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</a> </li> </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 data-toc-skip>Example evaluation of FOCUS Example Dataset D</h1> <h4 class="author">Johannes Ranke</h4> <h4 class="date">2020-05-27</h4> <small class="dont-index">Source: <a href="http://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> </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"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/library.html">library</a></span>(<span class="no">mkin</span>, <span class="kw">quietly</span> <span class="kw">=</span> <span class="fl">TRUE</span>) <span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">FOCUS_2006_D</span>)</pre></body></html></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>$diffs</code> of the <code>mkinmod</code> object. If a C compiler (gcc) is installed and functional, the differential equation model will be compiled from auto-generated C code.</p> <div class="sourceCode" id="cb3"><html><body><pre class="r"><span class="no">SFO_SFO</span> <span class="kw"><-</span> <span class="fu"><a href="../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"m1"</span>), <span class="kw">m1</span> <span class="kw">=</span> <span class="fu"><a href="../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</pre></body></html></div> <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre> <div class="sourceCode" id="cb5"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">SFO_SFO</span>$<span class="no">diffs</span>)</pre></body></html></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"><html><body><pre class="r"><span class="no">fit</span> <span class="kw"><-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOCUS_2006_D</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></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"><html><body><pre class="r"><span class="fu"><a href="../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">fit</span>, <span class="kw">lpos</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"topright"</span>, <span class="st">"bottomright"</span>))</pre></body></html></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"><html><body><pre class="r"><span class="fu"><a href="../reference/mkinparplot.html">mkinparplot</a></span>(<span class="no">fit</span>)</pre></body></html></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"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">fit</span>)</pre></body></html></div> <pre><code>## mkin version used for fitting: 0.9.50.2 ## R version used for fitting: 4.0.0 ## Date of fit: Wed May 27 07:05:33 2020 ## Date of summary: Wed May 27 07:05:34 2020 ## ## 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 421 model solutions performed in 0.166 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_ilr_1 0.000000 -Inf Inf ## ## Fixed parameter values: ## value type ## m1_0 0 state ## ## 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 96.40000 102.8000 ## log_k_parent -2.31600 0.04087 -2.39900 -2.2330 ## log_k_m1 -5.24800 0.13320 -5.51800 -4.9770 ## f_parent_ilr_1 0.04096 0.06312 -0.08746 0.1694 ## sigma 3.12600 0.35850 2.39600 3.8550 ## ## Parameter correlation: ## parent_0 log_k_parent log_k_m1 f_parent_ilr_1 sigma ## parent_0 1.000e+00 5.174e-01 -1.688e-01 -5.471e-01 -3.190e-07 ## log_k_parent 5.174e-01 1.000e+00 -3.263e-01 -5.426e-01 3.168e-07 ## log_k_m1 -1.688e-01 -3.263e-01 1.000e+00 7.478e-01 -1.406e-07 ## f_parent_ilr_1 -5.471e-01 -5.426e-01 7.478e-01 1.000e+00 -1.587e-10 ## sigma -3.190e-07 3.168e-07 -1.406e-07 -1.587e-10 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(>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 49.91206 2.408e+00 ## 7 parent 55.13 49.91206 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 -7.381e-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 36.69002 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 36.44703 3.643e+00 ## 75 m1 33.85 36.44703 -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="pkgdown-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> 1.5.1.</p> </div> </footer> </div> </body> </html>