dmta_pathway.rmd</code></a></small>
<div class="hidden name"><code>2022_dmta_pathway.rmd</code></div>
</div>
<div class="section level2">
<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a>
</h2>
<p>The purpose of this document is to test demonstrate how nonlinear
hierarchical models (NLHM) based on the parent degradation models SFO,
FOMC, DFOP and HS, with parallel formation of two or more metabolites
can be fitted with the mkin package.</p>
<p>It was assembled in the course of work package 1.2 of Project Number
173340 (Application of nonlinear hierarchical models to the kinetic
evaluation of chemical degradation data) of the German Environment
Agency carried out in 2022 and 2023.</p>
<p>The mkin package is used in version 1.2.5, which is currently under
development. It contains the test data, and the functions used in the
evaluations. The <code>saemix</code> package is used as a backend for
fitting the NLHM, but is also loaded to make the convergence plot
function available.</p>
<p>This document is processed with the <code>knitr</code> package, which
also provides the <code>kable</code> function that is used to improve
the display of tabular data in R markdown documents. For parallel
processing, the <code>parallel</code> package is used.</p>
<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span><span class="op">)</span></span>
<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span>
<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span></span>
<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span>
<span><span class="va">n_cores</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span></span>
<span></span>
<span><span class="co"># We need to start a new cluster after defining a compiled model that is</span></span>
<span><span class="co"># saved as a DLL to the user directory, therefore we define a function</span></span>
<span><span class="co"># This is used again after defining the pathway model</span></span>
<span><span class="va">start_cluster</span> <span class="op"><-</span> <span class="kw">function</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span> <span class="op">{</span></span>
<span> <span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="op">{</span></span>
<span> <span class="va">ret</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makePSOCKcluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span>
<span> <span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span>
<span> <span class="va">ret</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makeForkCluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span>
<span> <span class="op">}</span></span>
<span> <span class="kw"><a href="https://rdrr.io/r/base/function.html" class="external-link">return</a></span><span class="op">(</span><span class="va">ret</span><span class="op">)</span></span>
<span><span class="op">}</span></span></code></pre></div>
</div>
<div class="section level2">
<h2 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a>
</h2>
<p>The test data are available in the mkin package as an object of class
<code>mkindsg</code> (mkin dataset group) under the identifier
<code>dimethenamid_2018</code>. The following preprocessing steps are
done in this document.</p>
<ul>
<li>The data available for the enantiomer dimethenamid-P (DMTAP) are
renamed to have the same substance name as the data for the racemic
mixture dimethenamid (DMTA). The reason for this is that no difference
between their degradation behaviour was identified in the EU risk
assessment.</li>
<li>Unnecessary columns are discarded</li>
<li>The observation times of each dataset are multiplied with the
corresponding normalisation factor also available in the dataset, in
order to make it possible to describe all datasets with a single set of
parameters that are independent of temperature</li>
<li>Finally, datasets observed in the same soil (<code>Elliot 1</code>
and <code>Elliot 2</code>) are combined, resulting in dimethenamid
(DMTA) data from six soils.</li>
</ul>
<p>The following commented R code performs this preprocessing.</p>
<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="co"># Apply a function to each of the seven datasets in the mkindsg object to create a list</span></span>
<span><span class="va">dmta_ds</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span>, <span class="kw">function</span><span class="op">(</span><span class="va">i</span><span class="op">)</span> <span class="op">{</span></span>
<span> <span class="va">ds_i</span> <span class="op"><-</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span><span class="op">[[</span><span class="va">i</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span> <span class="co"># Get a dataset</span></span>
<span> <span class="va">ds_i</span><span class="op">[</span><span class="va">ds_i</span><span class="op">$</span><span class="va">name</span> <span class="op">==</span> <span class="st">"DMTAP"</span>, <span class="st">"name"</span><span class="op">]</span> <span class="op"><-</span> <span class="st">"DMTA"</span> <span class="co"># Rename DMTAP to DMTA</span></span>
<span> <span class="va">ds_i</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html" class="external-link">subset</a></span><span class="op">(</span><span class="va">ds_i</span>, select <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"name"</span>, <span class="st">"time"</span>, <span class="st">"value"</span><span class="op">)</span><span class="op">)</span> <span class="co"># Select data</span></span>
<span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op"><-</span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op">*</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">f_time_norm</span><span class="op">[</span><span class="va">i</span><span class="op">]</span> <span class="co"># Normalise time</span></span>
<span> <span class="va">ds_i</span> <span class="co"># Return the dataset</span></span>
<span><span class="op">}</span><span class="op">)</span></span>
<span></span>
<span><span class="co"># Use dataset titles as names for the list elements</span></span>
<span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span>, <span class="kw">function</span><span class="op">(</span><span class="va">ds</span><span class="op">)</span> <span class="va">ds</span><span class="op">$</span><span class="va">title</span><span class="op">)</span></span>
<span></span>
<span><span class="co"># Combine data for Elliot soil to obtain a named list with six elements</span></span>
<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span> <span class="co">#</span></span>
<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span>
<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span></code></pre></div>
<p>The following tables show the 6 datasets.</p>
<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="kw">for</span> <span class="op">(</span><span class="va">ds_name</span> <span class="kw">in</span> <span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span>
<span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span></span>
<span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mkin_long_to_wide.html">mkin_long_to_wide</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="va">ds_name</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>,</span>
<span> caption <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"Dataset"</span>, <span class="va">ds_name</span><span class="op">)</span>,</span>
<span> booktabs <span class="op">=</span> <span class="cn">TRUE</span>, row.names <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span></span>
<span> <span class="fu"><a href="https://rdrr.io/r/base/cat.html" class="external-link">cat</a></span><span class="op">(</span><span class="st">"\n\\clearpage\n"</span><span class="op">)</span></span>
<span><span class="op">}</span></span></code></pre></div>
<table class="table">
<caption>Dataset Calke</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">DMTA</th>
<th align="right">M23</th>
<th align="right">M27</th>
<th align="right">M31</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0</td>
<td align="right">95.8</td>
<td align="right">NA</td>
<td align="right">NA</td>
<td align="right">NA</td>
</tr>
<tr class="even">
<td align="right">0</td>
<td align="right">98.7</td>
<td align="right">NA</td>
<td align="right">NA</td>
<td align="right">NA</td>
</tr>
<tr class="odd">
<td align="right">14</td>
<td align="right">60.5</td>
<td align="right">4.1</td>
<td align="right">1.5</td>
<td align="right">2.0</td>
</tr>
<tr class="even">
<td align="right">30</td>
<td align="right">39.1</td>
<td align="right">5.3</td>
<td align="right">2.4</td>
<td align="right">2.1</td>
</tr>
<tr class="odd">
<td align="right">59</td>
<td align="right">15.2</td>
<td align="right">6.0</td>
<td align="right">3.2</td>
<td align="right">2.2</td>
</tr>
<tr class="even">
<td align="right">120</td>
<td align="right">4.8</td>
<td align="right">4.3</td>
<td align="right">3.8</td>
<td align="right">1.8</td>
</tr>
<tr class="odd">
<td align="right">120</td>
<td align="right">4.6</td>
<td align="right">4.1</td>
<td align="right">3.7</td>
<td align="right">2.1</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset Borstel</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">DMTA</th>
<th align="right">M23</th>
<th align="right">M27</th>
<th align="right">M31</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.000000</td>
<td align="right">100.5</td>
<td align="right">NA</td>
<td align="right">NA</td>
<td align="right">NA</td>
</tr>
<tr class="even">
<td align="right">0.000000</td>
<td align="right">99.6</td>
<td align="right">NA</td>
<td align="right">NA</td>
<td align="right">NA</td>
</tr>
<tr class="odd">
<td align="right">1.941295</td>
<td align="right">91.9</td>
<td align="right">0.4</td>
<td align="right">NA</td>
<td align="right">NA</td>
</tr>
<tr class="even">
<td align="right">1.941295</td>
<td align="right">91.3</td>
<td align="right">0.5</td>
<td align="right">0.3</td>
<td align="right">0.1</td>
</tr>
<tr class="odd">
<td align="right">6.794534</td>
<td align="right">81.8</td>
<td align="right">1.2</td>
<td align="right">0.8</td>
<td align="right">1.0</td>
</tr>
<tr class="even">
<td align="right">6.794534</td>
<td align="right">82.1</td>
<td align="right">1.3</td>
<td align="right">0.9</td>
<td align="right">0.9</td>
</tr>
<tr class="odd">
<td align="right">13.589067</td>
<td align="right">69.1</td>
<td align="right">2.8</td>
<td align="right">1.4</td>
<td align="right">2.0</td>
</tr>
<tr class="even">
<td align="right">13.589067</td>
<td align="right">68.0</td>
<td align="right">2.0</td>
<td align="right">1.4</td>
<td align="right">2.5</td>
</tr>
<tr class="odd">
<td align="right">27.178135</td>
<td align="right">51.4</td>
<td align="right">2.9</td>
<td align="right">2.7</td>
<td align="right">4.3</td>
</tr>
<tr class="even">
<td align="right">27.178135</td>
<td align="right">51.4</td>
<td align="right">4.9</td>
<td align="right">2.6</td>
<td align="right">3.2</td>
</tr>
<tr class="odd">
<td align="right">56.297565</td>
<td align="right">27.6</td>
<td align="right">12.2</td>
<td align="right">4.4</td>
<td align="right">4.3</td>
</tr>
<tr class="even">
<td align="right">56.297565</td>
<td align="right">26.8</td>
<td align="right">12.2</td>
<td align="right">4.7</td>
<td align="right">4.8</td>
</tr>
<tr class="odd">
<td align="right">86.387643</td>
<td align="right">15.7</td>
<td align="right">12.2</td>
<td align="right">5.4</td>
<td align="right">5.0</td>
</tr>
<tr class="even">
<td align="right">86.387643</td>
<td align="right">15.3</td>
<td align="right">12.0</td>
<td align="right">5.2</td>
<td align="right">5.1</td>
</tr>
<tr class="odd">
<td align="right">115.507073</td>
<td align="right">7.9</td>
<td align="right">10.4</td>
<td align="right">5.4</td>
<td align="right">4.3</td>
</tr>
<tr class="even">
<td align="right">115.507073</td>
<td align="right">8.1</td>
<td align="right">11.6</td>
<td align="right">5.4</td>
<td align="right">4.4</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset Flaach</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">DMTA</th>
<th align="right">M23</th>
<th align="right">M27</th>
<th align="right">M31</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.0000000</td>
<td align="right">96.5</td>
<td align="right">NA</td>
<td align="right">NA</td>
<td align="right">NA</td>
</tr>
<tr class="even">
<td align="right">0.0000000</td>
<td align="right">96.8</td>
<td align="right">NA</td>
<td align="right">NA</td>
<td align="right">NA</td>
</tr>
<tr class="odd">
<td align="right">0.0000000</td>
<td align="right">97.0</td>
<td align="right">NA</td>
<td align="right">NA</td>
<td align="right">NA</td>
</tr>
<tr class="even">
<td align="right">0.6233856</td>
<td align="right">82.9</td>
<td align="right">0.7</td>
<td align="right">1.1</td>
<td align="right">0.3</td>
</tr>
<tr class="odd">
<td align="right">0.6233856</td>
<td align="right">86.7</td>
<td align="right">0.7</td>
<td align="right">1.1</td>
<td align="right">0.3</td>
</tr>
<tr class="even">
<td align="right">0.6233856</td>
<td align="right">87.4</td>
<td align="right">0.2</td>
<td align="right">0.3</td>
<td align="right">0.1</td>
</tr>
<tr class="odd">
<td align="right">1.8701567</td>
<td align="right">72.8</td>
<td align="right">2.2</td>
<td align="right">2.6</td>
<td align="right">0.7</td>
</tr>
<tr class="even">
<td align="right">1.8701567</td>
<td align="right">69.9</td>
<td align="right">1.8</td>
<td align="right">2.4</td>
<td align="right">0.6</td>
</tr>
<tr class="odd">
<td align="right">1.8701567</td>
<td align="right">71.9</td>
<td align="right">1.6</td>
<td align="right">2.3</td>
<td align="right">0.7</td>
</tr>
<tr class="even">
<td align="right">4.3636989</td>
<td align="right">51.4</td>
<td align="right">4.1</td>
<td align="right">5.0</td>
<td align="right">1.3</td>
</tr>
<tr class="odd">
<td align="right">4.3636989</td>
<td align="right">52.9</td>
<td align="right">4.2</td>
<td align="right">5.9</td>
<td align="right">1.2</td>
</tr>
<tr class="even">
<td align="right">4.3636989</td>
<td align="right">48.6</td>
<td align="right">4.2</td>
<td align="right">4.8</td>
<td align="right">1.4</td>
</tr>
<tr class="odd">
<td align="right">8.7273979</td>
<td align="right">28.5</td>
<td align="right">7.5</td>
<td align="right">8.5</td>
<td align="right">2.4</td>
</tr>
<tr class="even">
<td align="right">8.7273979</td>
<td align="right">27.3</td>
<td align="right">7.1</td>
<td align="right">8.5</td>
<td align="right">2.1</td>
</tr>
<tr class="odd">
<td align="right">8.7273979</td>
<td align="right">27.5</td>
<td align="right">7.5</td>
<td align="right">8.3</td>
<td align="right">2.3</td>
</tr>
<tr class="even">
<td align="right">13.0910968</td>
<td align="right">14.8</td>
<td align="right">8.4</td>
<td align="right">9.3</td>
<td align="right">3.3</td>
</tr>
<tr class="odd">
<td align="right">13.0910968</td>
<td align="right">13.4</td>
<td align="right">6.8</td>
<td align="right">8.7</td>
<td align="right">2.4</td>
</tr>
<tr class="even">
<td align="right">13.0910968</td>
<td align="right">14.4</td>
<td align="right">8.0</td>
<td align="right">9.1</td>
<td align="right">2.6</td>
</tr>
<tr class="odd">
<td align="right">17.4547957</td>
<td align="right">7.7</td>
<td align="right">7.2</td>
<td align="right">8.6</td>
<td align="right">4.0</td>
</tr>
<tr class="even">
<td align="right">17.4547957</td>
<td align="right">7.3</td>
<td align="right">7.2</td>
<td align="right">8.5</td>
<td align="right">3.6</td>
</tr>
<tr class="odd">
<td align="right">17.4547957</td>
<td align="right">8.1</td>
<td align="right">6.9</td>
<td align="right">8.9</td>
<td align="right">3.3</td>
</tr>
<tr class="even">
<td align="right">26.1821936</td>
<td align="right">2.0</td>
<td align="right">4.9</td>
<td align="right">8.1</td>
<td align="right">2.1</td>
</tr>
<tr class="odd">
<td align="right">26.1821936</td>
<td align="right">1.5</td>
<td align="right">4.3</td>
<td align="right">7.7</td>
<td align="right">1.7</td>
</tr>
<tr class="even">
<td align="right">26.1821936</td>
<td align="right">1.9</td>
<td align="right">4.5</td>
<td align="right">7.4</td>
<td align="right">1.8</td>
</tr>
<tr class="odd">
<td align="right">34.9095915</td>
<td align="right">1.3</td>
<td align="right">3.8</td>
<td align="right">5.9</td>
<td align="right">1.6</td>
</tr>
<tr class="even">
<td align="right">34.9095915</td>
<td align="right">1.0</td>
<td align="right">3.1</td>
<td align="right">6.0</td>
<td align="right">1.6</td>
</tr>
<tr class="odd">
<td align="right">34.9095915</td>
<td align="right">1.1</td>
<td align="right">3.1</td>
<td align="right">5.9</td>
<td align="right">1.4</td>
</tr>
<tr class="even">
<td align="right">43.6369893</td>
<td align="right">0.9</td>
<td align="right">2.7</td>
<td align="right">5.6</td>
<td align="right">1.8</td>
</tr>
<tr class="odd">
<td align="right">43.6369893</td>
<td align="right">0.7</td>
<td align="right">2.3</td>
<td align="right">5.2</td>
<td align="right">1.5</td>
</tr>
<tr class="even">
<td align="right">43.6369893</td>
<td align="right">0.7</td>
<td align="right">2.1</td>
<td align="right">5.6</td>
<td align="right">1.3</td>
</tr>
<tr class="odd">
<td align="right">52.3643872</td>
<td align="right">0.6</td>
<td align="right">1.6</td>
<td align="right">4.3</td>
<td align="right">1.2</td>
</tr>
<tr class="even">
<td align="right">52.3643872</td>
<td align="right">0.4</td>
<td align="right">1.1</td>
<td align="right">3.7</td>
<td align="right">0.9</td>
</tr>
<tr class="odd">
<td align="right">52.3643872</td>
<td align="right">0.5</td>
<td align="right">1.3</td>
<td align="right">3.9</td>
<td align="right">1.1</td>
</tr>
<tr class="even">
<td align="right">74.8062674</td>
<td align="right">0.4</td>
<td align="right">0.4</td>
<td align="right">2.5</td>
<td align="right">0.5</td>
</tr>
<tr class="odd">
<td align="right">74.8062674</td>
<td align="right">0.3</td>
<td align="right">0.4</td>
<td align="right">2.4</td>
<td align="right">0.5</td>
</tr>
<tr class="even">
<td align="right">74.8062674</td>
<td align="right">0.3</td>
<td align="right">0.3</td>
<td align="right">2.2</td>
<td align="right">0.3</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset BBA 2.2</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">DMTA</th>
<th align="right">M23</th>
<th align="right">M27</th>
<th align="right">M31</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.0000000</td>
<td align="right">98.09</td>
<td align="right">NA</td>
<td align="right">NA</td>
<td align="right">NA</td>
</tr>
<tr class="even">
<td align="right">0.0000000</td>
<td align="right">98.77</td>
<td align="right">NA</td>
<td align="right">NA</td>
<td align="right">NA</td>
</tr>
<tr class="odd">
<td align="right">0.7678922</td>
<td align="right">93.52</td>
<td align="right">0.36</td>
<td align="right">0.42</td>
<td align="right">0.36</td>
</tr>
<tr class="even">
<td align="right">0.7678922</td>
<td align="right">92.03</td>
<td align="right">0.40</td>
<td align="right">0.47</td>
<td align="right">0.33</td>
</tr>
<tr class="odd">
<td align="right">2.3036765</td>
<td align="right">88.39</td>
<td align="right">1.03</td>
<td align="right">0.71</td>
<td align="right">0.55</td>
</tr>
<tr class="even">
<td align="right">2.3036765</td>
<td align="right">87.18</td>
<td align="right">1.07</td>
<td align="right">0.82</td>
<td align="right">0.64</td>
</tr>
<tr class="odd">
<td align="right">5.3752452</td>
<td align="right">69.38</td>
<td align="right">3.60</td>
<td align="right">2.19</td>
<td align="right">1.94</td>
</tr>
<tr class="even">
<td align="right">5.3752452</td>
<td align="right">71.06</td>
<td align="right">3.66</td>
<td align="right">2.28</td>
<td align="right">1.62</td>
</tr>
<tr class="odd">
<td align="right">10.7504904</td>
<td align="right">45.21</td>
<td align="right">6.97</td>
<td align="right">5.45</td>
<td align="right">4.22</td>
</tr>
<tr class="even">
<td align="right">10.7504904</td>
<td align="right">46.81</td>
<td align="right">7.22</td>
<td align="right">5.19</td>
<td align="right">4.37</td>
</tr>
<tr class="odd">
<td align="right">16.1257355</td>
<td align="right">30.54</td>
<td align="right">8.65</td>
<td align="right">8.81</td>
<td align="right">6.31</td>
</tr>
<tr class="even">
<td align="right">16.1257355</td>
<td align="right">30.07</td>
<td align="right">8.38</td>
<td align="right">7.93</td>
<td align="right">6.85</td>
</tr>
<tr class="odd">
<td align="right">21.5009807</td>
<td align="right">21.60</td>
<td align="right">9.10</td>
<td align="right">10.25</td>
<td align="right">7.05</td>
</tr>
<tr class="even">
<td align="right">21.5009807</td>
<td align="right">20.41</td>
<td align="right">8.63</td>
<td align="right">10.77</td>
<td align="right">6.84</td>
</tr>
<tr class="odd">
<td align="right">32.2514711</td>
<td align="right">9.10</td>
<td align="right">7.63</td>
<td align="right">10.89</td>
<td align="right">6.53</td>
</tr>
<tr class="even">
<td align="right">32.2514711</td>
<td align="right">9.70</td>
<td align="right">8.01</td>
<td align="right">10.85</td>
<td align="right">7.11</td>
</tr>
<tr class="odd">
<td align="right">43.0019614</td>
<td align="right">6.58</td>
<td align="right">6.40</td>
<td align="right">10.41</td>
<td align="right">6.06</td>
</tr>
<tr class="even">
<td align="right">43.0019614</td>
<td align="right">6.31</td>
<td align="right">6.35</td>
<td align="right">10.35</td>
<td align="right">6.05</td>
</tr>
<tr class="odd">
<td align="right">53.7524518</td>
<td align="right">3.47</td>
<td align="right">5.35</td>
<td align="right">9.92</td>
<td align="right">5.50</td>
</tr>
<tr class="even">
<td align="right">53.7524518</td>
<td align="right">3.52</td>
<td align="right">5.06</td>
<td align="right">9.42</td>
<td align="right">5.07</td>
</tr>
<tr class="odd">
<td align="right">64.5029421</td>
<td align="right">3.40</td>
<td align="right">5.14</td>
<td align="right">9.15</td>
<td align="right">4.94</td>
</tr>
<tr class="even">
<td align="right">64.5029421</td>
<td align="right">3.67</td>
<td align="right">5.91</td>
<td align="right">9.25</td>
<td align="right">4.39</td>
</tr>
<tr class="odd">
<td align="right">91.3791680</td>
<td align="right">1.62</td>
<td align="right">3.35</td>
<td align="right">7.14</td>
<td align="right">3.64</td>
</tr>
<tr class="even">
<td align="right">91.3791680</td>
<td align="right">1.62</td>
<td align="right">2.87</td>
<td align="right">7.13</td>
<td align="right">3.55</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset BBA 2.3</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">DMTA</th>
<th align="right">M23</th>
<th align="right">M27</th>
<th align="right">M31</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.0000000</td>
<td align="right">99.33</td>
<td align="right">NA</td>
<td align="right">NA</td>
<td align="right">NA</td>
</tr>
<tr class="even">
<td align="right">0.0000000</td>
<td align="right">97.44</td>
<td align="right">NA</td>
<td align="right">NA</td>
<td align="right">NA</td>
</tr>
<tr class="odd">
<td align="right">0.6733938</td>
<td align="right">93.73</td>
<td align="right">0.18</td>
<td align="right">0.50</td>
<td align="right">0.47</td>
</tr>
<tr class="even">
<td align="right">0.6733938</td>
<td align="right">93.77</td>
<td align="right">0.18</td>
<td align="right">0.83</td>
<td align="right">0.34</td>
</tr>
<tr class="odd">
<td align="right">2.0201814</td>
<td align="right">87.84</td>
<td align="right">0.52</td>
<td align="right">1.25</td>
<td align="right">1.00</td>
</tr>
<tr class="even">
<td align="right">2.0201814</td>
<td align="right">89.82</td>
<td align="right">0.43</td>
<td align="right">1.09</td>
<td align="right">0.89</td>
</tr>
<tr class="odd">
<td align="right">4.7137565</td>
<td align="right">71.61</td>
<td align="right">1.19</td>
<td align="right">3.28</td>
<td align="right">3.58</td>
</tr>
<tr class="even">
<td align="right">4.7137565</td>
<td align="right">71.42</td>
<td align="right">1.11</td>
<td align="right">3.24</td>
<td align="right">3.41</td>
</tr>
<tr class="odd">
<td align="right">9.4275131</td>
<td align="right">45.60</td>
<td align="right">2.26</td>
<td align="right">7.17</td>
<td align="right">8.74</td>
</tr>
<tr class="even">
<td align="right">9.4275131</td>
<td align="right">45.42</td>
<td align="right">1.99</td>
<td align="right">7.91</td>
<td align="right">8.28</td>
</tr>
<tr class="odd">
<td align="right">14.1412696</td>
<td align="right">31.12</td>
<td align="right">2.81</td>
<td align="right">10.15</td>
<td align="right">9.67</td>
</tr>
<tr class="even">
<td align="right">14.1412696</td>
<td align="right">31.68</td>
<td align="right">2.83</td>
<td align="right">9.55</td>
<td align="right">8.95</td>
</tr>
<tr class="odd">
<td align="right">18.8550262</td>
<td align="right">23.20</td>
<td align="right">3.39</td>
<td align="right">12.09</td>
<td align="right">10.34</td>
</tr>
<tr class="even">
<td align="right">18.8550262</td>
<td align="right">24.13</td>
<td align="right">3.56</td>
<td align="right">11.89</td>
<td align="right">10.00</td>
</tr>
<tr class="odd">
<td align="right">28.2825393</td>
<td align="right">9.43</td>
<td align="right">3.49</td>
<td align="right">13.32</td>
<td align="right">7.89</td>
</tr>
<tr class="even">
<td align="right">28.2825393</td>
<td align="right">9.82</td>
<td align="right">3.28</td>
<td align="right">12.05</td>
<td align="right">8.13</td>
</tr>
<tr class="odd">
<td align="right">37.7100523</td>
<td align="right">7.08</td>
<td align="right">2.80</td>
<td align="right">10.04</td>
<td align="right">5.06</td>
</tr>
<tr class="even">
<td align="right">37.7100523</td>
<td align="right">8.64</td>
<td align="right">2.97</td>
<td align="right">10.78</td>
<td align="right">5.54</td>
</tr>
<tr class="odd">
<td align="right">47.1375654</td>
<td align="right">4.41</td>
<td align="right">2.42</td>
<td align="right">9.32</td>
<td align="right">3.79</td>
</tr>
<tr class="even">
<td align="right">47.1375654</td>
<td align="right">4.78</td>
<td align="right">2.51</td>
<td align="right">9.62</td>
<td align="right">4.11</td>
</tr>
<tr class="odd">
<td align="right">56.5650785</td>
<td align="right">4.92</td>
<td align="right">2.22</td>
<td align="right">8.00</td>
<td align="right">3.11</td>
</tr>
<tr class="even">
<td align="right">56.5650785</td>
<td align="right">5.08</td>
<td align="right">1.95</td>
<td align="right">8.45</td>
<td align="right">2.98</td>
</tr>
<tr class="odd">
<td align="right">80.1338612</td>
<td align="right">2.13</td>
<td align="right">1.28</td>
<td align="right">5.71</td>
<td align="right">1.78</td>
</tr>
<tr class="even">
<td align="right">80.1338612</td>
<td align="right">2.23</td>
<td align="right">0.99</td>
<td align="right">3.33</td>
<td align="right">1.55</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset Elliot</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">DMTA</th>
<th align="right">M23</th>
<th align="right">M27</th>
<th align="right">M31</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.000000</td>
<td align="right">97.5</td>
<td align="right">NA</td>
<td align="right">NA</td>
<td align="right">NA</td>
</tr>
<tr class="even">
<td align="right">0.000000</td>
<td align="right">100.7</td>
<td align="right">NA</td>
<td align="right">NA</td>
<td align="right">NA</td>
</tr>
<tr class="odd">
<td align="right">1.228478</td>
<td align="right">86.4</td>
<td align="right">NA</td>
<td align="right">NA</td>
<td align="right">NA</td>
</tr>
<tr class="even">
<td align="right">1.228478</td>
<td align="right">88.5</td>
<td align="right">NA</td>
<td align="right">NA</td>
<td align="right">1.5</td>
</tr>
<tr class="odd">
<td align="right">3.685435</td>
<td align="right">69.8</td>
<td align="right">2.8</td>
<td align="right">2.3</td>
<td align="right">5.0</td>
</tr>
<tr class="even">
<td align="right">3.685435</td>
<td align="right">77.1</td>
<td align="right">1.7</td>
<td align="right">2.1</td>
<td align="right">2.4</td>
</tr>
<tr class="odd">
<td align="right">8.599349</td>
<td align="right">59.0</td>
<td align="right">4.3</td>
<td align="right">4.0</td>
<td align="right">4.3</td>
</tr>
<tr class="even">
<td align="right">8.599349</td>
<td align="right">54.2</td>
<td align="right">5.8</td>
<td align="right">3.4</td>
<td align="right">5.0</td>
</tr>
<tr class="odd">
<td align="right">17.198697</td>
<td align="right">31.3</td>
<td align="right">8.2</td>
<td align="right">6.6</td>
<td align="right">8.0</td>
</tr>
<tr class="even">
<td align="right">17.198697</td>
<td align="right">33.5</td>
<td align="right">5.2</td>
<td align="right">6.9</td>
<td align="right">7.7</td>
</tr>
<tr class="odd">
<td align="right">25.798046</td>
<td align="right">19.6</td>
<td align="right">5.1</td>
<td align="right">8.2</td>
<td align="right">7.8</td>
</tr>
<tr class="even">
<td align="right">25.798046</td>
<td align="right">20.9</td>
<td align="right">6.1</td>
<td align="right">8.8</td>
<td align="right">6.5</td>
</tr>
<tr class="odd">
<td align="right">34.397395</td>
<td align="right">13.3</td>
<td align="right">6.0</td>
<td align="right">9.7</td>
<td align="right">8.0</td>
</tr>
<tr class="even">
<td align="right">34.397395</td>
<td align="right">15.8</td>
<td align="right">6.0</td>
<td align="right">8.8</td>
<td align="right">7.4</td>
</tr>
<tr class="odd">
<td align="right">51.596092</td>
<td align="right">6.7</td>
<td align="right">5.0</td>
<td align="right">8.3</td>
<td align="right">6.9</td>
</tr>
<tr class="even">
<td align="right">51.596092</td>
<td align="right">8.7</td>
<td align="right">4.2</td>
<td align="right">9.2</td>
<td align="right">9.0</td>
</tr>
<tr class="odd">
<td align="right">68.794789</td>
<td align="right">8.8</td>
<td align="right">3.9</td>
<td align="right">9.3</td>
<td align="right">5.5</td>
</tr>
<tr class="even">
<td align="right">68.794789</td>
<td align="right">8.7</td>
<td align="right">2.9</td>
<td align="right">8.5</td>
<td align="right">6.1</td>
</tr>
<tr class="odd">
<td align="right">103.192184</td>
<td align="right">6.0</td>
<td align="right">1.9</td>
<td align="right">8.6</td>
<td align="right">6.1</td>
</tr>
<tr class="even">
<td align="right">103.192184</td>
<td align="right">4.4</td>
<td align="right">1.5</td>
<td align="right">6.0</td>
<td align="right">4.0</td>
</tr>
<tr class="odd">
<td align="right">146.188928</td>
<td align="right">3.3</td>
<td align="right">2.0</td>
<td align="right">5.6</td>
<td align="right">3.1</td>
</tr>
<tr class="even">
<td align="right">146.188928</td>
<td align="right">2.8</td>
<td align="right">2.3</td>
<td align="right">4.5</td>
<td align="right">2.9</td>
</tr>
<tr class="odd">
<td align="right">223.583066</td>
<td align="right">1.4</td>
<td align="right">1.2</td>
<td align="right">4.1</td>
<td align="right">1.8</td>
</tr>
<tr class="even">
<td align="right">223.583066</td>
<td align="right">1.8</td>
<td align="right">1.9</td>
<td align="right">3.9</td>
<td align="right">2.6</td>
</tr>
<tr class="odd">
<td align="right">0.000000</td>
<td align="right">93.4</td>
<td align="right">NA</td>
<td align="right">NA</td>
<td align="right">NA</td>
</tr>
<tr class="even">
<td align="right">0.000000</td>
<td align="right">103.2</td>
<td align="right">NA</td>
<td align="right">NA</td>
<td align="right">NA</td>
</tr>
<tr class="odd">
<td align="right">1.228478</td>
<td align="right">89.2</td>
<td align="right">NA</td>
<td align="right">NA</td>
<td align="right">1.3</td>
</tr>
<tr class="even">
<td align="right">1.228478</td>
<td align="right">86.6</td>
<td align="right">NA</td>
<td align="right">NA</td>
<td align="right">NA</td>
</tr>
<tr class="odd">
<td align="right">3.685435</td>
<td align="right">78.2</td>
<td align="right">2.6</td>
<td align="right">1.0</td>
<td align="right">3.1</td>
</tr>
<tr class="even">
<td align="right">3.685435</td>
<td align="right">78.1</td>
<td align="right">2.4</td>
<td align="right">2.6</td>
<td align="right">2.3</td>
</tr>
<tr class="odd">
<td align="right">8.599349</td>
<td align="right">55.6</td>
<td align="right">5.5</td>
<td align="right">4.5</td>
<td align="right">3.4</td>
</tr>
<tr class="even">
<td align="right">8.599349</td>
<td align="right">53.0</td>
<td align="right">5.6</td>
<td align="right">4.6</td>
<td align="right">4.3</td>
</tr>
<tr class="odd">
<td align="right">17.198697</td>
<td align="right">33.7</td>
<td align="right">7.3</td>
<td align="right">7.6</td>
<td align="right">7.8</td>
</tr>
<tr class="even">
<td align="right">17.198697</td>
<td align="right">33.2</td>
<td align="right">6.5</td>
<td align="right">6.7</td>
<td align="right">8.7</td>
</tr>
<tr class="odd">
<td align="right">25.798046</td>
<td align="right">20.9</td>
<td align="right">5.8</td>
<td align="right">8.7</td>
<td align="right">7.7</td>
</tr>
<tr class="even">
<td align="right">25.798046</td>
<td align="right">19.9</td>
<td align="right">7.7</td>
<td align="right">7.6</td>
<td align="right">6.5</td>
</tr>
<tr class="odd">
<td align="right">34.397395</td>
<td align="right">18.2</td>
<td align="right">7.8</td>
<td align="right">8.0</td>
<td align="right">6.3</td>
</tr>
<tr class="even">
<td align="right">34.397395</td>
<td align="right">12.7</td>
<td align="right">7.3</td>
<td align="right">8.6</td>
<td align="right">8.7</td>
</tr>
<tr class="odd">
<td align="right">51.596092</td>
<td align="right">7.8</td>
<td align="right">7.0</td>
<td align="right">7.4</td>
<td align="right">5.7</td>
</tr>
<tr class="even">
<td align="right">51.596092</td>
<td align="right">9.0</td>
<td align="right">6.3</td>
<td align="right">7.2</td>
<td align="right">4.2</td>
</tr>
<tr class="odd">
<td align="right">68.794789</td>
<td align="right">11.4</td>
<td align="right">4.3</td>
<td align="right">10.3</td>
<td align="right">3.2</td>
</tr>
<tr class="even">
<td align="right">68.794789</td>
<td align="right">9.0</td>
<td align="right">3.8</td>
<td align="right">9.4</td>
<td align="right">4.2</td>
</tr>
<tr class="odd">
<td align="right">103.192184</td>
<td align="right">3.9</td>
<td align="right">2.6</td>
<td align="right">6.5</td>
<td align="right">3.8</td>
</tr>
<tr class="even">
<td align="right">103.192184</td>
<td align="right">4.4</td>
<td align="right">2.8</td>
<td align="right">6.9</td>
<td align="right">4.0</td>
</tr>
<tr class="odd">
<td align="right">146.188928</td>
<td align="right">2.6</td>
<td align="right">1.6</td>
<td align="right">4.6</td>
<td align="right">4.5</td>
</tr>
<tr class="even">
<td align="right">146.188928</td>
<td align="right">3.4</td>
<td align="right">1.1</td>
<td align="right">4.5</td>
<td align="right">4.5</td>
</tr>
<tr class="odd">
<td align="right">223.583066</td>
<td align="right">2.0</td>
<td align="right">1.4</td>
<td align="right">4.3</td>
<td align="right">3.8</td>
</tr>
<tr class="even">
<td align="right">223.583066</td>
<td align="right">1.7</td>
<td align="right">1.3</td>
<td align="right">4.2</td>
<td align="right">2.3</td>
</tr>
</tbody>
</table>
</div>
<div class="section level2">
<h2 id="separate-evaluations">Separate evaluations<a class="anchor" aria-label="anchor" href="#separate-evaluations"></a>
</h2>
<p>As a first step to obtain suitable starting parameters for the NLHM
fits, we do separate fits of several variants of the pathway model used
previously <span class="citation">(Ranke et al. 2021)</span>, varying
the kinetic model for the parent compound. Because the SFORB model often
provides faster convergence than the DFOP model, and can sometimes be
fitted where the DFOP model results in errors, it is included in the set
of parent models tested here.</p>
<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="op">!</span><span class="fu"><a href="https://rdrr.io/r/base/files2.html" class="external-link">dir.exists</a></span><span class="op">(</span><span class="st">"dmta_dlls"</span><span class="op">)</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/files2.html" class="external-link">dir.create</a></span><span class="op">(</span><span class="st">"dmta_dlls"</span><span class="op">)</span></span>
<span><span class="va">m_sfo_path_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span>
<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span>
<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span>
<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
<span> name <span class="op">=</span> <span class="st">"m_sfo_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span>
<span> unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span>
<span> quiet <span class="op">=</span> <span class="cn">TRUE</span></span>
<span><span class="op">)</span></span>
<span><span class="va">m_fomc_path_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span>
<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span>
<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span>
<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
<span> name <span class="op">=</span> <span class="st">"m_fomc_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span>
<span> unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span>
<span> quiet <span class="op">=</span> <span class="cn">TRUE</span></span>
<span><span class="op">)</span></span>
<span><span class="va">m_dfop_path_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span>
<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span>
<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span>
<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
<span> name <span class="op">=</span> <span class="st">"m_dfop_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span>
<span> unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span>
<span> quiet <span class="op">=</span> <span class="cn">TRUE</span></span>
<span><span class="op">)</span></span>
<span><span class="va">m_sforb_path_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span>
<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span>
<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span>
<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
<span> name <span class="op">=</span> <span class="st">"m_sforb_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span>
<span> unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span>
<span> quiet <span class="op">=</span> <span class="cn">TRUE</span></span>
<span><span class="op">)</span></span>
<span><span class="va">m_hs_path_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"HS"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span>
<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span>
<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span>
<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
<span> name <span class="op">=</span> <span class="st">"m_hs_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span>
<span> unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span>
<span> quiet <span class="op">=</span> <span class="cn">TRUE</span></span>
<span><span class="op">)</span></span>
<span><span class="va">cl</span> <span class="op"><-</span> <span class="fu">start_cluster</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span>
<span></span>
<span><span class="va">deg_mods_1</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span>
<span> sfo_path_1 <span class="op">=</span> <span class="va">m_sfo_path_1</span>,</span>
<span> fomc_path_1 <span class="op">=</span> <span class="va">m_fomc_path_1</span>,</span>
<span> dfop_path_1 <span class="op">=</span> <span class="va">m_dfop_path_1</span>,</span>
<span> sforb_path_1 <span class="op">=</span> <span class="va">m_sforb_path_1</span>,</span>
<span> hs_path_1 <span class="op">=</span> <span class="va">m_hs_path_1</span><span class="op">)</span></span>
<span></span>
<span><span class="va">sep_1_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span>
<span> <span class="va">deg_mods_1</span>,</span>
<span> <span class="va">dmta_ds</span>,</span>
<span> error_model <span class="op">=</span> <span class="st">"const"</span>,</span>
<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
<span></span>
<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">sep_1_const</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
<table class="table">
<thead><tr class="header">
<th align="left"></th>
<th align="left">Calke</th>
<th align="left">Borstel</th>
<th align="left">Flaach</th>
<th align="left">BBA 2.2</th>
<th align="left">BBA 2.3</th>
<th align="left">Elliot</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="left">sfo_path_1</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">OK</td>
</tr>
<tr class="even">
<td align="left">fomc_path_1</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">OK</td>
</tr>
<tr class="odd">
<td align="left">dfop_path_1</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">C</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">OK</td>
</tr>
<tr class="even">
<td align="left">sforb_path_1</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">C</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">OK</td>
</tr>
<tr class="odd">
<td align="left">hs_path_1</td>
<td align="left">C</td>
<td align="left">C</td>
<td align="left">C</td>
<td align="left">C</td>
<td align="left">C</td>
<td align="left">C</td>
</tr>
</tbody>
</table>
<p>All separate pathway fits with SFO or FOMC for the parent and
constant variance converged (status OK). Most fits with DFOP or SFORB
for the parent converged as well. The fits with HS for the parent did
not converge with default settings.</p>
<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">sep_1_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">sep_1_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span>
<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">sep_1_tc</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
<table class="table">
<thead><tr class="header">
<th align="left"></th>
<th align="left">Calke</th>
<th align="left">Borstel</th>
<th align="left">Flaach</th>
<th align="left">BBA 2.2</th>
<th align="left">BBA 2.3</th>
<th align="left">Elliot</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="left">sfo_path_1</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">OK</td>
</tr>
<tr class="even">
<td align="left">fomc_path_1</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">C</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">C</td>
</tr>
<tr class="odd">
<td align="left">dfop_path_1</td>
<td align="left">OK</td>
<td align="left">C</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">OK</td>
</tr>
<tr class="even">
<td align="left">sforb_path_1</td>
<td align="left">OK</td>
<td align="left">C</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">OK</td>
<td align="left">OK</td>
</tr>
<tr class="odd">
<td align="left">hs_path_1</td>
<td align="left">C</td>
<td align="left">C</td>
<td align="left">C</td>
<td align="left">C</td>
<td align="left">C</td>
<td align="left">OK</td>
</tr>
</tbody>
</table>
<p>With the two-component error model, the set of fits with convergence
problems is slightly different, with convergence problems appearing for
different data sets when applying the DFOP and SFORB model and some
additional convergence problems when using the FOMC model for the
parent.</p>
</div>
<div class="section level2">
<h2 id="hierarchichal-model-fits">Hierarchichal model fits<a class="anchor" aria-label="anchor" href="#hierarchichal-model-fits"></a>
</h2>
<p>The following code fits two sets of the corresponding hierarchical
models to the data, one assuming constant variance, and one assuming
two-component error.</p>
<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">saem_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">sep_1_const</span>, <span class="va">sep_1_tc</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
<p>The run time for these fits was around two hours on five year old
hardware. After a recent hardware upgrade these fits complete in less
than twenty minutes.</p>
<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
<table class="table">
<thead><tr class="header">
<th align="left"></th>
<th align="left">const</th>
<th align="left">tc</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="left">sfo_path_1</td>
<td align="left">OK</td>
<td align="left">OK</td>
</tr>
<tr class="even">
<td align="left">fomc_path_1</td>
<td align="left">OK</td>
<td align="left">OK</td>
</tr>
<tr class="odd">
<td align="left">dfop_path_1</td>
<td align="left">OK</td>
<td align="left">OK</td>
</tr>
<tr class="even">
<td align="left">sforb_path_1</td>
<td align="left">OK</td>
<td align="left">OK</td>
</tr>
<tr class="odd">
<td align="left">hs_path_1</td>
<td align="left">OK</td>
<td align="left">OK</td>
</tr>
</tbody>
</table>
<p>According to the <code>status</code> function, all fits terminated
successfully.</p>
<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div>
<pre><code>Warning in FUN(X[[i]], ...): Could not obtain log likelihood with 'is' method
for sforb_path_1 const</code></pre>
<table class="table">
<thead><tr class="header">
<th align="left"></th>
<th align="right">npar</th>
<th align="right">AIC</th>
<th align="right">BIC</th>
<th align="right">Lik</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="left">sfo_path_1 const</td>
<td align="right">17</td>
<td align="right">2291.8</td>
<td align="right">2288.3</td>
<td align="right">-1128.9</td>
</tr>
<tr class="even">
<td align="left">sfo_path_1 tc</td>
<td align="right">18</td>
<td align="right">2276.3</td>
<td align="right">2272.5</td>
<td align="right">-1120.1</td>
</tr>
<tr class="odd">
<td align="left">fomc_path_1 const</td>
<td align="right">19</td>
<td align="right">2099.0</td>
<td align="right">2095.0</td>
<td align="right">-1030.5</td>
</tr>
<tr class="even">
<td align="left">fomc_path_1 tc</td>
<td align="right">20</td>
<td align="right">1939.6</td>
<td align="right">1935.5</td>
<td align="right">-949.8</td>
</tr>
<tr class="odd">
<td align="left">dfop_path_1 const</td>
<td align="right">21</td>
<td align="right">2038.8</td>
<td align="right">2034.4</td>
<td align="right">-998.4</td>
</tr>
<tr class="even">
<td align="left">hs_path_1 const</td>
<td align="right">21</td>
<td align="right">2024.2</td>
<td align="right">2019.8</td>
<td align="right">-991.1</td>
</tr>
<tr class="odd">
<td align="left">dfop_path_1 tc</td>
<td align="right">22</td>
<td align="right">1879.8</td>
<td align="right">1875.2</td>
<td align="right">-917.9</td>
</tr>
<tr class="even">
<td align="left">sforb_path_1 tc</td>
<td align="right">22</td>
<td align="right">1832.9</td>
<td align="right">1828.3</td>
<td align="right">-894.4</td>
</tr>
<tr class="odd">
<td align="left">hs_path_1 tc</td>
<td align="right">22</td>
<td align="right">1831.4</td>
<td align="right">1826.8</td>
<td align="right">-893.7</td>
</tr>
</tbody>
</table>
<p>When the goodness-of-fit of the models is compared, a warning is
obtained, indicating that the likelihood of the pathway fit with SFORB
for the parent compound and constant variance could not be calculated
with importance sampling (method ‘is’). As this is the default method on
which all AIC and BIC comparisons are based, this variant is not
included in the model comparison table. Comparing the goodness-of-fit of
the remaining models, HS model model with two-component error provides
the best fit. However, for batch experiments performed with constant
conditions such as the experiments evaluated here, there is no reason to
assume a discontinuity, so the SFORB model is preferable from a
mechanistic viewpoint. In addition, the information criteria AIC and BIC
are very similar for HS and SFORB. Therefore, the SFORB model is
selected here for further refinements.</p>
<div class="section level3">
<h3 id="parameter-identifiability-based-on-the-fisher-information-matrix">Parameter identifiability based on the Fisher Information
Matrix<a class="anchor" aria-label="anchor" href="#parameter-identifiability-based-on-the-fisher-information-matrix"></a>
</h3>
<p>Using the <code>illparms</code> function, ill-defined statistical
model parameters such as standard deviations of the degradation
parameters in the population and error model parameters can be
found.</p>
<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
<table class="table">
<thead><tr class="header">
<th align="left"></th>
<th align="left">const</th>
<th align="left">tc</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="left">sfo_path_1</td>
<td align="left"></td>
<td align="left">sd(DMTA_0)</td>
</tr>
<tr class="even">
<td align="left">fomc_path_1</td>
<td align="left"></td>
<td align="left">sd(DMTA_0)</td>
</tr>
<tr class="odd">
<td align="left">dfop_path_1</td>
<td align="left"></td>
<td align="left"></td>
</tr>
<tr class="even">
<td align="left">sforb_path_1</td>
<td align="left"></td>
<td align="left">sd(log_k_DMTA_bound_free)</td>
</tr>
<tr class="odd">
<td align="left">hs_path_1</td>
<td align="left"></td>
<td align="left">sd(log_tb)</td>
</tr>
</tbody>
</table>
<p>When using constant variance, no ill-defined variance parameters are
identified with the <code>illparms</code> function in any of the
degradation models. When using the two-component error model, there is
one ill-defined variance parameter in all variants except for the
variant using DFOP for the parent compound.</p>
<p>For the selected combination of the SFORB pathway model with
two-component error, the random effect for the rate constant from
reversibly bound DMTA to the free DMTA (<code>k_DMTA_bound_free</code>)
is not well-defined. Therefore, the fit is updated without assuming a
random effect for this parameter.</p>
<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">saem_sforb_path_1_tc_reduced</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>,</span>
<span> no_random_effect <span class="op">=</span> <span class="st">"log_k_DMTA_bound_free"</span><span class="op">)</span></span>
<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced</span><span class="op">)</span></span></code></pre></div>
<p>As expected, no ill-defined parameters remain. The model comparison
below shows that the reduced model is preferable.</p>
<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>, <span class="va">saem_sforb_path_1_tc_reduced</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div>
<table class="table">
<thead><tr class="header">
<th align="left"></th>
<th align="right">npar</th>
<th align="right">AIC</th>
<th align="right">BIC</th>
<th align="right">Lik</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="left">saem_sforb_path_1_tc_reduced</td>
<td align="right">21</td>
<td align="right">1830.3</td>
<td align="right">1825.9</td>
<td align="right">-894.2</td>
</tr>
<tr class="even">
<td align="left">saem_1[[“sforb_path_1”, “tc”]]</td>
<td align="right">22</td>
<td align="right">1832.9</td>
<td align="right">1828.3</td>
<td align="right">-894.4</td>
</tr>
</tbody>
</table>
<p>The convergence plot of the refined fit is shown below.</p>
<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></span></code></pre></div>
<p><img src="2022_dmta_pathway_files/figure-html/saem-sforb-path-1-tc-reduced-convergence-1.png" width="700" style="display: block; margin: auto;"></p>
<p>For some parameters, for example for <code>f_DMTA_ilr_1</code> and
<code>f_DMTA_ilr_2</code>, i.e. for two of the parameters determining
the formation fractions of the parallel formation of the three
metabolites, some movement of the parameters is still visible in the
second phase of the algorithm. However, the amplitude of this movement
is in the range of the amplitude towards the end of the first phase.
Therefore, it is likely that an increase in iterations would not improve
the parameter estimates very much, and it is proposed that the fit is
acceptable. No numeric convergence criterion is implemented in
saemix.</p>
</div>
<div class="section level3">
<h3 id="alternative-check-of-parameter-identifiability">Alternative check of parameter identifiability<a class="anchor" aria-label="anchor" href="#alternative-check-of-parameter-identifiability"></a>
</h3>
<p>As an alternative check of parameter identifiability <span class="citation">(Duchesne et al. 2021)</span>, multistart runs were
performed on the basis of the refined fit shown above.</p>
<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">saem_sforb_path_1_tc_reduced_multi</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/multistart.html">multistart</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced</span>,</span>
<span> n <span class="op">=</span> <span class="fl">32</span>, cores <span class="op">=</span> <span class="fl">10</span><span class="op">)</span></span></code></pre></div>
<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced_multi</span><span class="op">)</span></span></code></pre></div>
<pre><code><multistart> object with 32 fits:
E OK
15 17
OK: Fit terminated successfully
E: Error</code></pre>
<p>Out of the 32 fits that were initiated, only 17 terminated without an
error. The reason for this is that the wide variation of starting
parameters in combination with the parameter variation that is used in
the SAEM algorithm leads to parameter combinations for the degradation
model that the numerical integration routine cannot cope with. Because
of this variation of initial parameters, some of the model fits take up
to two times more time than the original fit.</p>
<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/par.html" class="external-link">par</a></span><span class="op">(</span>mar <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">12.1</span>, <span class="fl">4.1</span>, <span class="fl">2.1</span>, <span class="fl">2.1</span><span class="op">)</span><span class="op">)</span></span>
<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced_multi</span>, ylim <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.5</span>, <span class="fl">2</span><span class="op">)</span>, las <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div>
<div class="figure" style="text-align: center">
<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-2-1.png" alt="Parameter boxplots for the multistart runs that succeeded" width="960"><p class="caption">
Parameter boxplots for the multistart runs that succeeded
</p>
</div>
<p>However, visual analysis of the boxplot of the parameters obtained in
the successful fits confirms that the results are sufficiently
independent of the starting parameters, and there are no remaining
ill-defined parameters.</p>
</div>
</div>
<div class="section level2">
<h2 id="plots-of-selected-fits">Plots of selected fits<a class="anchor" aria-label="anchor" href="#plots-of-selected-fits"></a>
</h2>
<p>The SFORB pathway fits with full and reduced parameter distribution
model are shown below.</p>
<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
<div class="figure" style="text-align: center">
<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-3-1.png" alt="SFORB pathway fit with two-component error" width="700"><p class="caption">
SFORB pathway fit with two-component error
</p>
</div>
<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced</span><span class="op">)</span></span></code></pre></div>
<div class="figure" style="text-align: center">
<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-4-1.png" alt="SFORB pathway fit with two-component error, reduced parameter model" width="700"><p class="caption">
SFORB pathway fit with two-component error, reduced parameter model
</p>
</div>
<p>Plots of the remaining fits and listings for all successful fits are
shown in the Appendix.</p>
<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">stopCluster</a></span><span class="op">(</span><span class="va">cl</span><span class="op">)</span></span></code></pre></div>
</div>
<div class="section level2">
<h2 id="conclusions">Conclusions<a class="anchor" aria-label="anchor" href="#conclusions"></a>
</h2>
<p>Pathway fits with SFO, FOMC, DFOP, SFORB and HS models for the parent
compound could be successfully performed.</p>
</div>
<div class="section level2">
<h2 id="acknowledgements">Acknowledgements<a class="anchor" aria-label="anchor" href="#acknowledgements"></a>
</h2>
<p>The helpful comments by Janina Wöltjen of the German Environment
Agency on earlier versions of this document are gratefully
acknowledged.</p>
</div>
<div class="section level2">
<h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a>
</h2>
<div id="refs" class="references csl-bib-body hanging-indent">
<div id="ref-duchesne_2021" class="csl-entry">
Duchesne, Ronan, Anissa Guillemin, Olivier Gandrillon, and Fabien
Crauste. 2021. <span>“Practical Identifiability in the Frame of
Nonlinear Mixed Effects Models: The Example of the in Vitro
Erythropoiesis.”</span> <em>BMC Bioinformatics</em> 22 (478). <a href="https://doi.org/10.1186/s12859-021-04373-4" class="external-link">https://doi.org/10.1186/s12859-021-04373-4</a>.
</div>
<div id="ref-ranke2021" class="csl-entry">
Ranke, Johannes, Janina Wöltjen, Jana Schmidt, and Emmanuelle Comets.
2021. <span>“Taking Kinetic Evaluations of Degradation Data to the Next
Level with Nonlinear Mixed-Effects Models.”</span> <em>Environments</em>
8 (8). <a href="https://doi.org/10.3390/environments8080071" class="external-link">https://doi.org/10.3390/environments8080071</a>.
</div>
</div>
</div>
<div class="section level2">
<h2 id="appendix">Appendix<a class="anchor" aria-label="anchor" href="#appendix"></a>
</h2>
<div class="section level3">
<h3 id="plots-of-hierarchical-fits-not-selected-for-refinement">Plots of hierarchical fits not selected for refinement<a class="anchor" aria-label="anchor" href="#plots-of-hierarchical-fits-not-selected-for-refinement"></a>
</h3>
<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sfo_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
<div class="figure" style="text-align: center">
<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-6-1.png" alt="SFO pathway fit with two-component error" width="700"><p class="caption">
SFO pathway fit with two-component error
</p>
</div>
<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"fomc_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
<div class="figure" style="text-align: center">
<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-7-1.png" alt="FOMC pathway fit with two-component error" width="700"><p class="caption">
FOMC pathway fit with two-component error
</p>
</div>
<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
<div class="figure" style="text-align: center">
<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-8-1.png" alt="HS pathway fit with two-component error" width="700"><p class="caption">
HS pathway fit with two-component error
</p>
</div>
</div>
<div class="section level3">
<h3 id="hierarchical-model-fit-listings">Hierarchical model fit listings<a class="anchor" aria-label="anchor" href="#hierarchical-model-fit-listings"></a>
</h3>
<div class="section level4">
<h4 id="fits-with-random-effects-for-all-degradation-parameters">Fits with random effects for all degradation parameters<a class="anchor" aria-label="anchor" href="#fits-with-random-effects-for-all-degradation-parameters"></a>
</h4>
</div>
<div class="section level4">
<h4 id="improved-fit-of-the-sforb-pathway-model-with-two-component-error">Improved fit of the SFORB pathway model with two-component
error<a class="anchor" aria-label="anchor" href="#improved-fit-of-the-sforb-pathway-model-with-two-component-error"></a>
</h4>
</div>
</div>
<div class="section level3">
<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a>
</h3>
<pre><code>R version 4.3.0 (2023-04-21)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Debian GNU/Linux 12 (bookworm)
Matrix products: default
BLAS: /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.21.so; LAPACK version 3.11.0
locale:
[1] LC_CTYPE=de_DE.UTF-8 LC_NUMERIC=C
[3] LC_TIME=de_DE.UTF-8 LC_COLLATE=de_DE.UTF-8
[5] LC_MONETARY=de_DE.UTF-8 LC_MESSAGES=de_DE.UTF-8
[7] LC_PAPER=de_DE.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C
time zone: Europe/Berlin
tzcode source: system (glibc)
attached base packages:
[1] parallel stats graphics grDevices utils datasets methods
[8] base
other attached packages:
[1] saemix_3.2 npde_3.3 knitr_1.42 mkin_1.2.5
loaded via a namespace (and not attached):
[1] sass_0.4.6 utf8_1.2.3 generics_0.1.3 stringi_1.7.12
[5] lattice_0.21-8 digest_0.6.31 magrittr_2.0.3 evaluate_0.21
[9] grid_4.3.0 fastmap_1.1.1 rprojroot_2.0.3 jsonlite_1.8.4
[13] processx_3.8.1 pkgbuild_1.4.0 deSolve_1.35 DBI_1.1.3
[17] mclust_6.0.0 ps_1.7.5 gridExtra_2.3 purrr_1.0.1
[21] fansi_1.0.4 scales_1.2.1 codetools_0.2-19 textshaping_0.3.6
[25] jquerylib_0.1.4 cli_3.6.1 crayon_1.5.2 rlang_1.1.1
[29] munsell_0.5.0 cachem_1.0.8 yaml_2.3.7 inline_0.3.19
[33] tools_4.3.0 memoise_2.0.1 dplyr_1.1.2 colorspace_2.1-0
[37] ggplot2_3.4.2 vctrs_0.6.2 R6_2.5.1 zoo_1.8-12
[41] lifecycle_1.0.3 stringr_1.5.0 fs_1.6.2 ragg_1.2.5
[45] callr_3.7.3 pkgconfig_2.0.3 desc_1.4.2 pkgdown_2.0.7
[49] bslib_0.4.2 pillar_1.9.0 gtable_0.3.3 glue_1.6.2
[53] systemfonts_1.0.4 highr_0.10 xfun_0.39 tibble_3.2.1
[57] lmtest_0.9-40 tidyselect_1.2.0 htmltools_0.5.5 nlme_3.1-162
[61] rmarkdown_2.21 compiler_4.3.0 prettyunits_1.1.1</code></pre>
</div>
<div class="section level3">
<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a>
</h3>
<pre><code>CPU model: AMD Ryzen 9 7950X 16-Core Processor</code></pre>
<pre><code>MemTotal: 64925476 kB</code></pre>
</div>
</div>
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