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      <h1 data-toc-skip>Example evaluation of FOCUS Example Dataset D</h1>
                        <h4 class="author">Johannes Ranke</h4>
            
            <h4 class="date">Last change 31 January 2019 (rebuilt 2021-02-15)</h4>
      
      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/FOCUS_D.rmd"><code>vignettes/FOCUS_D.rmd</code></a></small>
      <div class="hidden name"><code>FOCUS_D.rmd</code></div>

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<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 class="kw"><a href="https://rdrr.io/r/base/library.html">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 class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">FOCUS_2006_D</span><span class="op">)</span></code></pre></div>
<pre><code>##      name time  value
## 1  parent    0  99.46
## 2  parent    0 102.04
## 3  parent    1  93.50
## 4  parent    1  92.50
## 5  parent    3  63.23
## 6  parent    3  68.99
## 7  parent    7  52.32
## 8  parent    7  55.13
## 9  parent   14  27.27
## 10 parent   14  26.64
## 11 parent   21  11.50
## 12 parent   21  11.64
## 13 parent   35   2.85
## 14 parent   35   2.91
## 15 parent   50   0.69
## 16 parent   50   0.63
## 17 parent   75   0.05
## 18 parent   75   0.06
## 19 parent  100     NA
## 20 parent  100     NA
## 21 parent  120     NA
## 22 parent  120     NA
## 23     m1    0   0.00
## 24     m1    0   0.00
## 25     m1    1   4.84
## 26     m1    1   5.64
## 27     m1    3  12.91
## 28     m1    3  12.96
## 29     m1    7  22.97
## 30     m1    7  24.47
## 31     m1   14  41.69
## 32     m1   14  33.21
## 33     m1   21  44.37
## 34     m1   21  46.44
## 35     m1   35  41.22
## 36     m1   35  37.95
## 37     m1   50  41.19
## 38     m1   50  40.01
## 39     m1   75  40.09
## 40     m1   75  33.85
## 41     m1  100  31.04
## 42     m1  100  33.13
## 43     m1  120  25.15
## 44     m1  120  33.31</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>$diffs</code> of the <code>mkinmod</code> object. If a C compiler (gcc) is installed and functional, the differential equation model will be compiled from auto-generated C code.</p>
<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">SFO_SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fu"><a href="../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"m1"</span><span class="op">)</span>, m1 <span class="op">=</span> <span class="fu"><a href="../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span></code></pre></div>
<pre><code>## Temporary DLL for differentials generated and loaded</code></pre>
<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">SFO_SFO</span><span class="op">$</span><span class="va">diffs</span><span class="op">)</span></code></pre></div>
<pre><code>##                                                    parent 
##                          "d_parent = - k_parent * parent" 
##                                                        m1 
## "d_m1 = + f_parent_to_m1 * k_parent * parent - k_m1 * m1"</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 class="va">fit</span> <span class="op">&lt;-</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></code></pre></div>
<pre><code>## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE): Observations with value
## of zero were removed from the data</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 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">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></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 class="fu"><a href="../reference/mkinparplot.html">mkinparplot</a></span><span class="op">(</span><span class="va">fit</span><span class="op">)</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 class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html">summary</a></span><span class="op">(</span><span class="va">fit</span><span class="op">)</span></code></pre></div>
<pre><code>## mkin version used for fitting:    1.0.3.9000 
## R version used for fitting:       4.0.3 
## Date of fit:     Mon Feb 15 17:13:36 2021 
## Date of summary: Mon Feb 15 17:13:37 2021 
## 
## Equations:
## d_parent/dt = - k_parent * parent
## d_m1/dt = + f_parent_to_m1 * k_parent * parent - k_m1 * m1
## 
## Model predictions using solution type analytical 
## 
## Fitted using 401 model solutions performed in 0.161 s
## 
## Error model: Constant variance 
## 
## Error model algorithm: OLS 
## 
## Starting values for parameters to be optimised:
##                   value   type
## parent_0       100.7500  state
## k_parent         0.1000 deparm
## k_m1             0.1001 deparm
## f_parent_to_m1   0.5000 deparm
## 
## Starting values for the transformed parameters actually optimised:
##                      value lower upper
## parent_0        100.750000  -Inf   Inf
## log_k_parent     -2.302585  -Inf   Inf
## log_k_m1         -2.301586  -Inf   Inf
## f_parent_qlogis   0.000000  -Inf   Inf
## 
## Fixed parameter values:
##      value  type
## m1_0     0 state
## 
## 
## Warning(s): 
## Observations with value of zero were removed from the data
## 
## Results:
## 
##        AIC      BIC    logLik
##   204.4486 212.6365 -97.22429
## 
## Optimised, transformed parameters with symmetric confidence intervals:
##                 Estimate Std. Error   Lower    Upper
## parent_0        99.60000    1.57000 96.4000 102.8000
## log_k_parent    -2.31600    0.04087 -2.3990  -2.2330
## log_k_m1        -5.24700    0.13320 -5.5180  -4.9770
## f_parent_qlogis  0.05792    0.08926 -0.1237   0.2395
## sigma            3.12600    0.35850  2.3960   3.8550
## 
## Parameter correlation:
##                   parent_0 log_k_parent   log_k_m1 f_parent_qlogis      sigma
## parent_0         1.000e+00    5.174e-01 -1.688e-01      -5.471e-01 -1.172e-06
## log_k_parent     5.174e-01    1.000e+00 -3.263e-01      -5.426e-01 -8.483e-07
## log_k_m1        -1.688e-01   -3.263e-01  1.000e+00       7.478e-01  8.205e-07
## f_parent_qlogis -5.471e-01   -5.426e-01  7.478e-01       1.000e+00  1.305e-06
## sigma           -1.172e-06   -8.483e-07  8.205e-07       1.305e-06  1.000e+00
## 
## Backtransformed parameters:
## Confidence intervals for internally transformed parameters are asymmetric.
## t-test (unrealistically) based on the assumption of normal distribution
## for estimators of untransformed parameters.
##                 Estimate t value    Pr(&gt;t)     Lower     Upper
## parent_0       99.600000  63.430 2.298e-36 96.400000 1.028e+02
## k_parent        0.098700  24.470 4.955e-23  0.090820 1.073e-01
## k_m1            0.005261   7.510 6.165e-09  0.004012 6.898e-03
## f_parent_to_m1  0.514500  23.070 3.104e-22  0.469100 5.596e-01
## sigma           3.126000   8.718 2.235e-10  2.396000 3.855e+00
## 
## FOCUS Chi2 error levels in percent:
##          err.min n.optim df
## All data   6.398       4 15
## parent     6.459       2  7
## m1         4.690       2  8
## 
## Resulting formation fractions:
##                 ff
## parent_m1   0.5145
## parent_sink 0.4855
## 
## Estimated disappearance times:
##           DT50   DT90
## parent   7.023  23.33
## m1     131.761 437.70
## 
## Data:
##  time variable observed predicted   residual
##     0   parent    99.46  99.59848 -1.385e-01
##     0   parent   102.04  99.59848  2.442e+00
##     1   parent    93.50  90.23787  3.262e+00
##     1   parent    92.50  90.23787  2.262e+00
##     3   parent    63.23  74.07319 -1.084e+01
##     3   parent    68.99  74.07319 -5.083e+00
##     7   parent    52.32  49.91207  2.408e+00
##     7   parent    55.13  49.91207  5.218e+00
##    14   parent    27.27  25.01258  2.257e+00
##    14   parent    26.64  25.01258  1.627e+00
##    21   parent    11.50  12.53462 -1.035e+00
##    21   parent    11.64  12.53462 -8.946e-01
##    35   parent     2.85   3.14787 -2.979e-01
##    35   parent     2.91   3.14787 -2.379e-01
##    50   parent     0.69   0.71624 -2.624e-02
##    50   parent     0.63   0.71624 -8.624e-02
##    75   parent     0.05   0.06074 -1.074e-02
##    75   parent     0.06   0.06074 -7.382e-04
##     1       m1     4.84   4.80296  3.704e-02
##     1       m1     5.64   4.80296  8.370e-01
##     3       m1    12.91  13.02400 -1.140e-01
##     3       m1    12.96  13.02400 -6.400e-02
##     7       m1    22.97  25.04476 -2.075e+00
##     7       m1    24.47  25.04476 -5.748e-01
##    14       m1    41.69  36.69003  5.000e+00
##    14       m1    33.21  36.69003 -3.480e+00
##    21       m1    44.37  41.65310  2.717e+00
##    21       m1    46.44  41.65310  4.787e+00
##    35       m1    41.22  43.31313 -2.093e+00
##    35       m1    37.95  43.31313 -5.363e+00
##    50       m1    41.19  41.21832 -2.832e-02
##    50       m1    40.01  41.21832 -1.208e+00
##    75       m1    40.09  36.44704  3.643e+00
##    75       m1    33.85  36.44704 -2.597e+00
##   100       m1    31.04  31.98162 -9.416e-01
##   100       m1    33.13  31.98162  1.148e+00
##   120       m1    25.15  28.78984 -3.640e+00
##   120       m1    33.31  28.78984  4.520e+00</code></pre>
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