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    <h1>Synthetic datasets for one parent compound with two metabolites</h1>
    </div>

    
    <p>The 12 datasets were generated using four different models and three different
 variance components. The four models are either the SFO or the DFOP model with either
 two sequential or two parallel metabolites.</p>

    <p>Variance component &#39;a&#39; is based on a normal distribution with standard deviation of 3,
 Variance component &#39;b&#39; is also based on a normal distribution, but with a standard deviation of 7.
 Variance component &#39;c&#39; is based on the error model from Rocke and Lorenzato (1995), with the 
 minimum standard deviation (for small y values) of 0.5, and a proportionality constant of 0.07
 for the increase of the standard deviation with y.</p>

    <p>Initial concentrations for metabolites and all values where adding the variance component resulted
 in a value below the assumed limit of detection of 0.1 were set to <code>NA</code>.</p>

    <p>As an example, the first dataset has the title <code>SFO_lin_a</code> and is based on the SFO model
 with two sequential metabolites (linear pathway), with added variance component &#39;a&#39;.</p>

    <p>Compare also the code in the example section to see the degradation models.</p>
    

    <pre><span class='no'>synthetic_data_for_UBA_2014</span></pre>
        
    <h2 class="hasAnchor" id="format"><a class="anchor" href="#format"></a>Format</h2>

    <p>A list containing datasets in the form internally used by the &#39;gmkin&#39; package.
  The list has twelfe components. Each of the components is one dataset that has,
  among others, the following components
  <dl class='dl-horizontal'>
    <dt><code>title</code></dt><dd>The name of the dataset, e.g. <code>SFO_lin_a</code></dd>
    <dt><code>data</code></dt><dd>A data frame with the data in the form expected by <code><a href='mkinfit.html'>mkinfit</a></code></dd>
  </dl></p>
    
    <h2 class="hasAnchor" id="source"><a class="anchor" href="#source"></a>Source</h2>

    <p>Ranke (2014) Prüfung und Validierung von Modellierungssoftware als Alternative
  zu ModelMaker 4.0, Umweltbundesamt Projektnummer 27452</p>
    <p>Rocke, David M. und Lorenzato, Stefan (1995) A two-component model for
  measurement error in analytical chemistry. Technometrics 37(2), 176-184.</p>
    

    <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
    <pre class="examples"><div class='input'>
<span class='no'>m_synth_SFO_lin</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"M1"</span>),
                           <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"M2"</span>),
                           <span class='kw'>M2</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>

<span class='no'>m_synth_SFO_par</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fu'>c</span>(<span class='st'>"M1"</span>, <span class='st'>"M2"</span>),
                                         <span class='kw'>sink</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>),
                           <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>),
                           <span class='kw'>M2</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
<span class='no'>m_synth_DFOP_lin</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"DFOP"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"M1"</span>),
                            <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"M2"</span>),
                            <span class='kw'>M2</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
<span class='no'>m_synth_DFOP_par</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"DFOP"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fu'>c</span>(<span class='st'>"M1"</span>, <span class='st'>"M2"</span>),
                                          <span class='kw'>sink</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>),
                            <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>),
                            <span class='kw'>M2</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
<span class='no'>fit</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>m_synth_SFO_lin</span>, <span class='no'>synthetic_data_for_UBA_2014</span><span class='kw'>[[</span><span class='fl'>1</span>]]$<span class='no'>data</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
<span class='fu'><a href='plot.mkinfit.html'>plot_sep</a></span>(<span class='no'>fit</span>)</div><img src='synthetic_data_for_UBA_2014-10.png' alt='' width='540' height='400' /><div class='input'><span class='fu'>summary</span>(<span class='no'>fit</span>)</div><div class='output co'>#&gt; mkin version:    0.9.44.9000 
#&gt; R version:       3.3.2 
#&gt; Date of fit:     Fri Nov 18 16:16:12 2016 
#&gt; Date of summary: Fri Nov 18 16:16:12 2016 
#&gt; 
#&gt; Equations:
#&gt; d_parent/dt = - k_parent * parent
#&gt; d_M1/dt = + f_parent_to_M1 * k_parent * parent - k_M1 * M1
#&gt; d_M2/dt = + f_M1_to_M2 * k_M1 * M1 - k_M2 * M2
#&gt; 
#&gt; Model predictions using solution type deSolve 
#&gt; 
#&gt; Fitted with method Port using 351 model solutions performed in 2.193 s
#&gt; 
#&gt; Weighting: none
#&gt; 
#&gt; Starting values for parameters to be optimised:
#&gt;                   value   type
#&gt; parent_0       101.3500  state
#&gt; k_parent         0.1000 deparm
#&gt; k_M1             0.1001 deparm
#&gt; k_M2             0.1002 deparm
#&gt; f_parent_to_M1   0.5000 deparm
#&gt; f_M1_to_M2       0.5000 deparm
#&gt; 
#&gt; Starting values for the transformed parameters actually optimised:
#&gt;                     value lower upper
#&gt; parent_0       101.350000  -Inf   Inf
#&gt; log_k_parent    -2.302585  -Inf   Inf
#&gt; log_k_M1        -2.301586  -Inf   Inf
#&gt; log_k_M2        -2.300587  -Inf   Inf
#&gt; f_parent_ilr_1   0.000000  -Inf   Inf
#&gt; f_M1_ilr_1       0.000000  -Inf   Inf
#&gt; 
#&gt; Fixed parameter values:
#&gt;      value  type
#&gt; M1_0     0 state
#&gt; M2_0     0 state
#&gt; 
#&gt; Optimised, transformed parameters with symmetric confidence intervals:
#&gt;                Estimate Std. Error   Lower    Upper
#&gt; parent_0       102.1000    1.71400 98.5800 105.5000
#&gt; log_k_parent    -0.3020    0.04294 -0.3894  -0.2147
#&gt; log_k_M1        -1.2070    0.07599 -1.3610  -1.0520
#&gt; log_k_M2        -3.9010    0.06952 -4.0420  -3.7590
#&gt; f_parent_ilr_1   0.8492    0.18090  0.4812   1.2170
#&gt; f_M1_ilr_1       0.6780    0.18860  0.2943   1.0620
#&gt; 
#&gt; Parameter correlation:
#&gt;                parent_0 log_k_parent log_k_M1 log_k_M2 f_parent_ilr_1
#&gt; parent_0        1.00000      0.40213  -0.1693  0.02912        -0.4726
#&gt; log_k_parent    0.40213      1.00000  -0.4210  0.07241        -0.5837
#&gt; log_k_M1       -0.16931     -0.42102   1.0000 -0.37657         0.7438
#&gt; log_k_M2        0.02912      0.07241  -0.3766  1.00000        -0.2518
#&gt; f_parent_ilr_1 -0.47263     -0.58367   0.7438 -0.25177         1.0000
#&gt; f_M1_ilr_1      0.17148      0.42642  -0.8054  0.52648        -0.8602
#&gt;                f_M1_ilr_1
#&gt; parent_0           0.1715
#&gt; log_k_parent       0.4264
#&gt; log_k_M1          -0.8054
#&gt; log_k_M2           0.5265
#&gt; f_parent_ilr_1    -0.8602
#&gt; f_M1_ilr_1         1.0000
#&gt; 
#&gt; Residual standard error: 2.471 on 33 degrees of freedom
#&gt; 
#&gt; Backtransformed parameters:
#&gt; Confidence intervals for internally transformed parameters are asymmetric.
#&gt; t-test (unrealistically) based on the assumption of normal distribution
#&gt; for estimators of untransformed parameters.
#&gt;                 Estimate t value    Pr(&gt;t)    Lower    Upper
#&gt; parent_0       102.10000   59.55 1.815e-35 98.58000 105.5000
#&gt; k_parent         0.73930   23.29 2.337e-22  0.67750   0.8068
#&gt; k_M1             0.29920   13.16 5.552e-15  0.25630   0.3492
#&gt; k_M2             0.02023   14.38 4.497e-16  0.01756   0.0233
#&gt; f_parent_to_M1   0.76870   16.90 4.093e-18  0.66380   0.8483
#&gt; f_M1_to_M2       0.72290   13.53 2.557e-15  0.60260   0.8178
#&gt; 
#&gt; Chi2 error levels in percent:
#&gt;          err.min n.optim df
#&gt; All data   8.454       6 17
#&gt; parent     8.660       2  6
#&gt; M1        10.583       2  5
#&gt; M2         3.586       2  6
#&gt; 
#&gt; Resulting formation fractions:
#&gt;                 ff
#&gt; parent_M1   0.7687
#&gt; parent_sink 0.2313
#&gt; M1_M2       0.7229
#&gt; M1_sink     0.2771
#&gt; 
#&gt; Estimated disappearance times:
#&gt;           DT50    DT90
#&gt; parent  0.9376   3.114
#&gt; M1      2.3170   7.697
#&gt; M2     34.2689 113.839
#&gt; 
#&gt; Data:
#&gt;  time variable observed  predicted residual
#&gt;     0   parent    101.5  1.021e+02 -0.56248
#&gt;     0   parent    101.2  1.021e+02 -0.86248
#&gt;     1   parent     53.9  4.873e+01  5.17119
#&gt;     1   parent     47.5  4.873e+01 -1.22881
#&gt;     3   parent     10.4  1.111e+01 -0.70773
#&gt;     3   parent      7.6  1.111e+01 -3.50773
#&gt;     7   parent      1.1  5.772e-01  0.52283
#&gt;     7   parent      0.3  5.772e-01 -0.27717
#&gt;    14   parent       NA  3.264e-03       NA
#&gt;    14   parent      3.5  3.264e-03  3.49674
#&gt;    28   parent       NA  1.045e-07       NA
#&gt;    28   parent      3.2  1.045e-07  3.20000
#&gt;    60   parent       NA -1.054e-10       NA
#&gt;    60   parent       NA -1.054e-10       NA
#&gt;    90   parent      0.6 -1.875e-11  0.60000
#&gt;    90   parent       NA -1.875e-11       NA
#&gt;   120   parent       NA -2.805e-11       NA
#&gt;   120   parent      3.5 -2.805e-11  3.50000
#&gt;     0       M1       NA  0.000e+00       NA
#&gt;     0       M1       NA  0.000e+00       NA
#&gt;     1       M1     36.4  3.479e+01  1.61089
#&gt;     1       M1     37.4  3.479e+01  2.61089
#&gt;     3       M1     34.3  3.937e+01 -5.07027
#&gt;     3       M1     39.8  3.937e+01  0.42973
#&gt;     7       M1     15.1  1.549e+01 -0.38714
#&gt;     7       M1     17.8  1.549e+01  2.31286
#&gt;    14       M1      5.8  1.995e+00  3.80469
#&gt;    14       M1      1.2  1.995e+00 -0.79531
#&gt;    28       M1       NA  3.034e-02       NA
#&gt;    28       M1       NA  3.034e-02       NA
#&gt;    60       M1      0.5  2.111e-06  0.50000
#&gt;    60       M1       NA  2.111e-06       NA
#&gt;    90       M1       NA  2.913e-10       NA
#&gt;    90       M1      3.2  2.913e-10  3.20000
#&gt;   120       M1      1.5  3.625e-11  1.50000
#&gt;   120       M1      0.6  3.625e-11  0.60000
#&gt;     0       M2       NA  0.000e+00       NA
#&gt;     0       M2       NA  0.000e+00       NA
#&gt;     1       M2       NA  4.455e+00       NA
#&gt;     1       M2      4.8  4.455e+00  0.34517
#&gt;     3       M2     20.9  2.153e+01 -0.62527
#&gt;     3       M2     19.3  2.153e+01 -2.22527
#&gt;     7       M2     42.0  4.192e+01  0.07942
#&gt;     7       M2     43.1  4.192e+01  1.17942
#&gt;    14       M2     49.4  4.557e+01  3.83354
#&gt;    14       M2     44.3  4.557e+01 -1.26646
#&gt;    28       M2     34.6  3.547e+01 -0.87275
#&gt;    28       M2     33.0  3.547e+01 -2.47275
#&gt;    60       M2     18.8  1.858e+01  0.21837
#&gt;    60       M2     17.6  1.858e+01 -0.98163
#&gt;    90       M2     10.6  1.013e+01  0.47131
#&gt;    90       M2     10.8  1.013e+01  0.67131
#&gt;   120       M2      9.8  5.521e+00  4.27893
#&gt;   120       M2      3.3  5.521e+00 -2.22107</div><div class='input'>
</div></pre>
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