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<h1>Fit nonlinear mixed models with SAEM</h1>
<small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/saem.R'><code>R/saem.R</code></a></small>
<div class="hidden name"><code>saem.Rd</code></div>
</div>
<div class="ref-description">
<p>This function uses <code><a href='https://rdrr.io/pkg/saemix/man/saemix.html'>saemix::saemix()</a></code> as a backend for fitting nonlinear mixed
effects models created from <a href='mmkin.html'>mmkin</a> row objects using the Stochastic Approximation
Expectation Maximisation algorithm (SAEM).</p>
</div>
<pre class="usage"><span class='fu'>saem</span><span class='op'>(</span><span class='va'>object</span>, <span class='va'>control</span>, <span class='va'>...</span><span class='op'>)</span>
<span class='co'># S3 method for mmkin</span>
<span class='fu'>saem</span><span class='op'>(</span>
<span class='va'>object</span>,
control <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>displayProgress <span class='op'>=</span> <span class='cn'>FALSE</span>, print <span class='op'>=</span> <span class='cn'>FALSE</span>, save <span class='op'>=</span> <span class='cn'>FALSE</span>, save.graphs <span class='op'>=</span>
<span class='cn'>FALSE</span><span class='op'>)</span>,
cores <span class='op'>=</span> <span class='fl'>1</span>,
verbose <span class='op'>=</span> <span class='cn'>FALSE</span>,
suppressPlot <span class='op'>=</span> <span class='cn'>TRUE</span>,
quiet <span class='op'>=</span> <span class='cn'>FALSE</span>,
<span class='va'>...</span>
<span class='op'>)</span>
<span class='co'># S3 method for saem.mmkin</span>
<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span><span class='op'>(</span><span class='va'>x</span>, digits <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/Extremes.html'>max</a></span><span class='op'>(</span><span class='fl'>3</span>, <span class='fu'><a href='https://rdrr.io/r/base/options.html'>getOption</a></span><span class='op'>(</span><span class='st'>"digits"</span><span class='op'>)</span> <span class='op'>-</span> <span class='fl'>3</span><span class='op'>)</span>, <span class='va'>...</span><span class='op'>)</span>
<span class='fu'>saemix_model</span><span class='op'>(</span><span class='va'>object</span>, cores <span class='op'>=</span> <span class='fl'>1</span>, verbose <span class='op'>=</span> <span class='cn'>FALSE</span>, <span class='va'>...</span><span class='op'>)</span>
<span class='fu'>saemix_data</span><span class='op'>(</span><span class='va'>object</span>, verbose <span class='op'>=</span> <span class='cn'>FALSE</span>, <span class='va'>...</span><span class='op'>)</span></pre>
<h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
<table class="ref-arguments">
<colgroup><col class="name" /><col class="desc" /></colgroup>
<tr>
<th>object</th>
<td><p>An <a href='mmkin.html'>mmkin</a> row object containing several fits of the same
<a href='mkinmod.html'>mkinmod</a> model to different datasets</p></td>
</tr>
<tr>
<th>control</th>
<td><p>Passed to <a href='https://rdrr.io/pkg/saemix/man/saemix.html'>saemix::saemix</a></p></td>
</tr>
<tr>
<th>...</th>
<td><p>Further parameters passed to <a href='https://rdrr.io/pkg/saemix/man/saemixModel.html'>saemix::saemixModel</a>.</p></td>
</tr>
<tr>
<th>cores</th>
<td><p>The number of cores to be used for multicore processing using
<code><a href='https://rdrr.io/r/parallel/mclapply.html'>parallel::mclapply()</a></code>. Using more than 1 core is experimental and may
lead to excessive forking, apparently depending on the BLAS version
used.</p></td>
</tr>
<tr>
<th>verbose</th>
<td><p>Should we print information about created objects of
type <a href='https://rdrr.io/pkg/saemix/man/SaemixModel-class.html'>saemix::SaemixModel</a> and <a href='https://rdrr.io/pkg/saemix/man/SaemixData-class.html'>saemix::SaemixData</a>?</p></td>
</tr>
<tr>
<th>suppressPlot</th>
<td><p>Should we suppress any plotting that is done
by the saemix function?</p></td>
</tr>
<tr>
<th>quiet</th>
<td><p>Should we suppress the messages saemix prints at the beginning
and the end of the optimisation process?</p></td>
</tr>
<tr>
<th>x</th>
<td><p>An saem.mmkin object to print</p></td>
</tr>
<tr>
<th>digits</th>
<td><p>Number of digits to use for printing</p></td>
</tr>
</table>
<h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
<p>An S3 object of class 'saem.mmkin', containing the fitted
<a href='https://rdrr.io/pkg/saemix/man/SaemixObject-class.html'>saemix::SaemixObject</a> as a list component named 'so'. The
object also inherits from 'mixed.mmkin'.</p>
<p>An <a href='https://rdrr.io/pkg/saemix/man/SaemixModel-class.html'>saemix::SaemixModel</a> object.</p>
<p>An <a href='https://rdrr.io/pkg/saemix/man/SaemixData-class.html'>saemix::SaemixData</a> object.</p>
<h2 class="hasAnchor" id="details"><a class="anchor" href="#details"></a>Details</h2>
<p>An mmkin row object is essentially a list of mkinfit objects that have been
obtained by fitting the same model to a list of datasets using <a href='mkinfit.html'>mkinfit</a>.</p>
<p>Starting values for the fixed effects (population mean parameters, argument
psi0 of <code><a href='https://rdrr.io/pkg/saemix/man/saemixModel.html'>saemix::saemixModel()</a></code> are the mean values of the parameters found
using <a href='mmkin.html'>mmkin</a>.</p>
<h2 class="hasAnchor" id="see-also"><a class="anchor" href="#see-also"></a>See also</h2>
<div class='dont-index'><p><a href='summary.saem.mmkin.html'>summary.saem.mmkin</a> <a href='plot.mixed.mmkin.html'>plot.mixed.mmkin</a></p></div>
<h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
<pre class="examples"><div class='input'><span class='co'># \dontrun{</span>
<span class='va'>ds</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>lapply</a></span><span class='op'>(</span><span class='va'>experimental_data_for_UBA_2019</span><span class='op'>[</span><span class='fl'>6</span><span class='op'>:</span><span class='fl'>10</span><span class='op'>]</span>,
<span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span><span class='op'>(</span><span class='va'>x</span><span class='op'>$</span><span class='va'>data</span><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'>"name"</span>, <span class='st'>"time"</span>, <span class='st'>"value"</span><span class='op'>)</span><span class='op'>]</span><span class='op'>)</span><span class='op'>)</span>
<span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span><span class='op'>(</span><span class='va'>ds</span><span class='op'>)</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/paste.html'>paste</a></span><span class='op'>(</span><span class='st'>"Dataset"</span>, <span class='fl'>6</span><span class='op'>:</span><span class='fl'>10</span><span class='op'>)</span>
<span class='va'>f_mmkin_parent_p0_fixed</span> <span class='op'><-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span><span class='op'>(</span><span class='st'>"FOMC"</span>, <span class='va'>ds</span>, cores <span class='op'>=</span> <span class='fl'>1</span>,
state.ini <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fl'>100</span><span class='op'>)</span>, fixed_initials <span class='op'>=</span> <span class='st'>"parent"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
<span class='va'>f_saem_p0_fixed</span> <span class='op'><-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin_parent_p0_fixed</span><span class='op'>)</span>
</div><div class='output co'>#> Running main SAEM algorithm
#> [1] "Mon Nov 30 15:53:02 2020"
#> ....
#> Minimisation finished
#> [1] "Mon Nov 30 15:53:04 2020"</div><div class='input'>
<span class='va'>f_mmkin_parent</span> <span class='op'><-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span><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'>"SFO"</span>, <span class='st'>"FOMC"</span>, <span class='st'>"DFOP"</span><span class='op'>)</span>, <span class='va'>ds</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
<span class='va'>f_saem_sfo</span> <span class='op'><-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin_parent</span><span class='op'>[</span><span class='st'>"SFO"</span>, <span class='op'>]</span><span class='op'>)</span>
</div><div class='output co'>#> Running main SAEM algorithm
#> [1] "Mon Nov 30 15:53:05 2020"
#> ....
#> Minimisation finished
#> [1] "Mon Nov 30 15:53:07 2020"</div><div class='input'><span class='va'>f_saem_fomc</span> <span class='op'><-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin_parent</span><span class='op'>[</span><span class='st'>"FOMC"</span>, <span class='op'>]</span><span class='op'>)</span>
</div><div class='output co'>#> Running main SAEM algorithm
#> [1] "Mon Nov 30 15:53:07 2020"
#> ....
#> Minimisation finished
#> [1] "Mon Nov 30 15:53:09 2020"</div><div class='input'><span class='va'>f_saem_dfop</span> <span class='op'><-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin_parent</span><span class='op'>[</span><span class='st'>"DFOP"</span>, <span class='op'>]</span><span class='op'>)</span>
</div><div class='output co'>#> Running main SAEM algorithm
#> [1] "Mon Nov 30 15:53:10 2020"
#> ....
#> Minimisation finished
#> [1] "Mon Nov 30 15:53:13 2020"</div><div class='input'>
<span class='co'># The returned saem.mmkin object contains an SaemixObject, therefore we can use</span>
<span class='co'># functions from saemix</span>
<span class='kw'><a href='https://rdrr.io/r/base/library.html'>library</a></span><span class='op'>(</span><span class='va'>saemix</span><span class='op'>)</span>
</div><div class='output co'>#> <span class='message'>Package saemix, version 3.1.9000</span>
#> <span class='message'> please direct bugs, questions and feedback to emmanuelle.comets@inserm.fr</span></div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/compare.saemix.html'>compare.saemix</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span><span class='va'>f_saem_sfo</span><span class='op'>$</span><span class='va'>so</span>, <span class='va'>f_saem_fomc</span><span class='op'>$</span><span class='va'>so</span>, <span class='va'>f_saem_dfop</span><span class='op'>$</span><span class='va'>so</span><span class='op'>)</span><span class='op'>)</span>
</div><div class='output co'>#> Likelihoods computed by importance sampling </div><div class='output co'>#> AIC BIC
#> 1 624.2484 622.2956
#> 2 467.7096 464.9757
#> 3 495.4373 491.9222</div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html'>plot</a></span><span class='op'>(</span><span class='va'>f_saem_fomc</span><span class='op'>$</span><span class='va'>so</span>, plot.type <span class='op'>=</span> <span class='st'>"convergence"</span><span class='op'>)</span>
</div><div class='output co'>#> Plotting convergence plots</div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html'>plot</a></span><span class='op'>(</span><span class='va'>f_saem_fomc</span><span class='op'>$</span><span class='va'>so</span>, plot.type <span class='op'>=</span> <span class='st'>"individual.fit"</span><span class='op'>)</span>
</div><div class='img'><img src='saem-1.png' alt='' width='700' height='433' /></div><div class='output co'>#> Plotting individual fits</div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html'>plot</a></span><span class='op'>(</span><span class='va'>f_saem_fomc</span><span class='op'>$</span><span class='va'>so</span>, plot.type <span class='op'>=</span> <span class='st'>"npde"</span><span class='op'>)</span>
</div><div class='img'><img src='saem-2.png' alt='' width='700' height='433' /></div><div class='output co'>#> Simulating data using nsim = 1000 simulated datasets
#> Computing WRES and npde .
#> Plotting npde</div><div class='img'><img src='saem-3.png' alt='' width='700' height='433' /></div><div class='output co'>#> ---------------------------------------------
#> Distribution of npde:
#> mean= -0.01528 (SE= 0.098 )
#> variance= 0.862 (SE= 0.13 )
#> skewness= 0.5016
#> kurtosis= 1.18
#> ---------------------------------------------
#>
#> Statistical tests
#> Wilcoxon signed rank test : 0.679
#> Fisher variance test : 0.36
#> SW test of normality : 0.0855 .
#> Global adjusted p-value : 0.257
#> ---
#> Signif. codes: '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1
#> ---------------------------------------------</div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html'>plot</a></span><span class='op'>(</span><span class='va'>f_saem_fomc</span><span class='op'>$</span><span class='va'>so</span>, plot.type <span class='op'>=</span> <span class='st'>"vpc"</span><span class='op'>)</span>
</div><div class='output co'>#> Performing simulations under the model.
#> Plotting VPC
#> Method used for VPC: binning by quantiles on X , dividing into the following intervals
#> Interval Centered.On
#> 1 (-1,3] 1.3
#> 2 (3,8] 7.4
#> 3 (8,14] 13.2
#> 4 (14,21] 20.5
#> 5 (21,37.7] 29.5
#> 6 (37.7,60] 50.4
#> 7 (60,90] 76.6
#> 8 (90,120] 109.0
#> 9 (120,180] 156.0 </div><div class='img'><img src='saem-4.png' alt='' width='700' height='433' /></div><div class='input'>
<span class='va'>f_mmkin_parent_tc</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/stats/update.html'>update</a></span><span class='op'>(</span><span class='va'>f_mmkin_parent</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span><span class='op'>)</span>
<span class='va'>f_saem_fomc_tc</span> <span class='op'><-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin_parent_tc</span><span class='op'>[</span><span class='st'>"FOMC"</span>, <span class='op'>]</span><span class='op'>)</span>
</div><div class='output co'>#> Running main SAEM algorithm
#> [1] "Mon Nov 30 15:53:15 2020"
#> ....
#> Minimisation finished
#> [1] "Mon Nov 30 15:53:20 2020"</div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/compare.saemix.html'>compare.saemix</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span><span class='va'>f_saem_fomc</span><span class='op'>$</span><span class='va'>so</span>, <span class='va'>f_saem_fomc_tc</span><span class='op'>$</span><span class='va'>so</span><span class='op'>)</span><span class='op'>)</span>
</div><div class='output co'>#> Likelihoods computed by importance sampling </div><div class='output co'>#> AIC BIC
#> 1 467.7096 464.9757
#> 2 469.5208 466.3963</div><div class='input'>
<span class='va'>sfo_sfo</span> <span class='op'><-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinmod.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"A1"</span><span class='op'>)</span>,
A1 <span class='op'>=</span> <span class='fu'><a href='mkinmod.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span>
</div><div class='output co'>#> <span class='message'>Temporary DLL for differentials generated and loaded</span></div><div class='input'><span class='va'>fomc_sfo</span> <span class='op'><-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinmod.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"FOMC"</span>, <span class='st'>"A1"</span><span class='op'>)</span>,
A1 <span class='op'>=</span> <span class='fu'><a href='mkinmod.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span>
</div><div class='output co'>#> <span class='message'>Temporary DLL for differentials generated and loaded</span></div><div class='input'><span class='va'>dfop_sfo</span> <span class='op'><-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinmod.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"DFOP"</span>, <span class='st'>"A1"</span><span class='op'>)</span>,
A1 <span class='op'>=</span> <span class='fu'><a href='mkinmod.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span>
</div><div class='output co'>#> <span class='message'>Temporary DLL for differentials generated and loaded</span></div><div class='input'><span class='co'># The following fit uses analytical solutions for SFO-SFO and DFOP-SFO,</span>
<span class='co'># and compiled ODEs for FOMC that are much slower</span>
<span class='va'>f_mmkin</span> <span class='op'><-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>
<span class='st'>"SFO-SFO"</span> <span class='op'>=</span> <span class='va'>sfo_sfo</span>, <span class='st'>"FOMC-SFO"</span> <span class='op'>=</span> <span class='va'>fomc_sfo</span>, <span class='st'>"DFOP-SFO"</span> <span class='op'>=</span> <span class='va'>dfop_sfo</span><span class='op'>)</span>,
<span class='va'>ds</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
<span class='co'># These take about five seconds each on this system, as we use</span>
<span class='co'># analytical solutions written for saemix. When using the analytical</span>
<span class='co'># solutions written for mkin this took around four minutes</span>
<span class='va'>f_saem_sfo_sfo</span> <span class='op'><-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin</span><span class='op'>[</span><span class='st'>"SFO-SFO"</span>, <span class='op'>]</span><span class='op'>)</span>
</div><div class='output co'>#> Running main SAEM algorithm
#> [1] "Mon Nov 30 15:53:23 2020"
#> ....
#> Minimisation finished
#> [1] "Mon Nov 30 15:53:28 2020"</div><div class='input'><span class='va'>f_saem_dfop_sfo</span> <span class='op'><-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin</span><span class='op'>[</span><span class='st'>"DFOP-SFO"</span>, <span class='op'>]</span><span class='op'>)</span>
</div><div class='output co'>#> Running main SAEM algorithm
#> [1] "Mon Nov 30 15:53:29 2020"
#> ....
#> Minimisation finished
#> [1] "Mon Nov 30 15:53:38 2020"</div><div class='input'><span class='co'># We can use print, plot and summary methods to check the results</span>
<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span><span class='op'>(</span><span class='va'>f_saem_dfop_sfo</span><span class='op'>)</span>
</div><div class='output co'>#> Kinetic nonlinear mixed-effects model fit by SAEM
#> Structural model:
#> d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
#> time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
#> * parent
#> d_A1/dt = + f_parent_to_A1 * ((k1 * g * exp(-k1 * time) + k2 * (1 - g)
#> * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
#> exp(-k2 * time))) * parent - k_A1 * A1
#>
#> Data:
#> 170 observations of 2 variable(s) grouped in 5 datasets
#>
#> Likelihood computed by importance sampling
#> AIC BIC logLik
#> 841.6 836.5 -407.8
#>
#> Fitted parameters:
#> estimate lower upper
#> parent_0 93.76647 91.15312 96.3798
#> log_k_A1 -6.13235 -8.45788 -3.8068
#> f_parent_qlogis -0.97364 -1.36940 -0.5779
#> log_k1 -2.53176 -3.80372 -1.2598
#> log_k2 -3.58667 -5.29524 -1.8781
#> g_qlogis 0.01238 -1.07968 1.1044
#> Var.parent_0 7.61106 -3.34955 18.5717
#> Var.log_k_A1 4.64679 -2.73133 12.0249
#> Var.f_parent_qlogis 0.19693 -0.05498 0.4488
#> Var.log_k1 2.01717 -0.51980 4.5542
#> Var.log_k2 3.63412 -0.92964 8.1979
#> Var.g_qlogis 0.20045 -0.97425 1.3751
#> a.1 1.88335 1.66636 2.1004
#> SD.parent_0 2.75881 0.77234 4.7453
#> SD.log_k_A1 2.15564 0.44429 3.8670
#> SD.f_parent_qlogis 0.44377 0.15994 0.7276
#> SD.log_k1 1.42027 0.52714 2.3134
#> SD.log_k2 1.90634 0.70934 3.1033
#> SD.g_qlogis 0.44771 -0.86417 1.7596</div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html'>plot</a></span><span class='op'>(</span><span class='va'>f_saem_dfop_sfo</span><span class='op'>)</span>
</div><div class='img'><img src='saem-5.png' alt='' width='700' height='433' /></div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/summary-methods.html'>summary</a></span><span class='op'>(</span><span class='va'>f_saem_dfop_sfo</span>, data <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
</div><div class='output co'>#> saemix version used for fitting: 3.1.9000
#> mkin version used for pre-fitting: 0.9.50.4
#> R version used for fitting: 4.0.3
#> Date of fit: Mon Nov 30 15:53:38 2020
#> Date of summary: Mon Nov 30 15:53:39 2020
#>
#> Equations:
#> d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
#> time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
#> * parent
#> d_A1/dt = + f_parent_to_A1 * ((k1 * g * exp(-k1 * time) + k2 * (1 - g)
#> * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
#> exp(-k2 * time))) * parent - k_A1 * A1
#>
#> Data:
#> 170 observations of 2 variable(s) grouped in 5 datasets
#>
#> Model predictions using solution type analytical
#>
#> Fitted in 9.963 s using 300, 100 iterations
#>
#> Variance model: Constant variance
#>
#> Mean of starting values for individual parameters:
#> parent_0 log_k_A1 f_parent_qlogis log_k1 log_k2
#> 93.8101519 -9.7647455 -0.9711148 -1.8799371 -4.2708142
#> g_qlogis
#> 0.1356441
#>
#> Fixed degradation parameter values:
#> None
#>
#> Results:
#>
#> Likelihood computed by importance sampling
#> AIC BIC logLik
#> 841.6 836.5 -407.8
#>
#> Optimised, transformed parameters with symmetric confidence intervals:
#> est. lower upper
#> parent_0 93.76647 91.153 96.3798
#> log_k_A1 -6.13235 -8.458 -3.8068
#> f_parent_qlogis -0.97364 -1.369 -0.5779
#> log_k1 -2.53176 -3.804 -1.2598
#> log_k2 -3.58667 -5.295 -1.8781
#> g_qlogis 0.01238 -1.080 1.1044
#>
#> Correlation:
#> prnt_0 lg__A1 f_prn_ log_k1 log_k2
#> log_k_A1 -0.013
#> f_parent_qlogis -0.025 0.050
#> log_k1 0.030 0.000 -0.005
#> log_k2 0.010 0.005 -0.003 0.032
#> g_qlogis -0.063 -0.015 0.010 -0.167 -0.177
#>
#> Random effects:
#> est. lower upper
#> SD.parent_0 2.7588 0.7723 4.7453
#> SD.log_k_A1 2.1556 0.4443 3.8670
#> SD.f_parent_qlogis 0.4438 0.1599 0.7276
#> SD.log_k1 1.4203 0.5271 2.3134
#> SD.log_k2 1.9063 0.7093 3.1033
#> SD.g_qlogis 0.4477 -0.8642 1.7596
#>
#> Variance model:
#> est. lower upper
#> a.1 1.883 1.666 2.1
#>
#> Backtransformed parameters with asymmetric confidence intervals:
#> est. lower upper
#> parent_0 93.766473 9.115e+01 96.37983
#> k_A1 0.002171 2.122e-04 0.02222
#> f_parent_to_A1 0.274156 2.027e-01 0.35942
#> k1 0.079519 2.229e-02 0.28371
#> k2 0.027691 5.015e-03 0.15288
#> g 0.503095 2.536e-01 0.75109
#>
#> Resulting formation fractions:
#> ff
#> parent_A1 0.2742
#> parent_sink 0.7258
#>
#> Estimated disappearance times:
#> DT50 DT90 DT50back DT50_k1 DT50_k2
#> parent 14.11 59.53 17.92 8.717 25.03
#> A1 319.21 1060.38 NA NA NA
#>
#> Data:
#> ds name time observed predicted residual std standardized
#> Dataset 6 parent 0 97.2 95.79523 -1.40477 1.883 -0.745888
#> Dataset 6 parent 0 96.4 95.79523 -0.60477 1.883 -0.321114
#> Dataset 6 parent 3 71.1 71.32042 0.22042 1.883 0.117035
#> Dataset 6 parent 3 69.2 71.32042 2.12042 1.883 1.125873
#> Dataset 6 parent 6 58.1 56.45256 -1.64744 1.883 -0.874739
#> Dataset 6 parent 6 56.6 56.45256 -0.14744 1.883 -0.078288
#> Dataset 6 parent 10 44.4 44.48523 0.08523 1.883 0.045256
#> Dataset 6 parent 10 43.4 44.48523 1.08523 1.883 0.576224
#> Dataset 6 parent 20 33.3 29.75774 -3.54226 1.883 -1.880826
#> Dataset 6 parent 20 29.2 29.75774 0.55774 1.883 0.296141
#> Dataset 6 parent 34 17.6 19.35710 1.75710 1.883 0.932966
#> Dataset 6 parent 34 18.0 19.35710 1.35710 1.883 0.720578
#> Dataset 6 parent 55 10.5 10.48443 -0.01557 1.883 -0.008266
#> Dataset 6 parent 55 9.3 10.48443 1.18443 1.883 0.628895
#> Dataset 6 parent 90 4.5 3.78622 -0.71378 1.883 -0.378995
#> Dataset 6 parent 90 4.7 3.78622 -0.91378 1.883 -0.485188
#> Dataset 6 parent 112 3.0 1.99608 -1.00392 1.883 -0.533048
#> Dataset 6 parent 112 3.4 1.99608 -1.40392 1.883 -0.745435
#> Dataset 6 parent 132 2.3 1.11539 -1.18461 1.883 -0.628990
#> Dataset 6 parent 132 2.7 1.11539 -1.58461 1.883 -0.841377
#> Dataset 6 A1 3 4.3 4.66132 0.36132 1.883 0.191849
#> Dataset 6 A1 3 4.6 4.66132 0.06132 1.883 0.032559
#> Dataset 6 A1 6 7.0 7.41087 0.41087 1.883 0.218157
#> Dataset 6 A1 6 7.2 7.41087 0.21087 1.883 0.111964
#> Dataset 6 A1 10 8.2 9.50878 1.30878 1.883 0.694921
#> Dataset 6 A1 10 8.0 9.50878 1.50878 1.883 0.801114
#> Dataset 6 A1 20 11.0 11.69902 0.69902 1.883 0.371157
#> Dataset 6 A1 20 13.7 11.69902 -2.00098 1.883 -1.062455
#> Dataset 6 A1 34 11.5 12.67784 1.17784 1.883 0.625396
#> Dataset 6 A1 34 12.7 12.67784 -0.02216 1.883 -0.011765
#> Dataset 6 A1 55 14.9 12.78556 -2.11444 1.883 -1.122701
#> Dataset 6 A1 55 14.5 12.78556 -1.71444 1.883 -0.910314
#> Dataset 6 A1 90 12.1 11.52954 -0.57046 1.883 -0.302898
#> Dataset 6 A1 90 12.3 11.52954 -0.77046 1.883 -0.409092
#> Dataset 6 A1 112 9.9 10.43825 0.53825 1.883 0.285793
#> Dataset 6 A1 112 10.2 10.43825 0.23825 1.883 0.126503
#> Dataset 6 A1 132 8.8 9.42830 0.62830 1.883 0.333609
#> Dataset 6 A1 132 7.8 9.42830 1.62830 1.883 0.864577
#> Dataset 7 parent 0 93.6 90.91477 -2.68523 1.883 -1.425772
#> Dataset 7 parent 0 92.3 90.91477 -1.38523 1.883 -0.735514
#> Dataset 7 parent 3 87.0 84.76874 -2.23126 1.883 -1.184726
#> Dataset 7 parent 3 82.2 84.76874 2.56874 1.883 1.363919
#> Dataset 7 parent 7 74.0 77.62735 3.62735 1.883 1.926003
#> Dataset 7 parent 7 73.9 77.62735 3.72735 1.883 1.979100
#> Dataset 7 parent 14 64.2 67.52266 3.32266 1.883 1.764224
#> Dataset 7 parent 14 69.5 67.52266 -1.97734 1.883 -1.049904
#> Dataset 7 parent 30 54.0 52.41949 -1.58051 1.883 -0.839202
#> Dataset 7 parent 30 54.6 52.41949 -2.18051 1.883 -1.157783
#> Dataset 7 parent 60 41.1 39.36582 -1.73418 1.883 -0.920794
#> Dataset 7 parent 60 38.4 39.36582 0.96582 1.883 0.512818
#> Dataset 7 parent 90 32.5 33.75388 1.25388 1.883 0.665771
#> Dataset 7 parent 90 35.5 33.75388 -1.74612 1.883 -0.927132
#> Dataset 7 parent 120 28.1 30.41716 2.31716 1.883 1.230335
#> Dataset 7 parent 120 29.0 30.41716 1.41716 1.883 0.752464
#> Dataset 7 parent 180 26.5 25.66046 -0.83954 1.883 -0.445767
#> Dataset 7 parent 180 27.6 25.66046 -1.93954 1.883 -1.029832
#> Dataset 7 A1 3 3.9 2.69355 -1.20645 1.883 -0.640585
#> Dataset 7 A1 3 3.1 2.69355 -0.40645 1.883 -0.215811
#> Dataset 7 A1 7 6.9 5.81807 -1.08193 1.883 -0.574470
#> Dataset 7 A1 7 6.6 5.81807 -0.78193 1.883 -0.415180
#> Dataset 7 A1 14 10.4 10.22529 -0.17471 1.883 -0.092767
#> Dataset 7 A1 14 8.3 10.22529 1.92529 1.883 1.022265
#> Dataset 7 A1 30 14.4 16.75484 2.35484 1.883 1.250345
#> Dataset 7 A1 30 13.7 16.75484 3.05484 1.883 1.622022
#> Dataset 7 A1 60 22.1 22.22540 0.12540 1.883 0.066583
#> Dataset 7 A1 60 22.3 22.22540 -0.07460 1.883 -0.039610
#> Dataset 7 A1 90 27.5 24.38799 -3.11201 1.883 -1.652376
#> Dataset 7 A1 90 25.4 24.38799 -1.01201 1.883 -0.537344
#> Dataset 7 A1 120 28.0 25.53294 -2.46706 1.883 -1.309927
#> Dataset 7 A1 120 26.6 25.53294 -1.06706 1.883 -0.566572
#> Dataset 7 A1 180 25.8 26.94943 1.14943 1.883 0.610309
#> Dataset 7 A1 180 25.3 26.94943 1.64943 1.883 0.875793
#> Dataset 8 parent 0 91.9 91.53246 -0.36754 1.883 -0.195151
#> Dataset 8 parent 0 90.8 91.53246 0.73246 1.883 0.388914
#> Dataset 8 parent 1 64.9 67.73197 2.83197 1.883 1.503686
#> Dataset 8 parent 1 66.2 67.73197 1.53197 1.883 0.813428
#> Dataset 8 parent 3 43.5 41.58448 -1.91552 1.883 -1.017081
#> Dataset 8 parent 3 44.1 41.58448 -2.51552 1.883 -1.335661
#> Dataset 8 parent 8 18.3 19.62286 1.32286 1.883 0.702395
#> Dataset 8 parent 8 18.1 19.62286 1.52286 1.883 0.808589
#> Dataset 8 parent 14 10.2 10.77819 0.57819 1.883 0.306999
#> Dataset 8 parent 14 10.8 10.77819 -0.02181 1.883 -0.011582
#> Dataset 8 parent 27 4.9 3.26977 -1.63023 1.883 -0.865599
#> Dataset 8 parent 27 3.3 3.26977 -0.03023 1.883 -0.016051
#> Dataset 8 parent 48 1.6 0.48024 -1.11976 1.883 -0.594557
#> Dataset 8 parent 48 1.5 0.48024 -1.01976 1.883 -0.541460
#> Dataset 8 parent 70 1.1 0.06438 -1.03562 1.883 -0.549881
#> Dataset 8 parent 70 0.9 0.06438 -0.83562 1.883 -0.443688
#> Dataset 8 A1 1 9.6 7.61539 -1.98461 1.883 -1.053761
#> Dataset 8 A1 1 7.7 7.61539 -0.08461 1.883 -0.044923
#> Dataset 8 A1 3 15.0 15.47954 0.47954 1.883 0.254622
#> Dataset 8 A1 3 15.1 15.47954 0.37954 1.883 0.201525
#> Dataset 8 A1 8 21.2 20.22616 -0.97384 1.883 -0.517076
#> Dataset 8 A1 8 21.1 20.22616 -0.87384 1.883 -0.463979
#> Dataset 8 A1 14 19.7 20.00067 0.30067 1.883 0.159645
#> Dataset 8 A1 14 18.9 20.00067 1.10067 1.883 0.584419
#> Dataset 8 A1 27 17.5 16.38142 -1.11858 1.883 -0.593929
#> Dataset 8 A1 27 15.9 16.38142 0.48142 1.883 0.255619
#> Dataset 8 A1 48 9.5 10.25357 0.75357 1.883 0.400123
#> Dataset 8 A1 48 9.8 10.25357 0.45357 1.883 0.240833
#> Dataset 8 A1 70 6.2 5.95728 -0.24272 1.883 -0.128878
#> Dataset 8 A1 70 6.1 5.95728 -0.14272 1.883 -0.075781
#> Dataset 9 parent 0 99.8 97.47274 -2.32726 1.883 -1.235697
#> Dataset 9 parent 0 98.3 97.47274 -0.82726 1.883 -0.439246
#> Dataset 9 parent 1 77.1 79.72257 2.62257 1.883 1.392500
#> Dataset 9 parent 1 77.2 79.72257 2.52257 1.883 1.339404
#> Dataset 9 parent 3 59.0 56.26497 -2.73503 1.883 -1.452212
#> Dataset 9 parent 3 58.1 56.26497 -1.83503 1.883 -0.974342
#> Dataset 9 parent 8 27.4 31.66985 4.26985 1.883 2.267151
#> Dataset 9 parent 8 29.2 31.66985 2.46985 1.883 1.311410
#> Dataset 9 parent 14 19.1 22.39789 3.29789 1.883 1.751071
#> Dataset 9 parent 14 29.6 22.39789 -7.20211 1.883 -3.824090
#> Dataset 9 parent 27 10.1 14.21758 4.11758 1.883 2.186301
#> Dataset 9 parent 27 18.2 14.21758 -3.98242 1.883 -2.114537
#> Dataset 9 parent 48 4.5 7.27921 2.77921 1.883 1.475671
#> Dataset 9 parent 48 9.1 7.27921 -1.82079 1.883 -0.966780
#> Dataset 9 parent 70 2.3 3.61470 1.31470 1.883 0.698065
#> Dataset 9 parent 70 2.9 3.61470 0.71470 1.883 0.379485
#> Dataset 9 parent 91 2.0 1.85303 -0.14697 1.883 -0.078038
#> Dataset 9 parent 91 1.8 1.85303 0.05303 1.883 0.028155
#> Dataset 9 parent 120 2.0 0.73645 -1.26355 1.883 -0.670906
#> Dataset 9 parent 120 2.2 0.73645 -1.46355 1.883 -0.777099
#> Dataset 9 A1 1 4.2 3.87843 -0.32157 1.883 -0.170743
#> Dataset 9 A1 1 3.9 3.87843 -0.02157 1.883 -0.011453
#> Dataset 9 A1 3 7.4 8.90535 1.50535 1.883 0.799291
#> Dataset 9 A1 3 7.9 8.90535 1.00535 1.883 0.533807
#> Dataset 9 A1 8 14.5 13.75172 -0.74828 1.883 -0.397312
#> Dataset 9 A1 8 13.7 13.75172 0.05172 1.883 0.027462
#> Dataset 9 A1 14 14.2 14.97541 0.77541 1.883 0.411715
#> Dataset 9 A1 14 12.2 14.97541 2.77541 1.883 1.473650
#> Dataset 9 A1 27 13.7 14.94728 1.24728 1.883 0.662266
#> Dataset 9 A1 27 13.2 14.94728 1.74728 1.883 0.927750
#> Dataset 9 A1 48 13.6 13.66078 0.06078 1.883 0.032272
#> Dataset 9 A1 48 15.4 13.66078 -1.73922 1.883 -0.923470
#> Dataset 9 A1 70 10.4 11.84899 1.44899 1.883 0.769365
#> Dataset 9 A1 70 11.6 11.84899 0.24899 1.883 0.132204
#> Dataset 9 A1 91 10.0 10.09177 0.09177 1.883 0.048727
#> Dataset 9 A1 91 9.5 10.09177 0.59177 1.883 0.314211
#> Dataset 9 A1 120 9.1 7.91379 -1.18621 1.883 -0.629841
#> Dataset 9 A1 120 9.0 7.91379 -1.08621 1.883 -0.576745
#> Dataset 10 parent 0 96.1 93.65257 -2.44743 1.883 -1.299505
#> Dataset 10 parent 0 94.3 93.65257 -0.64743 1.883 -0.343763
#> Dataset 10 parent 8 73.9 77.85906 3.95906 1.883 2.102132
#> Dataset 10 parent 8 73.9 77.85906 3.95906 1.883 2.102132
#> Dataset 10 parent 14 69.4 70.17143 0.77143 1.883 0.409606
#> Dataset 10 parent 14 73.1 70.17143 -2.92857 1.883 -1.554974
#> Dataset 10 parent 21 65.6 63.99188 -1.60812 1.883 -0.853862
#> Dataset 10 parent 21 65.3 63.99188 -1.30812 1.883 -0.694572
#> Dataset 10 parent 41 55.9 54.64292 -1.25708 1.883 -0.667467
#> Dataset 10 parent 41 54.4 54.64292 0.24292 1.883 0.128985
#> Dataset 10 parent 63 47.0 49.61303 2.61303 1.883 1.387433
#> Dataset 10 parent 63 49.3 49.61303 0.31303 1.883 0.166207
#> Dataset 10 parent 91 44.7 45.17807 0.47807 1.883 0.253839
#> Dataset 10 parent 91 46.7 45.17807 -1.52193 1.883 -0.808096
#> Dataset 10 parent 120 42.1 41.27970 -0.82030 1.883 -0.435552
#> Dataset 10 parent 120 41.3 41.27970 -0.02030 1.883 -0.010778
#> Dataset 10 A1 8 3.3 3.99294 0.69294 1.883 0.367929
#> Dataset 10 A1 8 3.4 3.99294 0.59294 1.883 0.314832
#> Dataset 10 A1 14 3.9 5.92756 2.02756 1.883 1.076570
#> Dataset 10 A1 14 2.9 5.92756 3.02756 1.883 1.607538
#> Dataset 10 A1 21 6.4 7.47313 1.07313 1.883 0.569799
#> Dataset 10 A1 21 7.2 7.47313 0.27313 1.883 0.145025
#> Dataset 10 A1 41 9.1 9.76819 0.66819 1.883 0.354786
#> Dataset 10 A1 41 8.5 9.76819 1.26819 1.883 0.673367
#> Dataset 10 A1 63 11.7 10.94733 -0.75267 1.883 -0.399643
#> Dataset 10 A1 63 12.0 10.94733 -1.05267 1.883 -0.558933
#> Dataset 10 A1 91 13.3 11.93773 -1.36227 1.883 -0.723321
#> Dataset 10 A1 91 13.2 11.93773 -1.26227 1.883 -0.670224
#> Dataset 10 A1 120 14.3 12.77666 -1.52334 1.883 -0.808847
#> Dataset 10 A1 120 12.1 12.77666 0.67666 1.883 0.359282</div><div class='input'>
<span class='co'># Using a single core, the following takes about 6 minutes as we do not have an</span>
<span class='co'># analytical solution. Using 10 cores it is slower instead of faster</span>
<span class='va'>f_saem_fomc</span> <span class='op'><-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin</span><span class='op'>[</span><span class='st'>"FOMC-SFO"</span>, <span class='op'>]</span>, cores <span class='op'>=</span> <span class='fl'>1</span><span class='op'>)</span>
</div><div class='output co'>#> Running main SAEM algorithm
#> [1] "Mon Nov 30 15:53:39 2020"
#> DLSODA- At current T (=R1), MXSTEP (=I1) steps
#> taken on this call before reaching TOUT
#> In above message, I1 = 5000
#>
#> In above message, R1 = 0.00156238
#>
#> DLSODA- At T (=R1) and step size H (=R2), the
#> corrector convergence failed repeatedly
#> or with ABS(H) = HMIN
#> In above message, R1 = 0, R2 = 1.1373e-10
#>
#> DLSODA- At current T (=R1), MXSTEP (=I1) steps
#> taken on this call before reaching TOUT
#> In above message, I1 = 5000
#>
#> In above message, R1 = 2.24752e-06
#>
#> ....
#> Minimisation finished
#> [1] "Mon Nov 30 16:00:45 2020"</div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html'>plot</a></span><span class='op'>(</span><span class='va'>f_saem_fomc</span><span class='op'>)</span>
</div><div class='img'><img src='saem-6.png' alt='' width='700' height='433' /></div><div class='input'><span class='co'># }</span>
</div></pre>
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