<!DOCTYPE html> <!-- Generated by pkgdown: do not edit by hand --><html lang="en"> <head> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> <meta charset="utf-8"> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> <title>Example evaluation of FOCUS Example Dataset D • mkin</title> <!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js" integrity="sha256-FgpCb/KJQlLNfOu91ta32o/NMZxltwRo8QtmkMRdAu8=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.3.7/css/bootstrap.min.css" integrity="sha256-916EbMg70RQy9LHiGkXzG8hSg9EdNy97GazNG/aiY1w=" crossorigin="anonymous"> <script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.3.7/js/bootstrap.min.js" integrity="sha256-U5ZEeKfGNOja007MMD3YBI0A3OSZOQbeG6z2f2Y0hu8=" crossorigin="anonymous"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.7.0/css/font-awesome.min.css" integrity="sha256-eZrrJcwDc/3uDhsdt61sL2oOBY362qM3lon1gyExkL0=" crossorigin="anonymous"> <!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.4/clipboard.min.js" integrity="sha256-FiZwavyI2V6+EXO1U+xzLG3IKldpiTFf3153ea9zikQ=" crossorigin="anonymous"></script><!-- sticky kit --><script src="https://cdnjs.cloudflare.com/ajax/libs/sticky-kit/1.1.3/sticky-kit.min.js" integrity="sha256-c4Rlo1ZozqTPE2RLuvbusY3+SU1pQaJC0TjuhygMipw=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"> <script src="../pkgdown.js"></script><meta property="og:title" content="Example evaluation of FOCUS Example Dataset D"> <meta property="og:description" content=""> <meta name="twitter:card" content="summary"> <!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]> <script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script> <script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script> <![endif]--> </head> <body> <div class="container template-article"> <header><div class="navbar navbar-default navbar-fixed-top" role="navigation"> <div class="container"> <div class="navbar-header"> <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar" aria-expanded="false"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar"></span> <span class="icon-bar"></span> <span class="icon-bar"></span> </button> <span class="navbar-brand"> <a class="navbar-link" href="../index.html">mkin</a> <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.48.1</span> </span> </div> <div id="navbar" class="navbar-collapse collapse"> <ul class="nav navbar-nav"> <li> <a href="../reference/index.html">Functions and data</a> </li> <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false"> Articles <span class="caret"></span> </a> <ul class="dropdown-menu" role="menu"> <li> <a href="../articles/mkin.html">Introduction to mkin</a> </li> <li> <a href="../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a> </li> <li> <a href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a> </li> <li> <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> </li> <li> <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> </li> <li> <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> </li> </ul> </li> <li> <a href="../news/index.html">News</a> </li> </ul> <ul class="nav navbar-nav navbar-right"></ul> </div> <!--/.nav-collapse --> </div> <!--/.container --> </div> <!--/.navbar --> </header><div class="row"> <div class="col-md-9 contents"> <div class="page-header toc-ignore"> <h1>Example evaluation of FOCUS Example Dataset D</h1> <h4 class="author">Johannes Ranke</h4> <h4 class="date">2019-02-25</h4> <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="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb1-1" data-line-number="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/library">library</a></span>(mkin, <span class="dt">quietly =</span> <span class="ot">TRUE</span>)</a> <a class="sourceLine" id="cb1-2" data-line-number="2"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(FOCUS_<span class="dv">2006</span>_D)</a></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>$diffs</code> of the <code>mkinmod</code> object. If a C compiler (gcc) is installed and functional, the differential equation model will be compiled from auto-generated C code.</p> <div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb3-1" data-line-number="1">SFO_SFO <-<span class="st"> </span><span class="kw"><a href="../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">parent =</span> <span class="kw"><a href="../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"m1"</span>), <span class="dt">m1 =</span> <span class="kw"><a href="../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</a></code></pre></div> <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre> <div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb5-1" data-line-number="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(SFO_SFO<span class="op">$</span>diffs)</a></code></pre></div> <pre><code>## parent ## "d_parent = - k_parent_sink * parent - k_parent_m1 * parent" ## m1 ## "d_m1 = + k_parent_m1 * parent - k_m1_sink * m1"</code></pre> <p>We do the fitting without progress report (<code>quiet = TRUE</code>).</p> <div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb7-1" data-line-number="1">fit <-<span class="st"> </span><span class="kw"><a href="../reference/mkinfit.html">mkinfit</a></span>(SFO_SFO, FOCUS_<span class="dv">2006</span>_D, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a></code></pre></div> <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="cb8"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb8-1" data-line-number="1"><span class="kw"><a href="../reference/plot.mkinfit.html">plot_sep</a></span>(fit, <span class="dt">lpos =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="st">"topright"</span>, <span class="st">"bottomright"</span>))</a></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="cb9"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb9-1" data-line-number="1"><span class="kw"><a href="../reference/mkinparplot.html">mkinparplot</a></span>(fit)</a></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="cb10"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb10-1" data-line-number="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(fit)</a></code></pre></div> <pre><code>## mkin version used for fitting: 0.9.48.1 ## R version used for fitting: 3.5.2 ## Date of fit: Mon Feb 25 15:25:02 2019 ## Date of summary: Mon Feb 25 15:25:02 2019 ## ## Equations: ## d_parent/dt = - k_parent_sink * parent - k_parent_m1 * parent ## d_m1/dt = + k_parent_m1 * parent - k_m1_sink * m1 ## ## Model predictions using solution type deSolve ## ## Fitted with method Port using 153 model solutions performed in 0.689 s ## ## Weighting: none ## ## Starting values for parameters to be optimised: ## value type ## parent_0 100.7500 state ## k_parent_sink 0.1000 deparm ## k_parent_m1 0.1001 deparm ## k_m1_sink 0.1002 deparm ## ## Starting values for the transformed parameters actually optimised: ## value lower upper ## parent_0 100.750000 -Inf Inf ## log_k_parent_sink -2.302585 -Inf Inf ## log_k_parent_m1 -2.301586 -Inf Inf ## log_k_m1_sink -2.300587 -Inf Inf ## ## Fixed parameter values: ## value type ## m1_0 0 state ## ## Optimised, transformed parameters with symmetric confidence intervals: ## Estimate Std. Error Lower Upper ## parent_0 99.600 1.61400 96.330 102.900 ## log_k_parent_sink -3.038 0.07826 -3.197 -2.879 ## log_k_parent_m1 -2.980 0.04124 -3.064 -2.897 ## log_k_m1_sink -5.248 0.13610 -5.523 -4.972 ## ## Parameter correlation: ## parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink ## parent_0 1.00000 0.6075 -0.06625 -0.1701 ## log_k_parent_sink 0.60752 1.0000 -0.08740 -0.6253 ## log_k_parent_m1 -0.06625 -0.0874 1.00000 0.4716 ## log_k_m1_sink -0.17006 -0.6253 0.47164 1.0000 ## ## Residual standard error: 3.211 on 36 degrees of freedom ## ## 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(>t) Lower Upper ## parent_0 99.600000 61.720 2.024e-38 96.330000 1.029e+02 ## k_parent_sink 0.047920 12.780 3.050e-15 0.040890 5.616e-02 ## k_parent_m1 0.050780 24.250 3.407e-24 0.046700 5.521e-02 ## k_m1_sink 0.005261 7.349 5.758e-09 0.003992 6.933e-03 ## ## Chi2 error levels in percent: ## err.min n.optim df ## All data 6.398 4 15 ## parent 6.827 3 6 ## m1 4.490 1 9 ## ## Resulting formation fractions: ## ff ## parent_sink 0.4855 ## parent_m1 0.5145 ## m1_sink 1.0000 ## ## 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 74.07320 -1.084e+01 ## 3 parent 68.99 74.07320 -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 25.01257 2.257e+00 ## 14 parent 26.64 25.01257 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 ## 0 m1 0.00 0.00000 0.000e+00 ## 0 m1 0.00 0.00000 0.000e+00 ## 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 36.69002 5.000e+00 ## 14 m1 33.21 36.69002 -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 43.31312 -2.093e+00 ## 35 m1 37.95 43.31312 -5.363e+00 ## 50 m1 41.19 41.21831 -2.831e-02 ## 50 m1 40.01 41.21831 -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 31.98163 -9.416e-01 ## 100 m1 33.13 31.98163 1.148e+00 ## 120 m1 25.15 28.78984 -3.640e+00 ## 120 m1 33.31 28.78984 4.520e+00</code></pre> </div> <div class="col-md-3 hidden-xs hidden-sm" id="sidebar"> </div> </div> <footer><div class="copyright"> <p>Developed by Johannes Ranke.</p> </div> <div class="pkgdown"> <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.3.0.9000.</p> </div> </footer> </div> </body> </html>