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- </div> - - - -<p><a href="https://www.jrwb.de" class="external-link">Wissenschaftlicher Berater, Kronacher -Str. 12, 79639 Grenzach-Wyhlen, Germany</a><br> Privatdozent at the -University of Freiburg</p> -<div class="section level2"> -<h2 id="abstract">Abstract<a class="anchor" aria-label="anchor" href="#abstract"></a> -</h2> -<p>In the regulatory evaluation of chemical substances like plant -protection products (pesticides), biocides and other chemicals, -degradation data play an important role. For the evaluation of pesticide -degradation experiments, detailed guidance has been developed, based on -nonlinear optimisation. The <code>R</code> add-on package -<code>mkin</code> implements fitting some of the models recommended in -this guidance from within R and calculates some statistical measures for -data series within one or more compartments, for parent and -metabolites.</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="st"><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="co"># Define the kinetic model</span></span> -<span><span class="va">m_SFO_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>,</span> -<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="st">"M2"</span><span class="op">)</span>,</span> -<span> M2 <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>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span></span> -<span></span> -<span><span class="co"># Produce model predictions using some arbitrary parameters</span></span> -<span><span class="va">sampling_times</span> <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">1</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">28</span>, <span class="fl">60</span>, <span class="fl">90</span>, <span class="fl">120</span><span class="op">)</span></span> -<span><span class="va">d_SFO_SFO_SFO</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkinpredict.html">mkinpredict</a></span><span class="op">(</span><span class="va">m_SFO_SFO_SFO</span>,</span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>k_parent <span class="op">=</span> <span class="fl">0.03</span>,</span> -<span> f_parent_to_M1 <span class="op">=</span> <span class="fl">0.5</span>, k_M1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="fl">2</span><span class="op">)</span><span class="op">/</span><span class="fl">100</span>,</span> -<span> f_M1_to_M2 <span class="op">=</span> <span class="fl">0.9</span>, k_M2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="fl">2</span><span class="op">)</span><span class="op">/</span><span class="fl">50</span><span class="op">)</span>,</span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fl">100</span>, M1 <span class="op">=</span> <span class="fl">0</span>, M2 <span class="op">=</span> <span class="fl">0</span><span class="op">)</span>,</span> -<span> <span class="va">sampling_times</span><span class="op">)</span></span> -<span></span> -<span><span class="co"># Generate a dataset by adding normally distributed errors with</span></span> -<span><span class="co"># standard deviation 3, for two replicates at each sampling time</span></span> -<span><span class="va">d_SFO_SFO_SFO_err</span> <span class="op"><-</span> <span class="fu"><a href="../reference/add_err.html">add_err</a></span><span class="op">(</span><span class="va">d_SFO_SFO_SFO</span>, reps <span class="op">=</span> <span class="fl">2</span>,</span> -<span> sdfunc <span class="op">=</span> <span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="fl">3</span>,</span> -<span> n <span class="op">=</span> <span class="fl">1</span>, seed <span class="op">=</span> <span class="fl">123456789</span> <span class="op">)</span></span> -<span></span> -<span><span class="co"># Fit the model to the dataset</span></span> -<span><span class="va">f_SFO_SFO_SFO</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">m_SFO_SFO_SFO</span>, <span class="va">d_SFO_SFO_SFO_err</span><span class="op">[[</span><span class="fl">1</span><span class="op">]</span><span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span></span> -<span><span class="co"># Plot the results separately for parent and metabolites</span></span> -<span><span class="fu"><a href="../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">f_SFO_SFO_SFO</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="st">"bottomright"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> -<p><img src="mkin_files/figure-html/unnamed-chunk-2-1.png" width="768"></p> -</div> -<div class="section level2"> -<h2 id="background">Background<a class="anchor" aria-label="anchor" href="#background"></a> -</h2> -<p>The <code>mkin</code> package <span class="citation">(J. Ranke -2021)</span> implements the approach to degradation kinetics recommended -in the kinetics report provided by the FOrum for Co-ordination of -pesticide fate models and their USe <span class="citation">(FOCUS Work -Group on Degradation Kinetics 2006, 2014)</span>. It covers data series -describing the decline of one compound, data series with transformation -products (commonly termed metabolites) and data series for more than one -compartment. It is possible to include back reactions. Therefore, -equilibrium reactions and equilibrium partitioning can be specified, -although this often leads to an overparameterisation of the model.</p> -<p>When the first <code>mkin</code> code was published in 2010, the most -commonly used tools for fitting more complex kinetic degradation models -to experimental data were KinGUI <span class="citation">(Schäfer et al. -2007)</span>, a MATLAB based tool with a graphical user interface that -was specifically tailored to the task and included some output as -proposed by the FOCUS Kinetics Workgroup, and ModelMaker, a general -purpose compartment based tool providing infrastructure for fitting -dynamic simulation models based on differential equations to data.</p> -<p>The ‘mkin’ code was first uploaded to the BerliOS development -platform. When this was taken down, the version control history was -imported into the R-Forge site (see <em>e.g.</em> <a href="https://cgit.jrwb.de/mkin/commit/?id=30cbb4092f6d2d3beff5800603374a0d009ad770" class="external-link">the -initial commit on 11 May 2010</a>), where the code is still being -updated.</p> -<p>At that time, the R package <code>FME</code> (Flexible Modelling -Environment) <span class="citation">(Soetaert and Petzoldt 2010)</span> -was already available, and provided a good basis for developing a -package specifically tailored to the task. The remaining challenge was -to make it as easy as possible for the users (including the author of -this vignette) to specify the system of differential equations and to -include the output requested by the FOCUS guidance, such as the <span class="math inline">\(\chi^2\)</span> error level as defined in this -guidance.</p> -<p>Also, <code>mkin</code> introduced using analytical solutions for -parent only kinetics for improved optimization speed. Later, Eigenvalue -based solutions were introduced to <code>mkin</code> for the case of -linear differential equations (<em>i.e.</em> where the FOMC or DFOP -models were not used for the parent compound), greatly improving the -optimization speed for these cases. This, has become somehow obsolete, -as the use of compiled code described below gives even faster execution -times.</p> -<p>The possibility to specify back-reactions and a biphasic model -(SFORB) for metabolites were present in <code>mkin</code> from the very -beginning.</p> -<div class="section level3"> -<h3 id="derived-software-tools">Derived software tools<a class="anchor" aria-label="anchor" href="#derived-software-tools"></a> -</h3> -<p>Soon after the publication of <code>mkin</code>, two derived tools -were published, namely KinGUII (developed at Bayer Crop Science) and -CAKE (commissioned to Tessella by Syngenta), which added a graphical -user interface (GUI), and added fitting by iteratively reweighted least -squares (IRLS) and characterisation of likely parameter distributions by -Markov Chain Monte Carlo (MCMC) sampling.</p> -<p>CAKE focuses on a smooth use experience, sacrificing some flexibility -in the model definition, originally allowing only two primary -metabolites in parallel. The current version 3.4 of CAKE released in May -2020 uses a scheme for up to six metabolites in a flexible arrangement -and supports biphasic modelling of metabolites, but does not support -back-reactions (non-instantaneous equilibria).</p> -<p>KinGUI offers an even more flexible widget for specifying complex -kinetic models. Back-reactions (non-instantaneous equilibria) were -supported early on, but until 2014, only simple first-order models could -be specified for transformation products. Starting with KinGUII version -2.1, biphasic modelling of metabolites was also available in -KinGUII.</p> -<p>A further graphical user interface (GUI) that has recently been -brought to a decent degree of maturity is the browser based GUI named -<code>gmkin</code>. Please see its <a href="https://pkgdown.jrwb.de/gmkin/" class="external-link">documentation page</a> and <a href="https://pkgdown.jrwb.de/gmkin/articles/gmkin_manual.html" class="external-link">manual</a> -for further information.</p> -<p>A comparison of scope, usability and numerical results obtained with -these tools has been recently been published by <span class="citation">Johannes Ranke, Wöltjen, and Meinecke -(2018)</span>.</p> -</div> -</div> -<div class="section level2"> -<h2 id="unique-features">Unique features<a class="anchor" aria-label="anchor" href="#unique-features"></a> -</h2> -<p>Currently, the main unique features available in <code>mkin</code> -are</p> -<ul> -<li>the <a href="https://pkgdown.jrwb.de/mkin/articles/web_only/compiled_models.html">speed -increase</a> by using compiled code when a compiler is present,</li> -<li>parallel model fitting on multicore machines using the <a href="https://pkgdown.jrwb.de/mkin/reference/mmkin.html"><code>mmkin</code> -function</a>,</li> -<li>the estimation of parameter confidence intervals based on -transformed parameters (see below) and</li> -<li>the possibility to use the <a href="https://pkgdown.jrwb.de/mkin/reference/sigma_twocomp.html">two-component -error model</a> -</li> -</ul> -<p>The iteratively reweighted least squares fitting of different -variances for each variable as introduced by <span class="citation">Gao -et al. (2011)</span> has been available in mkin since <a href="https://pkgdown.jrwb.de/mkin/news/index.html#mkin-0-9-22-2013-10-26">version -0.9-22</a>. With <a href="https://pkgdown.jrwb.de/mkin/news/index.html#mkin-0-9-49-5-2019-07-04">release -0.9.49.5</a>, the IRLS algorithm has been complemented by direct or -step-wise maximisation of the likelihood function, which makes it -possible not only to fit the variance by variable error model but also a -<a href="https://pkgdown.jrwb.de/mkin/reference/sigma_twocomp.html">two-component -error model</a> inspired by error models developed in analytical -chemistry <span class="citation">(Johannes Ranke and Meinecke -2019)</span>.</p> -</div> -<div class="section level2"> -<h2 id="internal-parameter-transformations">Internal parameter transformations<a class="anchor" aria-label="anchor" href="#internal-parameter-transformations"></a> -</h2> -<p>For rate constants, the log transformation is used, as proposed by -Bates and Watts <span class="citation">(1988, 77, 149)</span>. -Approximate intervals are constructed for the transformed rate constants -<span class="citation">(compare Bates and Watts 1988, 135)</span>, -<em>i.e.</em> for their logarithms. Confidence intervals for the rate -constants are then obtained using the appropriate backtransformation -using the exponential function.</p> -<p>In the first version of <code>mkin</code> allowing for specifying -models using formation fractions, a home-made reparameterisation was -used in order to ensure that the sum of formation fractions would not -exceed unity.</p> -<p>This method is still used in the current version of KinGUII (v2.1 -from April 2014), with a modification that allows for fixing the pathway -to sink to zero. CAKE uses penalties in the objective function in order -to enforce this constraint.</p> -<p>In 2012, an alternative reparameterisation of the formation fractions -was proposed together with René Lehmann <span class="citation">(J. Ranke -and Lehmann 2012)</span>, based on isometric logratio transformation -(ILR). The aim was to improve the validity of the linear approximation -of the objective function during the parameter estimation procedure as -well as in the subsequent calculation of parameter confidence intervals. -In the current version of mkin, a logit transformation is used for -parameters that are bound between 0 and 1, such as the g parameter of -the DFOP model.</p> -<div class="section level3"> -<h3 id="confidence-intervals-based-on-transformed-parameters">Confidence intervals based on transformed parameters<a class="anchor" aria-label="anchor" href="#confidence-intervals-based-on-transformed-parameters"></a> -</h3> -<p>In the first attempt at providing improved parameter confidence -intervals introduced to <code>mkin</code> in 2013, confidence intervals -obtained from FME on the transformed parameters were simply all -backtransformed one by one to yield asymmetric confidence intervals for -the backtransformed parameters.</p> -<p>However, while there is a 1:1 relation between the rate constants in -the model and the transformed parameters fitted in the model, the -parameters obtained by the isometric logratio transformation are -calculated from the set of formation fractions that quantify the paths -to each of the compounds formed from a specific parent compound, and no -such 1:1 relation exists.</p> -<p>Therefore, parameter confidence intervals for formation fractions -obtained with this method only appear valid for the case of a single -transformation product, where currently the logit transformation is used -for the formation fraction.</p> -<p>The confidence intervals obtained by backtransformation for the cases -where a 1:1 relation between transformed and original parameter exist -are considered by the author of this vignette to be more accurate than -those obtained using a re-estimation of the Hessian matrix after -backtransformation, as implemented in the FME package.</p> -</div> -<div class="section level3"> -<h3 id="parameter-t-test-based-on-untransformed-parameters">Parameter t-test based on untransformed parameters<a class="anchor" aria-label="anchor" href="#parameter-t-test-based-on-untransformed-parameters"></a> -</h3> -<p>The standard output of many nonlinear regression software packages -includes the results from a test for significant difference from zero -for all parameters. Such a test is also recommended to check the -validity of rate constants in the FOCUS guidance <span class="citation">(FOCUS Work Group on Degradation Kinetics 2014, -96ff)</span>.</p> -<p>It has been argued that the precondition for this test, <em>i.e.</em> -normal distribution of the estimator for the parameters, is not -fulfilled in the case of nonlinear regression <span class="citation">(J. -Ranke and Lehmann 2015)</span>. However, this test is commonly used by -industry, consultants and national authorities in order to decide on the -reliability of parameter estimates, based on the FOCUS guidance -mentioned above. Therefore, the results of this one-sided t-test are -included in the summary output from <code>mkin</code>.</p> -<p>As it is not reasonable to test for significant difference of the -transformed parameters (<em>e.g.</em> <span class="math inline">\(log(k)\)</span>) from zero, the t-test is -calculated based on the model definition before parameter -transformation, <em>i.e.</em> in a similar way as in packages that do -not apply such an internal parameter transformation. A note is included -in the <code>mkin</code> output, pointing to the fact that the t-test is -based on the unjustified assumption of normal distribution of the -parameter estimators.</p> -</div> -</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-bates1988" class="csl-entry"> -Bates, D., and D. Watts. 1988. <em>Nonlinear Regression and Its -Applications</em>. Wiley-Interscience. -</div> -<div id="ref-FOCUS2006" class="csl-entry"> -FOCUS Work Group on Degradation Kinetics. 2006. <em>Guidance Document on -Estimating Persistence and Degradation Kinetics from Environmental Fate -Studies on Pesticides in EU Registration. Report of the FOCUS Work Group -on Degradation Kinetics</em>. <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 id="ref-FOCUSkinetics2014" class="csl-entry"> -———. 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 id="ref-gao11" class="csl-entry"> -Gao, Z., J. W. Green, J. Vanderborght, and W. Schmitt. 2011. -<span>“Improving Uncertainty Analysis in Kinetic Evaluations Using -Iteratively Reweighted Least Squares.”</span> Journal. <em>Environmental -Science and Technology</em> 45: 4429–37. -</div> -<div id="ref-pkg:mkin" class="csl-entry"> -Ranke, J. 2021. <em>‘<span class="nocase">mkin</span>‘: -<span>K</span>inetic Evaluation of Chemical Degradation Data</em>. <a href="https://CRAN.R-project.org/package=mkin" class="external-link">https://CRAN.R-project.org/package=mkin</a>. -</div> -<div id="ref-ranke2012" class="csl-entry"> -Ranke, J., and R. Lehmann. 2012. <span>“Parameter Reliability in Kinetic -Evaluation of Environmental Metabolism Data - Assessment and the -Influence of Model Specification.”</span> In <em>SETAC World 20-24 -May</em>. Berlin. <a href="https://jrwb.de/posters/Poster_SETAC_2012_Kinetic_parameter_uncertainty_model_parameterization_Lehmann_Ranke.pdf" class="external-link">https://jrwb.de/posters/Poster_SETAC_2012_Kinetic_parameter_uncertainty_model_parameterization_Lehmann_Ranke.pdf</a>. -</div> -<div id="ref-ranke2015" class="csl-entry"> -———. 2015. <span>“To t-Test or Not to t-Test, That Is the -Question.”</span> In <em>XV Symposium on Pesticide Chemistry 2-4 -September 2015</em>. Piacenza. <a href="https://jrwb.de/posters/piacenza_2015.pdf" class="external-link">https://jrwb.de/posters/piacenza_2015.pdf</a>. -</div> -<div id="ref-ranke2019" class="csl-entry"> -Ranke, Johannes, and Stefan Meinecke. 2019. <span>“Error Models for the -Kinetic Evaluation of Chemical Degradation Data.”</span> -<em>Environments</em> 6 (12). <a href="https://doi.org/10.3390/environments6120124" class="external-link">https://doi.org/10.3390/environments6120124</a>. -</div> -<div id="ref-ranke2018" class="csl-entry"> -Ranke, Johannes, Janina Wöltjen, and Stefan Meinecke. 2018. -<span>“Comparison of Software Tools for Kinetic Evaluation of Chemical -Degradation Data.”</span> <em>Environmental Sciences Europe</em> 30 (1): -17. <a href="https://doi.org/10.1186/s12302-018-0145-1" class="external-link">https://doi.org/10.1186/s12302-018-0145-1</a>. -</div> -<div id="ref-schaefer2007" class="csl-entry"> -Schäfer, D., B. Mikolasch, P. Rainbird, and B. Harvey. 2007. -<span>“<span>KinGUI</span>: A New Kinetic Software Tool for Evaluations -According to <span>FOCUS</span> Degradation Kinetics.”</span> In -<em>Proceedings of the XIII Symposium Pesticide Chemistry</em>, edited -by Del Re A. A. M., Capri E., Fragoulis G., and Trevisan M., 916–23. -Piacenza. -</div> -<div id="ref-soetaert2010" class="csl-entry"> -Soetaert, Karline, and Thomas Petzoldt. 2010. <span>“Inverse Modelling, -Sensitivity and Monte Carlo Analysis in <span>R</span> Using Package -<span>FME</span>.”</span> <em>Journal of Statistical Software</em> 33 -(3): 1–28. <a href="https://doi.org/10.18637/jss.v033.i03" class="external-link">https://doi.org/10.18637/jss.v033.i03</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> |