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| author | Johannes Ranke <johannes.ranke@jrwb.de> | 2025-02-14 07:19:15 +0100 |
|---|---|---|
| committer | Johannes Ranke <johannes.ranke@jrwb.de> | 2025-02-14 07:19:15 +0100 |
| commit | b0f08271d1dae8ffaf57f557c27eba1314ece1d5 (patch) | |
| tree | 98da899d455d6945849d6f4b4e98adfb98dc8b2b /docs/dev/articles/web_only/FOCUS_Z.html | |
| parent | 7dc59c522d0639f6473463340e518e2e8074e364 (diff) | |
| parent | 55d9c2331e468efd364472555dbfae84603a4f73 (diff) | |
Merge branch 'main' into dev
Diffstat (limited to 'docs/dev/articles/web_only/FOCUS_Z.html')
| -rw-r--r-- | docs/dev/articles/web_only/FOCUS_Z.html | 504 |
1 files changed, 0 insertions, 504 deletions
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class="page-header toc-ignore"> - <h1 data-toc-skip>Example evaluation of FOCUS dataset Z</h1> - <h4 data-toc-skip class="author">Johannes -Ranke</h4> - - <h4 data-toc-skip class="date">Last change 16 January 2018 -(rebuilt 2023-04-16)</h4> - - <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/FOCUS_Z.rmd" class="external-link"><code>vignettes/web_only/FOCUS_Z.rmd</code></a></small> - <div class="hidden name"><code>FOCUS_Z.rmd</code></div> - - </div> - - - -<p><a href="http://www.jrwb.de" class="external-link">Wissenschaftlicher Berater, Kronacher -Str. 12, 79639 Grenzach-Wyhlen, Germany</a><br><a href="http://chem.uft.uni-bremen.de/ranke" class="external-link">Privatdozent at the -University of Bremen</a></p> -<div class="section level2"> -<h2 id="the-data">The data<a class="anchor" aria-label="anchor" href="#the-data"></a> -</h2> -<p>The following code defines the example dataset from Appendix 7 to the -FOCUS kinetics report <span class="citation">(FOCUS Work Group on -Degradation Kinetics 2014, 354)</span>.</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>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span><span class="va">LOD</span> <span class="op">=</span> <span class="fl">0.5</span></span> -<span><span class="va">FOCUS_2006_Z</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span></span> -<span> t <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</span>, <span class="fl">0.04</span>, <span class="fl">0.125</span>, <span class="fl">0.29</span>, <span class="fl">0.54</span>, <span class="fl">1</span>, <span class="fl">2</span>, <span class="fl">3</span>, <span class="fl">4</span>, <span class="fl">7</span>, <span class="fl">10</span>, <span class="fl">14</span>, <span class="fl">21</span>,</span> -<span> <span class="fl">42</span>, <span class="fl">61</span>, <span class="fl">96</span>, <span class="fl">124</span><span class="op">)</span>,</span> -<span> Z0 <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">100</span>, <span class="fl">81.7</span>, <span class="fl">70.4</span>, <span class="fl">51.1</span>, <span class="fl">41.2</span>, <span class="fl">6.6</span>, <span class="fl">4.6</span>, <span class="fl">3.9</span>, <span class="fl">4.6</span>, <span class="fl">4.3</span>, <span class="fl">6.8</span>,</span> -<span> <span class="fl">2.9</span>, <span class="fl">3.5</span>, <span class="fl">5.3</span>, <span class="fl">4.4</span>, <span class="fl">1.2</span>, <span class="fl">0.7</span><span class="op">)</span>,</span> -<span> Z1 <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</span>, <span class="fl">18.3</span>, <span class="fl">29.6</span>, <span class="fl">46.3</span>, <span class="fl">55.1</span>, <span class="fl">65.7</span>, <span class="fl">39.1</span>, <span class="fl">36</span>, <span class="fl">15.3</span>, <span class="fl">5.6</span>, <span class="fl">1.1</span>,</span> -<span> <span class="fl">1.6</span>, <span class="fl">0.6</span>, <span class="fl">0.5</span> <span class="op">*</span> <span class="va">LOD</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="cn">NA</span><span class="op">)</span>,</span> -<span> Z2 <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</span>, <span class="cn">NA</span>, <span class="fl">0.5</span> <span class="op">*</span> <span class="va">LOD</span>, <span class="fl">2.6</span>, <span class="fl">3.8</span>, <span class="fl">15.3</span>, <span class="fl">37.2</span>, <span class="fl">31.7</span>, <span class="fl">35.6</span>, <span class="fl">14.5</span>,</span> -<span> <span class="fl">0.8</span>, <span class="fl">2.1</span>, <span class="fl">1.9</span>, <span class="fl">0.5</span> <span class="op">*</span> <span class="va">LOD</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="cn">NA</span><span class="op">)</span>,</span> -<span> Z3 <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</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="fl">0.5</span> <span class="op">*</span> <span class="va">LOD</span>, <span class="fl">9.2</span>, <span class="fl">13.1</span>, <span class="fl">22.3</span>, <span class="fl">28.4</span>, <span class="fl">32.5</span>,</span> -<span> <span class="fl">25.2</span>, <span class="fl">17.2</span>, <span class="fl">4.8</span>, <span class="fl">4.5</span>, <span class="fl">2.8</span>, <span class="fl">4.4</span><span class="op">)</span><span class="op">)</span></span> -<span></span> -<span><span class="va">FOCUS_2006_Z_mkin</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_Z</span><span class="op">)</span></span></code></pre></div> -</div> -<div class="section level2"> -<h2 id="parent-and-one-metabolite">Parent and one metabolite<a class="anchor" aria-label="anchor" href="#parent-and-one-metabolite"></a> -</h2> -<p>The next step is to set up the models used for the kinetic analysis. -As the simultaneous fit of parent and the first metabolite is usually -straightforward, Step 1 (SFO for parent only) is skipped here. We start -with the model 2a, with formation and decline of metabolite Z1 and the -pathway from parent directly to sink included (default in mkin).</p> -<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">Z.2a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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">"Z1"</span><span class="op">)</span>,</span> -<span> Z1 <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 class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> -<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.Z.2a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.2a</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span></span> -<span><span class="co">## value of zero were removed from the data</span></span></code></pre> -<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.2a</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png" width="700"></p> -<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.2a</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div> -<pre><code><span><span class="co">## Estimate se_notrans t value Pr(>t) Lower Upper</span></span> -<span><span class="co">## Z0_0 97.01488 3.301084 29.3888 3.2971e-21 91.66556 102.3642</span></span> -<span><span class="co">## k_Z0 2.23601 0.207078 10.7979 3.3309e-11 1.95303 2.5600</span></span> -<span><span class="co">## k_Z1 0.48212 0.063265 7.6207 2.8154e-08 0.40341 0.5762</span></span> -<span><span class="co">## f_Z0_to_Z1 1.00000 0.094764 10.5525 5.3560e-11 0.00000 1.0000</span></span> -<span><span class="co">## sigma 4.80411 0.635638 7.5579 3.2592e-08 3.52677 6.0815</span></span></code></pre> -<p>As obvious from the parameter summary (the component of the summary), -the kinetic rate constant from parent compound Z to sink is very small -and the t-test for this parameter suggests that it is not significantly -different from zero. This suggests, in agreement with the analysis in -the FOCUS kinetics report, to simplify the model by removing the pathway -to sink.</p> -<p>A similar result can be obtained when formation fractions are used in -the model formulation:</p> -<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">Z.2a.ff</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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">"Z1"</span><span class="op">)</span>,</span> -<span> Z1 <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> use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> -<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.Z.2a.ff</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.2a.ff</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span></span> -<span><span class="co">## value of zero were removed from the data</span></span></code></pre> -<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.2a.ff</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png" width="700"></p> -<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.2a.ff</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div> -<pre><code><span><span class="co">## Estimate se_notrans t value Pr(>t) Lower Upper</span></span> -<span><span class="co">## Z0_0 97.01488 3.301084 29.3888 3.2971e-21 91.66556 102.3642</span></span> -<span><span class="co">## k_Z0 2.23601 0.207078 10.7979 3.3309e-11 1.95303 2.5600</span></span> -<span><span class="co">## k_Z1 0.48212 0.063265 7.6207 2.8154e-08 0.40341 0.5762</span></span> -<span><span class="co">## f_Z0_to_Z1 1.00000 0.094764 10.5525 5.3560e-11 0.00000 1.0000</span></span> -<span><span class="co">## sigma 4.80411 0.635638 7.5579 3.2592e-08 3.52677 6.0815</span></span></code></pre> -<p>Here, the ilr transformed formation fraction fitted in the model -takes a very large value, and the backtransformed formation fraction -from parent Z to Z1 is practically unity. Here, the covariance matrix -used for the calculation of confidence intervals is not returned as the -model is overparameterised.</p> -<p>A simplified model is obtained by removing the pathway to the sink. -</p> -<p>In the following, we use the parameterisation with formation -fractions in order to be able to compare with the results in the FOCUS -guidance, and as it makes it easier to use parameters obtained in a -previous fit when adding a further metabolite.</p> -<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">Z.3</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z1 <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>, use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> -<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.Z.3</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.3</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span></span> -<span><span class="co">## value of zero were removed from the data</span></span></code></pre> -<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.3</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png" width="700"></p> -<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.3</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div> -<pre><code><span><span class="co">## Estimate se_notrans t value Pr(>t) Lower Upper</span></span> -<span><span class="co">## Z0_0 97.01488 2.597342 37.352 2.0106e-24 91.67597 102.3538</span></span> -<span><span class="co">## k_Z0 2.23601 0.146904 15.221 9.1477e-15 1.95354 2.5593</span></span> -<span><span class="co">## k_Z1 0.48212 0.041727 11.554 4.8268e-12 0.40355 0.5760</span></span> -<span><span class="co">## sigma 4.80411 0.620208 7.746 1.6110e-08 3.52925 6.0790</span></span></code></pre> -<p>As there is only one transformation product for Z0 and no pathway to -sink, the formation fraction is internally fixed to unity.</p> -</div> -<div class="section level2"> -<h2 id="metabolites-z2-and-z3">Metabolites Z2 and Z3<a class="anchor" aria-label="anchor" href="#metabolites-z2-and-z3"></a> -</h2> -<p>As suggested in the FOCUS report, the pathway to sink was removed for -metabolite Z1 as well in the next step. While this step appears -questionable on the basis of the above results, it is followed here for -the purpose of comparison. Also, in the FOCUS report, it is assumed that -there is additional empirical evidence that Z1 quickly and exclusively -hydrolyses to Z2.</p> -<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">Z.5</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z1 <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">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z2 <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>, use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> -<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.Z.5</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.5</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span></span> -<span><span class="co">## value of zero were removed from the data</span></span></code></pre> -<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.5</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png" width="700"></p> -<p>Finally, metabolite Z3 is added to the model. We use the optimised -differential equation parameter values from the previous fit in order to -accelerate the optimization.</p> -<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">Z.FOCUS</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z1 <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">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z2 <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">"Z3"</span><span class="op">)</span>,</span> -<span> Z3 <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> use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> -<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.Z.FOCUS</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.FOCUS</span>, <span class="va">FOCUS_2006_Z_mkin</span>,</span> -<span> parms.ini <span class="op">=</span> <span class="va">m.Z.5</span><span class="op">$</span><span class="va">bparms.ode</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, :</span></span> -<span><span class="co">## Observations with value of zero were removed from the data</span></span></code></pre> -<pre><code><span><span class="co">## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, : Optimisation did not converge:</span></span> -<span><span class="co">## false convergence (8)</span></span></code></pre> -<div class="sourceCode" id="cb33"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.FOCUS</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png" width="700"></p> -<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.FOCUS</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div> -<pre><code><span><span class="co">## Estimate se_notrans t value Pr(>t) Lower Upper</span></span> -<span><span class="co">## Z0_0 96.838822 1.994274 48.5584 4.0280e-42 92.826981 100.850664</span></span> -<span><span class="co">## k_Z0 2.215393 0.118458 18.7019 1.0413e-23 1.989456 2.466989</span></span> -<span><span class="co">## k_Z1 0.478305 0.028258 16.9266 6.2418e-22 0.424708 0.538666</span></span> -<span><span class="co">## k_Z2 0.451627 0.042139 10.7176 1.6314e-14 0.374339 0.544872</span></span> -<span><span class="co">## k_Z3 0.058692 0.015245 3.8499 1.7803e-04 0.034808 0.098965</span></span> -<span><span class="co">## f_Z2_to_Z3 0.471502 0.058351 8.0805 9.6608e-11 0.357769 0.588274</span></span> -<span><span class="co">## sigma 3.984431 0.383402 10.3923 4.5575e-14 3.213126 4.755736</span></span></code></pre> -<div class="sourceCode" id="cb36"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">m.Z.FOCUS</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## $ff</span></span> -<span><span class="co">## Z2_Z3 Z2_sink </span></span> -<span><span class="co">## 0.4715 0.5285 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $distimes</span></span> -<span><span class="co">## DT50 DT90</span></span> -<span><span class="co">## Z0 0.31288 1.0394</span></span> -<span><span class="co">## Z1 1.44917 4.8141</span></span> -<span><span class="co">## Z2 1.53478 5.0984</span></span> -<span><span class="co">## Z3 11.80986 39.2315</span></span></code></pre> -<p>This fit corresponds to the final result chosen in Appendix 7 of the -FOCUS report. Confidence intervals returned by mkin are based on -internally transformed parameters, however.</p> -</div> -<div class="section level2"> -<h2 id="using-the-sforb-model">Using the SFORB model<a class="anchor" aria-label="anchor" href="#using-the-sforb-model"></a> -</h2> -<p>As the FOCUS report states, there is a certain tailing of the time -course of metabolite Z3. Also, the time course of the parent compound is -not fitted very well using the SFO model, as residues at a certain low -level remain.</p> -<p>Therefore, an additional model is offered here, using the single -first-order reversible binding (SFORB) model for metabolite Z3. As -expected, the <span class="math inline">\(\chi^2\)</span> error level is -lower for metabolite Z3 using this model and the graphical fit for Z3 is -improved. However, the covariance matrix is not returned.</p> -<div class="sourceCode" id="cb38"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">Z.mkin.1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z1 <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">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z2 <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">"Z3"</span><span class="op">)</span>,</span> -<span> Z3 <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="op">)</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> -<div class="sourceCode" id="cb40"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.Z.mkin.1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.1</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE): Observations</span></span> -<span><span class="co">## with value of zero were removed from the data</span></span></code></pre> -<div class="sourceCode" id="cb42"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.1</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png" width="700"></p> -<div class="sourceCode" id="cb43"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.mkin.1</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">cov.unscaled</span></span></code></pre></div> -<pre><code><span><span class="co">## NULL</span></span></code></pre> -<p>Therefore, a further stepwise model building is performed starting -from the stage of parent and two metabolites, starting from the -assumption that the model fit for the parent compound can be improved by -using the SFORB model.</p> -<div class="sourceCode" id="cb45"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">Z.mkin.3</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z1 <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">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z2 <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 class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> -<div class="sourceCode" id="cb47"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.Z.mkin.3</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.3</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations</span></span> -<span><span class="co">## with value of zero were removed from the data</span></span></code></pre> -<div class="sourceCode" id="cb49"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.3</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png" width="700"></p> -<p>This results in a much better representation of the behaviour of the -parent compound Z0.</p> -<p>Finally, Z3 is added as well. These models appear overparameterised -(no covariance matrix returned) if the sink for Z1 is left in the -models.</p> -<div class="sourceCode" id="cb50"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">Z.mkin.4</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z1 <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">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z2 <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">"Z3"</span><span class="op">)</span>,</span> -<span> Z3 <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 class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> -<div class="sourceCode" id="cb52"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.Z.mkin.4</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.4</span>, <span class="va">FOCUS_2006_Z_mkin</span>,</span> -<span> parms.ini <span class="op">=</span> <span class="va">m.Z.mkin.3</span><span class="op">$</span><span class="va">bparms.ode</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, parms.ini =</span></span> -<span><span class="co">## m.Z.mkin.3$bparms.ode, : Observations with value of zero were removed from the</span></span> -<span><span class="co">## data</span></span></code></pre> -<div class="sourceCode" id="cb54"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.4</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png" width="700"></p> -<p>The error level of the fit, but especially of metabolite Z3, can be -improved if the SFORB model is chosen for this metabolite, as this model -is capable of representing the tailing of the metabolite decline -phase.</p> -<div class="sourceCode" id="cb55"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">Z.mkin.5</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z1 <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">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z2 <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">"Z3"</span><span class="op">)</span>,</span> -<span> Z3 <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="op">)</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> -<div class="sourceCode" id="cb57"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.Z.mkin.5</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.5</span>, <span class="va">FOCUS_2006_Z_mkin</span>,</span> -<span> parms.ini <span class="op">=</span> <span class="va">m.Z.mkin.4</span><span class="op">$</span><span class="va">bparms.ode</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini =</span></span> -<span><span class="co">## m.Z.mkin.4$bparms.ode[1:4], : Observations with value of zero were removed from</span></span> -<span><span class="co">## the data</span></span></code></pre> -<div class="sourceCode" id="cb59"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.5</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png" width="700"></p> -<p>The summary view of the backtransformed parameters shows that we get -no confidence intervals due to overparameterisation. As the optimized is -excessively small, it seems reasonable to fix it to zero.</p> -<div class="sourceCode" id="cb60"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.Z.mkin.5a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.5</span>, <span class="va">FOCUS_2006_Z_mkin</span>,</span> -<span> parms.ini <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="va">m.Z.mkin.5</span><span class="op">$</span><span class="va">bparms.ode</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span><span class="op">]</span>,</span> -<span> k_Z3_bound_free <span class="op">=</span> <span class="fl">0</span><span class="op">)</span>,</span> -<span> fixed_parms <span class="op">=</span> <span class="st">"k_Z3_bound_free"</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini =</span></span> -<span><span class="co">## c(m.Z.mkin.5$bparms.ode[1:7], : Observations with value of zero were removed</span></span> -<span><span class="co">## from the data</span></span></code></pre> -<div class="sourceCode" id="cb62"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.5a</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png" width="700"></p> -<p>As expected, the residual plots for Z0 and Z3 are more random than in -the case of the all SFO model for which they were shown above. In -conclusion, the model is proposed as the best-fit model for the dataset -from Appendix 7 of the FOCUS report.</p> -<p>A graphical representation of the confidence intervals can finally be -obtained.</p> -<div class="sourceCode" id="cb63"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/mkinparplot.html">mkinparplot</a></span><span class="op">(</span><span class="va">m.Z.mkin.5a</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png" width="700"></p> -<p>The endpoints obtained with this model are</p> -<div class="sourceCode" id="cb64"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">m.Z.mkin.5a</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## $ff</span></span> -<span><span class="co">## Z0_free Z2_Z3 Z2_sink Z3_free </span></span> -<span><span class="co">## 1.00000 0.53656 0.46344 1.00000 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $SFORB</span></span> -<span><span class="co">## Z0_b1 Z0_b2 Z0_g Z3_b1 Z3_b2 Z3_g </span></span> -<span><span class="co">## 2.4471322 0.0075125 0.9519862 0.0800069 0.0000000 0.9347820 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $distimes</span></span> -<span><span class="co">## DT50 DT90 DT50back DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2</span></span> -<span><span class="co">## Z0 0.3043 1.1848 0.35666 0.28325 92.266 NA NA</span></span> -<span><span class="co">## Z1 1.5148 5.0320 NA NA NA NA NA</span></span> -<span><span class="co">## Z2 1.6414 5.4526 NA NA NA NA NA</span></span> -<span><span class="co">## Z3 NA NA NA NA NA 8.6636 Inf</span></span></code></pre> -<p>It is clear the degradation rate of Z3 towards the end of the -experiment is very low as DT50_Z3_b2 (the second Eigenvalue of the -system of two differential equations representing the SFORB system for -Z3, corresponding to the slower rate constant of the DFOP model) is -reported to be infinity. However, this appears to be a feature of the -data.</p> -</div> -<div class="section level2"> -<h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a> -</h2> -<!-- vim: set foldmethod=syntax: --> -<div id="refs" class="references csl-bib-body hanging-indent"> -<div id="ref-FOCUSkinetics2014" class="csl-entry"> -FOCUS Work Group on Degradation Kinetics. 2014. <em>Generic Guidance for -Estimating Persistence and Degradation Kinetics from Environmental Fate -Studies on Pesticides in EU Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="external-link">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>. -</div> -</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> |