Merge branch 'v1.2.3_pkgdown'

author: Johannes Ranke <jranke@uni-bremen.de> 2023-04-20 20:17:12 +0200
committer: Johannes Ranke <jranke@uni-bremen.de> 2023-04-20 20:17:12 +0200
commit: 7b7c4bf493ba15824ea43bed764661678b4aca03 (patch)
tree: 48de1e32327c36ee49fc476dc76ece8397ab55c6 /docs/articles/prebuilt/2022_dmta_pathway.html
parent: 842998b688037c007d8876d7e1110c929fe2374c (diff)
parent: 9ae42bd20bc2543a94cf1581ba9820c2f9e3afbd (diff)
1 files changed, 2053 insertions, 0 deletions
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+      <a href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a>
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+    <div class="page-header toc-ignore">
+      <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 20 April 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 1.2.3, 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">&lt;-</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">&lt;-</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">&lt;-</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">&lt;-</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">&lt;-</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">&lt;-</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">$</span><span class="va">name</span> <span class="op">==</span> <span class="st">"DMTAP"</span>, <span class="st">"name"</span><span class="op">]</span> <span class="op">&lt;-</span>  <span class="st">"DMTA"</span>              <span class="co"># Rename DMTAP to DMTA</span></span>
+<span>  <span class="va">ds_i</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html" class="external-link">subset</a></span><span class="op">(</span><span class="va">ds_i</span>, select <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"name"</span>, <span class="st">"time"</span>, <span class="st">"value"</span><span class="op">)</span><span class="op">)</span> <span class="co"># Select data</span></span>
+<span>  <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op">&lt;-</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">&lt;-</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">&lt;-</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">&lt;-</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">&lt;-</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">&lt;-</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">&lt;-</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">&lt;-</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">&lt;-</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">&lt;-</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">&lt;-</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">&lt;-</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">&lt;-</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">|&gt;</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">&lt;-</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">|&gt;</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">&lt;-</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">|&gt;</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">|&gt;</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">|&gt;</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">&lt;-</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">|&gt;</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">&lt;-</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>&lt;multistart&gt; 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 4.2.3 (2023-03-15)
+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
+
+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       
+
+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_1.2.3
+
+loaded via a namespace (and not attached):
+ [1] deSolve_1.35      zoo_1.8-12        tidyselect_1.2.0  xfun_0.38        
+ [5] bslib_0.4.2       purrr_1.0.1       lattice_0.21-8    colorspace_2.1-0 
+ [9] vctrs_0.6.1       generics_0.1.3    htmltools_0.5.5   yaml_2.3.7       
+[13] utf8_1.2.3        rlang_1.1.0       pkgbuild_1.4.0    pkgdown_2.0.7    
+[17] jquerylib_0.1.4   pillar_1.9.0      glue_1.6.2        DBI_1.1.3        
+[21] lifecycle_1.0.3   stringr_1.5.0     munsell_0.5.0     gtable_0.3.3     
+[25] ragg_1.2.5        codetools_0.2-19  memoise_2.0.1     evaluate_0.20    
+[29] inline_0.3.19     callr_3.7.3       fastmap_1.1.1     ps_1.7.4         
+[33] lmtest_0.9-40     fansi_1.0.4       highr_0.10        scales_1.2.1     
+[37] cachem_1.0.7      desc_1.4.2        jsonlite_1.8.4    systemfonts_1.0.4
+[41] fs_1.6.1          textshaping_0.3.6 gridExtra_2.3     ggplot2_3.4.2    
+[45] digest_0.6.31     stringi_1.7.12    processx_3.8.0    dplyr_1.1.1      
+[49] grid_4.2.3        rprojroot_2.0.3   cli_3.6.1         tools_4.2.3      
+[53] magrittr_2.0.3    sass_0.4.5        tibble_3.2.1      crayon_1.5.2     
+[57] pkgconfig_2.0.3   prettyunits_1.1.1 rmarkdown_2.21    R6_2.5.1         
+[61] mclust_6.0.0      nlme_3.1-162      compiler_4.2.3   </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:       64936316 kB</code></pre>
+</div>
+</div>
+  </div>
+
+  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
+
+        <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2>
+    </nav>
+</div>
+
+</div>
+
+
+
+      <footer><div class="copyright">
+  <p></p>
+<p>Developed by Johannes Ranke.</p>
+</div>
+
+<div class="pkgdown">
+  <p></p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p>
+</div>
+
+      </footer>
+</div>
+
+  
+
+
+  
+
+  </body>
+</html>
author	Johannes Ranke <jranke@uni-bremen.de>	2023-04-20 20:17:12 +0200
committer	Johannes Ranke <jranke@uni-bremen.de>	2023-04-20 20:17:12 +0200
commit	7b7c4bf493ba15824ea43bed764661678b4aca03 (patch)
tree	48de1e32327c36ee49fc476dc76ece8397ab55c6 /docs/articles/prebuilt/2022_dmta_pathway.html
parent	842998b688037c007d8876d7e1110c929fe2374c (diff)
parent	9ae42bd20bc2543a94cf1581ba9820c2f9e3afbd (diff)