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<h1 data-toc-skip>Example evaluation of FOCUS Example Dataset D</h1>
<h4 data-toc-skip class="author">Johannes Ranke</h4>
<h4 data-toc-skip class="date">Last change 31 January 2019 (rebuilt 2022-11-24)</h4>
<small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/FOCUS_D.rmd" class="external-link"><code>vignettes/FOCUS_D.rmd</code></a></small>
<div class="hidden name"><code>FOCUS_D.rmd</code></div>
</div>
<p>This is just a very simple vignette showing how to fit a degradation model for a parent compound with one transformation product using <code>mkin</code>. After loading the library we look at the data. We have observed concentrations in the column named <code>value</code> at the times specified in column <code>time</code> for the two observed variables named <code>parent</code> and <code>m1</code>.</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="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">FOCUS_2006_D</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## name time value</span></span>
<span><span class="co">## 1 parent 0 99.46</span></span>
<span><span class="co">## 2 parent 0 102.04</span></span>
<span><span class="co">## 3 parent 1 93.50</span></span>
<span><span class="co">## 4 parent 1 92.50</span></span>
<span><span class="co">## 5 parent 3 63.23</span></span>
<span><span class="co">## 6 parent 3 68.99</span></span>
<span><span class="co">## 7 parent 7 52.32</span></span>
<span><span class="co">## 8 parent 7 55.13</span></span>
<span><span class="co">## 9 parent 14 27.27</span></span>
<span><span class="co">## 10 parent 14 26.64</span></span>
<span><span class="co">## 11 parent 21 11.50</span></span>
<span><span class="co">## 12 parent 21 11.64</span></span>
<span><span class="co">## 13 parent 35 2.85</span></span>
<span><span class="co">## 14 parent 35 2.91</span></span>
<span><span class="co">## 15 parent 50 0.69</span></span>
<span><span class="co">## 16 parent 50 0.63</span></span>
<span><span class="co">## 17 parent 75 0.05</span></span>
<span><span class="co">## 18 parent 75 0.06</span></span>
<span><span class="co">## 19 parent 100 NA</span></span>
<span><span class="co">## 20 parent 100 NA</span></span>
<span><span class="co">## 21 parent 120 NA</span></span>
<span><span class="co">## 22 parent 120 NA</span></span>
<span><span class="co">## 23 m1 0 0.00</span></span>
<span><span class="co">## 24 m1 0 0.00</span></span>
<span><span class="co">## 25 m1 1 4.84</span></span>
<span><span class="co">## 26 m1 1 5.64</span></span>
<span><span class="co">## 27 m1 3 12.91</span></span>
<span><span class="co">## 28 m1 3 12.96</span></span>
<span><span class="co">## 29 m1 7 22.97</span></span>
<span><span class="co">## 30 m1 7 24.47</span></span>
<span><span class="co">## 31 m1 14 41.69</span></span>
<span><span class="co">## 32 m1 14 33.21</span></span>
<span><span class="co">## 33 m1 21 44.37</span></span>
<span><span class="co">## 34 m1 21 46.44</span></span>
<span><span class="co">## 35 m1 35 41.22</span></span>
<span><span class="co">## 36 m1 35 37.95</span></span>
<span><span class="co">## 37 m1 50 41.19</span></span>
<span><span class="co">## 38 m1 50 40.01</span></span>
<span><span class="co">## 39 m1 75 40.09</span></span>
<span><span class="co">## 40 m1 75 33.85</span></span>
<span><span class="co">## 41 m1 100 31.04</span></span>
<span><span class="co">## 42 m1 100 33.13</span></span>
<span><span class="co">## 43 m1 120 25.15</span></span>
<span><span class="co">## 44 m1 120 33.31</span></span></code></pre>
<p>Next we specify the degradation model: The parent compound degrades with simple first-order kinetics (SFO) to one metabolite named m1, which also degrades with SFO kinetics.</p>
<p>The call to mkinmod returns a degradation model. The differential equations represented in R code can be found in the character vector <code>$diffs</code> of the <code>mkinmod</code> object. If a C compiler (gcc) is installed and functional, the differential equation model will be compiled from auto-generated C code.</p>
<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">SFO_SFO</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fu"><a href="../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"m1"</span><span class="op">)</span>, m1 <span class="op">=</span> <span class="fu"><a href="../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">SFO_SFO</span><span class="op">$</span><span class="va">diffs</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## parent </span></span>
<span><span class="co">## "d_parent = - k_parent * parent" </span></span>
<span><span class="co">## m1 </span></span>
<span><span class="co">## "d_m1 = + f_parent_to_m1 * k_parent * parent - k_m1 * m1"</span></span></code></pre>
<p>We do the fitting without progress report (<code>quiet = TRUE</code>).</p>
<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">fit</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_2006_D</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(SFO_SFO, FOCUS_2006_D, quiet = TRUE): Observations with value</span></span>
<span><span class="co">## of zero were removed from the data</span></span></code></pre>
<p>A plot of the fit including a residual plot for both observed variables is obtained using the <code>plot_sep</code> method for <code>mkinfit</code> objects, which shows separate graphs for all compounds and their residuals.</p>
<div class="sourceCode" id="cb9"><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">fit</span>, lpos <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">"topright"</span>, <span class="st">"bottomright"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
<p><img src="FOCUS_D_files/figure-html/plot-1.png" width="768"></p>
<p>Confidence intervals for the parameter estimates are obtained using the <code>mkinparplot</code> function.</p>
<div class="sourceCode" id="cb10"><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">fit</span><span class="op">)</span></span></code></pre></div>
<p><img src="FOCUS_D_files/figure-html/plot_2-1.png" width="768"></p>
<p>A comprehensive report of the results is obtained using the <code>summary</code> method for <code>mkinfit</code> objects.</p>
<div class="sourceCode" id="cb11"><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">fit</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## mkin version used for fitting: 1.2.2 </span></span>
<span><span class="co">## R version used for fitting: 4.2.2 </span></span>
<span><span class="co">## Date of fit: Thu Nov 24 08:12:04 2022 </span></span>
<span><span class="co">## Date of summary: Thu Nov 24 08:12:05 2022 </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Equations:</span></span>
<span><span class="co">## d_parent/dt = - k_parent * parent</span></span>
<span><span class="co">## d_m1/dt = + f_parent_to_m1 * k_parent * parent - k_m1 * m1</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Model predictions using solution type analytical </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Fitted using 401 model solutions performed in 0.152 s</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Error model: Constant variance </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Error model algorithm: OLS </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Starting values for parameters to be optimised:</span></span>
<span><span class="co">## value type</span></span>
<span><span class="co">## parent_0 100.7500 state</span></span>
<span><span class="co">## k_parent 0.1000 deparm</span></span>
<span><span class="co">## k_m1 0.1001 deparm</span></span>
<span><span class="co">## f_parent_to_m1 0.5000 deparm</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Starting values for the transformed parameters actually optimised:</span></span>
<span><span class="co">## value lower upper</span></span>
<span><span class="co">## parent_0 100.750000 -Inf Inf</span></span>
<span><span class="co">## log_k_parent -2.302585 -Inf Inf</span></span>
<span><span class="co">## log_k_m1 -2.301586 -Inf Inf</span></span>
<span><span class="co">## f_parent_qlogis 0.000000 -Inf Inf</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Fixed parameter values:</span></span>
<span><span class="co">## value type</span></span>
<span><span class="co">## m1_0 0 state</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Warning(s): </span></span>
<span><span class="co">## Observations with value of zero were removed from the data</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Results:</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## AIC BIC logLik</span></span>
<span><span class="co">## 204.4486 212.6365 -97.22429</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Optimised, transformed parameters with symmetric confidence intervals:</span></span>
<span><span class="co">## Estimate Std. Error Lower Upper</span></span>
<span><span class="co">## parent_0 99.60000 1.57000 96.4000 102.8000</span></span>
<span><span class="co">## log_k_parent -2.31600 0.04087 -2.3990 -2.2330</span></span>
<span><span class="co">## log_k_m1 -5.24700 0.13320 -5.5180 -4.9770</span></span>
<span><span class="co">## f_parent_qlogis 0.05792 0.08926 -0.1237 0.2395</span></span>
<span><span class="co">## sigma 3.12600 0.35850 2.3960 3.8550</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Parameter correlation:</span></span>
<span><span class="co">## parent_0 log_k_parent log_k_m1 f_parent_qlogis sigma</span></span>
<span><span class="co">## parent_0 1.000e+00 5.174e-01 -1.688e-01 -5.471e-01 -1.172e-06</span></span>
<span><span class="co">## log_k_parent 5.174e-01 1.000e+00 -3.263e-01 -5.426e-01 -8.483e-07</span></span>
<span><span class="co">## log_k_m1 -1.688e-01 -3.263e-01 1.000e+00 7.478e-01 8.205e-07</span></span>
<span><span class="co">## f_parent_qlogis -5.471e-01 -5.426e-01 7.478e-01 1.000e+00 1.305e-06</span></span>
<span><span class="co">## sigma -1.172e-06 -8.483e-07 8.205e-07 1.305e-06 1.000e+00</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Backtransformed parameters:</span></span>
<span><span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span></span>
<span><span class="co">## t-test (unrealistically) based on the assumption of normal distribution</span></span>
<span><span class="co">## for estimators of untransformed parameters.</span></span>
<span><span class="co">## Estimate t value Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 99.600000 63.430 2.298e-36 96.400000 1.028e+02</span></span>
<span><span class="co">## k_parent 0.098700 24.470 4.955e-23 0.090820 1.073e-01</span></span>
<span><span class="co">## k_m1 0.005261 7.510 6.165e-09 0.004012 6.898e-03</span></span>
<span><span class="co">## f_parent_to_m1 0.514500 23.070 3.104e-22 0.469100 5.596e-01</span></span>
<span><span class="co">## sigma 3.126000 8.718 2.235e-10 2.396000 3.855e+00</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## FOCUS Chi2 error levels in percent:</span></span>
<span><span class="co">## err.min n.optim df</span></span>
<span><span class="co">## All data 6.398 4 15</span></span>
<span><span class="co">## parent 6.459 2 7</span></span>
<span><span class="co">## m1 4.690 2 8</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Resulting formation fractions:</span></span>
<span><span class="co">## ff</span></span>
<span><span class="co">## parent_m1 0.5145</span></span>
<span><span class="co">## parent_sink 0.4855</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Estimated disappearance times:</span></span>
<span><span class="co">## DT50 DT90</span></span>
<span><span class="co">## parent 7.023 23.33</span></span>
<span><span class="co">## m1 131.761 437.70</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Data:</span></span>
<span><span class="co">## time variable observed predicted residual</span></span>
<span><span class="co">## 0 parent 99.46 99.59848 -1.385e-01</span></span>
<span><span class="co">## 0 parent 102.04 99.59848 2.442e+00</span></span>
<span><span class="co">## 1 parent 93.50 90.23787 3.262e+00</span></span>
<span><span class="co">## 1 parent 92.50 90.23787 2.262e+00</span></span>
<span><span class="co">## 3 parent 63.23 74.07319 -1.084e+01</span></span>
<span><span class="co">## 3 parent 68.99 74.07319 -5.083e+00</span></span>
<span><span class="co">## 7 parent 52.32 49.91207 2.408e+00</span></span>
<span><span class="co">## 7 parent 55.13 49.91207 5.218e+00</span></span>
<span><span class="co">## 14 parent 27.27 25.01258 2.257e+00</span></span>
<span><span class="co">## 14 parent 26.64 25.01258 1.627e+00</span></span>
<span><span class="co">## 21 parent 11.50 12.53462 -1.035e+00</span></span>
<span><span class="co">## 21 parent 11.64 12.53462 -8.946e-01</span></span>
<span><span class="co">## 35 parent 2.85 3.14787 -2.979e-01</span></span>
<span><span class="co">## 35 parent 2.91 3.14787 -2.379e-01</span></span>
<span><span class="co">## 50 parent 0.69 0.71624 -2.624e-02</span></span>
<span><span class="co">## 50 parent 0.63 0.71624 -8.624e-02</span></span>
<span><span class="co">## 75 parent 0.05 0.06074 -1.074e-02</span></span>
<span><span class="co">## 75 parent 0.06 0.06074 -7.382e-04</span></span>
<span><span class="co">## 1 m1 4.84 4.80296 3.704e-02</span></span>
<span><span class="co">## 1 m1 5.64 4.80296 8.370e-01</span></span>
<span><span class="co">## 3 m1 12.91 13.02400 -1.140e-01</span></span>
<span><span class="co">## 3 m1 12.96 13.02400 -6.400e-02</span></span>
<span><span class="co">## 7 m1 22.97 25.04476 -2.075e+00</span></span>
<span><span class="co">## 7 m1 24.47 25.04476 -5.748e-01</span></span>
<span><span class="co">## 14 m1 41.69 36.69003 5.000e+00</span></span>
<span><span class="co">## 14 m1 33.21 36.69003 -3.480e+00</span></span>
<span><span class="co">## 21 m1 44.37 41.65310 2.717e+00</span></span>
<span><span class="co">## 21 m1 46.44 41.65310 4.787e+00</span></span>
<span><span class="co">## 35 m1 41.22 43.31313 -2.093e+00</span></span>
<span><span class="co">## 35 m1 37.95 43.31313 -5.363e+00</span></span>
<span><span class="co">## 50 m1 41.19 41.21832 -2.832e-02</span></span>
<span><span class="co">## 50 m1 40.01 41.21832 -1.208e+00</span></span>
<span><span class="co">## 75 m1 40.09 36.44704 3.643e+00</span></span>
<span><span class="co">## 75 m1 33.85 36.44704 -2.597e+00</span></span>
<span><span class="co">## 100 m1 31.04 31.98162 -9.416e-01</span></span>
<span><span class="co">## 100 m1 33.13 31.98162 1.148e+00</span></span>
<span><span class="co">## 120 m1 25.15 28.78984 -3.640e+00</span></span>
<span><span class="co">## 120 m1 33.31 28.78984 4.520e+00</span></span></code></pre>
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