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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'>...</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>,
transformations <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'>"mkin"</span>, <span class='st'>"saemix"</span><span class='op'>)</span>,
degparms_start <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/numeric.html'>numeric</a></span><span class='op'>(</span><span class='op'>)</span>,
test_log_parms <span class='op'>=</span> <span class='cn'>TRUE</span>,
conf.level <span class='op'>=</span> <span class='fl'>0.6</span>,
solution_type <span class='op'>=</span> <span class='st'>"auto"</span>,
nbiter.saemix <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='fl'>300</span>, <span class='fl'>100</span><span class='op'>)</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>, nbiter.saemix <span class='op'>=</span> <span class='va'>nbiter.saemix</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>,
fail_with_errors <span class='op'>=</span> <span class='cn'>TRUE</span>,
verbose <span class='op'>=</span> <span class='cn'>FALSE</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>,
solution_type <span class='op'>=</span> <span class='st'>"auto"</span>,
transformations <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'>"mkin"</span>, <span class='st'>"saemix"</span><span class='op'>)</span>,
degparms_start <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/numeric.html'>numeric</a></span><span class='op'>(</span><span class='op'>)</span>,
test_log_parms <span class='op'>=</span> <span class='cn'>FALSE</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>...</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>transformations</th>
<td><p>Per default, all parameter transformations are done
in mkin. If this argument is set to 'saemix', parameter transformations
are done in 'saemix' for the supported cases. Currently this is only
supported in cases where the initial concentration of the parent is not fixed,
SFO or DFOP is used for the parent and there is either no metabolite or one.</p></td>
</tr>
<tr>
<th>degparms_start</th>
<td><p>Parameter values given as a named numeric vector will
be used to override the starting values obtained from the 'mmkin' object.</p></td>
</tr>
<tr>
<th>test_log_parms</th>
<td><p>If TRUE, an attempt is made to use more robust starting
values for population parameters fitted as log parameters in mkin (like
rate constants) by only considering rate constants that pass the t-test
when calculating mean degradation parameters using <a href='mean_degparms.html'>mean_degparms</a>.</p></td>
</tr>
<tr>
<th>conf.level</th>
<td><p>Possibility to adjust the required confidence level
for parameter that are tested if requested by 'test_log_parms'.</p></td>
</tr>
<tr>
<th>solution_type</th>
<td><p>Possibility to specify the solution type in case the
automatic choice is not desired</p></td>
</tr>
<tr>
<th>nbiter.saemix</th>
<td><p>Convenience option to increase the number of
iterations</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>fail_with_errors</th>
<td><p>Should a failure to compute standard errors
from the inverse of the Fisher Information Matrix be a failure?</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>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>,
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] "Wed Aug 4 16:22:05 2021"
#> ....
#> Minimisation finished
#> [1] "Wed Aug 4 16:22:06 2021"</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] "Wed Aug 4 16:22:08 2021"
#> ....
#> Minimisation finished
#> [1] "Wed Aug 4 16:22:10 2021"</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] "Wed Aug 4 16:22:10 2021"
#> ....
#> Minimisation finished
#> [1] "Wed Aug 4 16:22:12 2021"</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] "Wed Aug 4 16:22:12 2021"
#> ....
#> Minimisation finished
#> [1] "Wed Aug 4 16:22:16 2021"</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='output co'>#> <span class='message'></span>
#> <span class='message'>Attaching package: ‘saemix’</span></div><div class='output co'>#> <span class='message'>The following object is masked from ‘package:RxODE’:</span>
#> <span class='message'></span>
#> <span class='message'> phi</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='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>
</div><div class='output co'>#> <span class='message'>Likelihoods calculated by importance sampling</span></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] "Wed Aug 4 16:22:19 2021"
#> ....
#> Minimisation finished
#> [1] "Wed Aug 4 16:22:24 2021"</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='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>
</div><div class='output co'>#> <span class='message'>Likelihoods calculated by importance sampling</span></div><div class='output co'>#> AIC BIC
#> 1 467.7096 464.9757
#> 2 469.6831 466.5586</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'># saem fits of SFO-SFO and DFOP-SFO to these data take about five seconds</span>
<span class='co'># each on this system, as we use analytical solutions written for saemix.</span>
<span class='co'># When using the analytical solutions written for mkin this took around</span>
<span class='co'># 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] "Wed Aug 4 16:22:27 2021"
#> ....
#> Minimisation finished
#> [1] "Wed Aug 4 16:22:32 2021"</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] "Wed Aug 4 16:22:33 2021"
#> ....
#> Minimisation finished
#> [1] "Wed Aug 4 16:22:42 2021"</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
#> 839.6 834.6 -406.8
#>
#> Fitted parameters:
#> estimate lower upper
#> parent_0 93.80521 91.22487 96.3856
#> log_k_A1 -6.06244 -8.26517 -3.8597
#> f_parent_qlogis -0.97319 -1.37024 -0.5761
#> log_k1 -2.55394 -4.00815 -1.0997
#> log_k2 -3.47160 -5.18763 -1.7556
#> g_qlogis -0.09324 -1.42737 1.2409
#> Var.parent_0 7.42157 -3.25683 18.1000
#> Var.log_k_A1 4.22850 -2.46339 10.9204
#> Var.f_parent_qlogis 0.19803 -0.05541 0.4515
#> Var.log_k1 2.28644 -0.86079 5.4337
#> Var.log_k2 3.35626 -1.14639 7.8589
#> Var.g_qlogis 0.20084 -1.32516 1.7268
#> a.1 1.88399 1.66794 2.1000
#> SD.parent_0 2.72425 0.76438 4.6841
#> SD.log_k_A1 2.05633 0.42919 3.6835
#> SD.f_parent_qlogis 0.44501 0.16025 0.7298
#> SD.log_k1 1.51210 0.47142 2.5528
#> SD.log_k2 1.83201 0.60313 3.0609
#> SD.g_qlogis 0.44816 -1.25437 2.1507</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: 1.0.5
#> R version used for fitting: 4.1.0
#> Date of fit: Wed Aug 4 16:22:43 2021
#> Date of summary: Wed Aug 4 16:22:43 2021
#>
#> 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 10.143 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
#> 93.8102 -5.3734 -0.9711 -1.8799 -4.2708
#> g_qlogis
#> 0.1356
#>
#> Fixed degradation parameter values:
#> None
#>
#> Results:
#>
#> Likelihood computed by importance sampling
#> AIC BIC logLik
#> 839.6 834.6 -406.8
#>
#> Optimised parameters:
#> est. lower upper
#> parent_0 93.80521 91.225 96.3856
#> log_k_A1 -6.06244 -8.265 -3.8597
#> f_parent_qlogis -0.97319 -1.370 -0.5761
#> log_k1 -2.55394 -4.008 -1.0997
#> log_k2 -3.47160 -5.188 -1.7556
#> g_qlogis -0.09324 -1.427 1.2409
#>
#> Correlation:
#> prnt_0 lg__A1 f_prn_ log_k1 log_k2
#> log_k_A1 -0.014
#> f_parent_qlogis -0.025 0.054
#> log_k1 0.027 -0.003 -0.005
#> log_k2 0.011 0.005 -0.002 -0.070
#> g_qlogis -0.067 -0.009 0.011 -0.189 -0.171
#>
#> Random effects:
#> est. lower upper
#> SD.parent_0 2.7243 0.7644 4.6841
#> SD.log_k_A1 2.0563 0.4292 3.6835
#> SD.f_parent_qlogis 0.4450 0.1602 0.7298
#> SD.log_k1 1.5121 0.4714 2.5528
#> SD.log_k2 1.8320 0.6031 3.0609
#> SD.g_qlogis 0.4482 -1.2544 2.1507
#>
#> Variance model:
#> est. lower upper
#> a.1 1.884 1.668 2.1
#>
#> Backtransformed parameters:
#> est. lower upper
#> parent_0 93.805214 9.122e+01 96.38556
#> k_A1 0.002329 2.573e-04 0.02107
#> f_parent_to_A1 0.274245 2.026e-01 0.35982
#> k1 0.077775 1.817e-02 0.33296
#> k2 0.031067 5.585e-03 0.17281
#> g 0.476707 1.935e-01 0.77572
#>
#> Resulting formation fractions:
#> ff
#> parent_A1 0.2742
#> parent_sink 0.7258
#>
#> Estimated disappearance times:
#> DT50 DT90 DT50back DT50_k1 DT50_k2
#> parent 13.96 55.4 16.68 8.912 22.31
#> A1 297.65 988.8 NA NA NA
#>
#> Data:
#> ds name time observed predicted residual std standardized
#> Dataset 6 parent 0 97.2 95.75408 1.445920 1.884 0.767479
#> Dataset 6 parent 0 96.4 95.75408 0.645920 1.884 0.342847
#> Dataset 6 parent 3 71.1 71.22466 -0.124662 1.884 -0.066169
#> Dataset 6 parent 3 69.2 71.22466 -2.024662 1.884 -1.074669
#> Dataset 6 parent 6 58.1 56.42290 1.677100 1.884 0.890187
#> Dataset 6 parent 6 56.6 56.42290 0.177100 1.884 0.094003
#> Dataset 6 parent 10 44.4 44.55255 -0.152554 1.884 -0.080974
#> Dataset 6 parent 10 43.4 44.55255 -1.152554 1.884 -0.611763
#> Dataset 6 parent 20 33.3 29.88846 3.411537 1.884 1.810807
#> Dataset 6 parent 20 29.2 29.88846 -0.688463 1.884 -0.365429
#> Dataset 6 parent 34 17.6 19.40826 -1.808260 1.884 -0.959805
#> Dataset 6 parent 34 18.0 19.40826 -1.408260 1.884 -0.747489
#> Dataset 6 parent 55 10.5 10.45560 0.044398 1.884 0.023566
#> Dataset 6 parent 55 9.3 10.45560 -1.155602 1.884 -0.613381
#> Dataset 6 parent 90 4.5 3.74026 0.759744 1.884 0.403264
#> Dataset 6 parent 90 4.7 3.74026 0.959744 1.884 0.509421
#> Dataset 6 parent 112 3.0 1.96015 1.039853 1.884 0.551943
#> Dataset 6 parent 112 3.4 1.96015 1.439853 1.884 0.764258
#> Dataset 6 parent 132 2.3 1.08940 1.210603 1.884 0.642575
#> Dataset 6 parent 132 2.7 1.08940 1.610603 1.884 0.854890
#> Dataset 6 A1 3 4.3 4.75601 -0.456009 1.884 -0.242045
#> Dataset 6 A1 3 4.6 4.75601 -0.156009 1.884 -0.082808
#> Dataset 6 A1 6 7.0 7.53839 -0.538391 1.884 -0.285772
#> Dataset 6 A1 6 7.2 7.53839 -0.338391 1.884 -0.179614
#> Dataset 6 A1 10 8.2 9.64728 -1.447276 1.884 -0.768198
#> Dataset 6 A1 10 8.0 9.64728 -1.647276 1.884 -0.874356
#> Dataset 6 A1 20 11.0 11.83954 -0.839545 1.884 -0.445621
#> Dataset 6 A1 20 13.7 11.83954 1.860455 1.884 0.987509
#> Dataset 6 A1 34 11.5 12.81233 -1.312327 1.884 -0.696569
#> Dataset 6 A1 34 12.7 12.81233 -0.112327 1.884 -0.059622
#> Dataset 6 A1 55 14.9 12.87919 2.020809 1.884 1.072624
#> Dataset 6 A1 55 14.5 12.87919 1.620809 1.884 0.860308
#> Dataset 6 A1 90 12.1 11.52464 0.575364 1.884 0.305397
#> Dataset 6 A1 90 12.3 11.52464 0.775364 1.884 0.411555
#> Dataset 6 A1 112 9.9 10.37694 -0.476938 1.884 -0.253153
#> Dataset 6 A1 112 10.2 10.37694 -0.176938 1.884 -0.093917
#> Dataset 6 A1 132 8.8 9.32474 -0.524742 1.884 -0.278528
#> Dataset 6 A1 132 7.8 9.32474 -1.524742 1.884 -0.809317
#> Dataset 7 parent 0 93.6 90.16918 3.430816 1.884 1.821040
#> Dataset 7 parent 0 92.3 90.16918 2.130816 1.884 1.131014
#> Dataset 7 parent 3 87.0 84.05442 2.945583 1.884 1.563483
#> Dataset 7 parent 3 82.2 84.05442 -1.854417 1.884 -0.984304
#> Dataset 7 parent 7 74.0 77.00960 -3.009596 1.884 -1.597461
#> Dataset 7 parent 7 73.9 77.00960 -3.109596 1.884 -1.650540
#> Dataset 7 parent 14 64.2 67.15684 -2.956840 1.884 -1.569459
#> Dataset 7 parent 14 69.5 67.15684 2.343160 1.884 1.243724
#> Dataset 7 parent 30 54.0 52.66290 1.337101 1.884 0.709719
#> Dataset 7 parent 30 54.6 52.66290 1.937101 1.884 1.028192
#> Dataset 7 parent 60 41.1 40.04995 1.050050 1.884 0.557355
#> Dataset 7 parent 60 38.4 40.04995 -1.649950 1.884 -0.875775
#> Dataset 7 parent 90 32.5 34.09675 -1.596746 1.884 -0.847535
#> Dataset 7 parent 90 35.5 34.09675 1.403254 1.884 0.744832
#> Dataset 7 parent 120 28.1 30.12281 -2.022814 1.884 -1.073688
#> Dataset 7 parent 120 29.0 30.12281 -1.122814 1.884 -0.595977
#> Dataset 7 parent 180 26.5 24.10888 2.391123 1.884 1.269182
#> Dataset 7 parent 180 27.6 24.10888 3.491123 1.884 1.853050
#> Dataset 7 A1 3 3.9 2.77684 1.123161 1.884 0.596161
#> Dataset 7 A1 3 3.1 2.77684 0.323161 1.884 0.171530
#> Dataset 7 A1 7 6.9 5.96705 0.932950 1.884 0.495200
#> Dataset 7 A1 7 6.6 5.96705 0.632950 1.884 0.335963
#> Dataset 7 A1 14 10.4 10.40535 -0.005348 1.884 -0.002839
#> Dataset 7 A1 14 8.3 10.40535 -2.105348 1.884 -1.117496
#> Dataset 7 A1 30 14.4 16.83722 -2.437216 1.884 -1.293648
#> Dataset 7 A1 30 13.7 16.83722 -3.137216 1.884 -1.665200
#> Dataset 7 A1 60 22.1 22.15018 -0.050179 1.884 -0.026635
#> Dataset 7 A1 60 22.3 22.15018 0.149821 1.884 0.079523
#> Dataset 7 A1 90 27.5 24.36286 3.137143 1.884 1.665161
#> Dataset 7 A1 90 25.4 24.36286 1.037143 1.884 0.550504
#> Dataset 7 A1 120 28.0 25.64064 2.359361 1.884 1.252323
#> Dataset 7 A1 120 26.6 25.64064 0.959361 1.884 0.509218
#> Dataset 7 A1 180 25.8 27.25486 -1.454858 1.884 -0.772223
#> Dataset 7 A1 180 25.3 27.25486 -1.954858 1.884 -1.037617
#> Dataset 8 parent 0 91.9 91.72652 0.173479 1.884 0.092081
#> Dataset 8 parent 0 90.8 91.72652 -0.926521 1.884 -0.491787
#> Dataset 8 parent 1 64.9 67.22810 -2.328104 1.884 -1.235732
#> Dataset 8 parent 1 66.2 67.22810 -1.028104 1.884 -0.545706
#> Dataset 8 parent 3 43.5 41.46375 2.036251 1.884 1.080820
#> Dataset 8 parent 3 44.1 41.46375 2.636251 1.884 1.399293
#> Dataset 8 parent 8 18.3 19.83597 -1.535968 1.884 -0.815275
#> Dataset 8 parent 8 18.1 19.83597 -1.735968 1.884 -0.921433
#> Dataset 8 parent 14 10.2 10.34793 -0.147927 1.884 -0.078518
#> Dataset 8 parent 14 10.8 10.34793 0.452073 1.884 0.239956
#> Dataset 8 parent 27 4.9 2.67641 2.223595 1.884 1.180260
#> Dataset 8 parent 27 3.3 2.67641 0.623595 1.884 0.330997
#> Dataset 8 parent 48 1.6 0.30218 1.297822 1.884 0.688870
#> Dataset 8 parent 48 1.5 0.30218 1.197822 1.884 0.635791
#> Dataset 8 parent 70 1.1 0.03075 1.069248 1.884 0.567545
#> Dataset 8 parent 70 0.9 0.03075 0.869248 1.884 0.461388
#> Dataset 8 A1 1 9.6 7.74066 1.859342 1.884 0.986918
#> Dataset 8 A1 1 7.7 7.74066 -0.040658 1.884 -0.021581
#> Dataset 8 A1 3 15.0 15.37549 -0.375495 1.884 -0.199309
#> Dataset 8 A1 3 15.1 15.37549 -0.275495 1.884 -0.146230
#> Dataset 8 A1 8 21.2 19.95900 1.241003 1.884 0.658711
#> Dataset 8 A1 8 21.1 19.95900 1.141003 1.884 0.605632
#> Dataset 8 A1 14 19.7 19.92898 -0.228978 1.884 -0.121539
#> Dataset 8 A1 14 18.9 19.92898 -1.028978 1.884 -0.546170
#> Dataset 8 A1 27 17.5 16.34046 1.159536 1.884 0.615469
#> Dataset 8 A1 27 15.9 16.34046 -0.440464 1.884 -0.233793
#> Dataset 8 A1 48 9.5 10.12131 -0.621313 1.884 -0.329786
#> Dataset 8 A1 48 9.8 10.12131 -0.321313 1.884 -0.170550
#> Dataset 8 A1 70 6.2 5.84753 0.352469 1.884 0.187087
#> Dataset 8 A1 70 6.1 5.84753 0.252469 1.884 0.134008
#> Dataset 9 parent 0 99.8 98.23600 1.564002 1.884 0.830155
#> Dataset 9 parent 0 98.3 98.23600 0.064002 1.884 0.033972
#> Dataset 9 parent 1 77.1 79.68007 -2.580074 1.884 -1.369475
#> Dataset 9 parent 1 77.2 79.68007 -2.480074 1.884 -1.316396
#> Dataset 9 parent 3 59.0 55.81142 3.188584 1.884 1.692465
#> Dataset 9 parent 3 58.1 55.81142 2.288584 1.884 1.214755
#> Dataset 9 parent 8 27.4 31.81995 -4.419948 1.884 -2.346060
#> Dataset 9 parent 8 29.2 31.81995 -2.619948 1.884 -1.390640
#> Dataset 9 parent 14 19.1 22.78328 -3.683282 1.884 -1.955046
#> Dataset 9 parent 14 29.6 22.78328 6.816718 1.884 3.618240
#> Dataset 9 parent 27 10.1 14.15172 -4.051720 1.884 -2.150609
#> Dataset 9 parent 27 18.2 14.15172 4.048280 1.884 2.148783
#> Dataset 9 parent 48 4.5 6.86094 -2.360941 1.884 -1.253162
#> Dataset 9 parent 48 9.1 6.86094 2.239059 1.884 1.188468
#> Dataset 9 parent 70 2.3 3.21580 -0.915798 1.884 -0.486096
#> Dataset 9 parent 70 2.9 3.21580 -0.315798 1.884 -0.167622
#> Dataset 9 parent 91 2.0 1.56010 0.439897 1.884 0.233492
#> Dataset 9 parent 91 1.8 1.56010 0.239897 1.884 0.127335
#> Dataset 9 parent 120 2.0 0.57458 1.425424 1.884 0.756600
#> Dataset 9 parent 120 2.2 0.57458 1.625424 1.884 0.862757
#> Dataset 9 A1 1 4.2 4.01796 0.182037 1.884 0.096623
#> Dataset 9 A1 1 3.9 4.01796 -0.117963 1.884 -0.062613
#> Dataset 9 A1 3 7.4 9.08527 -1.685270 1.884 -0.894523
#> Dataset 9 A1 3 7.9 9.08527 -1.185270 1.884 -0.629129
#> Dataset 9 A1 8 14.5 13.75054 0.749457 1.884 0.397804
#> Dataset 9 A1 8 13.7 13.75054 -0.050543 1.884 -0.026827
#> Dataset 9 A1 14 14.2 14.91180 -0.711804 1.884 -0.377818
#> Dataset 9 A1 14 12.2 14.91180 -2.711804 1.884 -1.439396
#> Dataset 9 A1 27 13.7 14.97813 -1.278129 1.884 -0.678417
#> Dataset 9 A1 27 13.2 14.97813 -1.778129 1.884 -0.943812
#> Dataset 9 A1 48 13.6 13.75574 -0.155745 1.884 -0.082668
#> Dataset 9 A1 48 15.4 13.75574 1.644255 1.884 0.872753
#> Dataset 9 A1 70 10.4 11.92861 -1.528608 1.884 -0.811369
#> Dataset 9 A1 70 11.6 11.92861 -0.328608 1.884 -0.174422
#> Dataset 9 A1 91 10.0 10.14395 -0.143947 1.884 -0.076405
#> Dataset 9 A1 91 9.5 10.14395 -0.643947 1.884 -0.341800
#> Dataset 9 A1 120 9.1 7.93869 1.161307 1.884 0.616409
#> Dataset 9 A1 120 9.0 7.93869 1.061307 1.884 0.563330
#> Dataset 10 parent 0 96.1 93.65914 2.440862 1.884 1.295583
#> Dataset 10 parent 0 94.3 93.65914 0.640862 1.884 0.340163
#> Dataset 10 parent 8 73.9 77.83065 -3.930647 1.884 -2.086344
#> Dataset 10 parent 8 73.9 77.83065 -3.930647 1.884 -2.086344
#> Dataset 10 parent 14 69.4 70.15862 -0.758619 1.884 -0.402667
#> Dataset 10 parent 14 73.1 70.15862 2.941381 1.884 1.561253
#> Dataset 10 parent 21 65.6 64.00840 1.591600 1.884 0.844804
#> Dataset 10 parent 21 65.3 64.00840 1.291600 1.884 0.685567
#> Dataset 10 parent 41 55.9 54.71192 1.188076 1.884 0.630618
#> Dataset 10 parent 41 54.4 54.71192 -0.311924 1.884 -0.165566
#> Dataset 10 parent 63 47.0 49.66775 -2.667747 1.884 -1.416011
#> Dataset 10 parent 63 49.3 49.66775 -0.367747 1.884 -0.195196
#> Dataset 10 parent 91 44.7 45.17119 -0.471186 1.884 -0.250101
#> Dataset 10 parent 91 46.7 45.17119 1.528814 1.884 0.811478
#> Dataset 10 parent 120 42.1 41.20430 0.895699 1.884 0.475427
#> Dataset 10 parent 120 41.3 41.20430 0.095699 1.884 0.050796
#> Dataset 10 A1 8 3.3 4.00920 -0.709204 1.884 -0.376438
#> Dataset 10 A1 8 3.4 4.00920 -0.609204 1.884 -0.323359
#> Dataset 10 A1 14 3.9 5.94267 -2.042668 1.884 -1.084226
#> Dataset 10 A1 14 2.9 5.94267 -3.042668 1.884 -1.615015
#> Dataset 10 A1 21 6.4 7.48222 -1.082219 1.884 -0.574430
#> Dataset 10 A1 21 7.2 7.48222 -0.282219 1.884 -0.149799
#> Dataset 10 A1 41 9.1 9.76246 -0.662460 1.884 -0.351626
#> Dataset 10 A1 41 8.5 9.76246 -1.262460 1.884 -0.670100
#> Dataset 10 A1 63 11.7 10.93972 0.760278 1.884 0.403547
#> Dataset 10 A1 63 12.0 10.93972 1.060278 1.884 0.562784
#> Dataset 10 A1 91 13.3 11.93666 1.363337 1.884 0.723645
#> Dataset 10 A1 91 13.2 11.93666 1.263337 1.884 0.670566
#> Dataset 10 A1 120 14.3 12.78218 1.517817 1.884 0.805641
#> Dataset 10 A1 120 12.1 12.78218 -0.682183 1.884 -0.362095</div><div class='input'>
<span class='co'># The following takes about 6 minutes</span>
<span class='co'>#f_saem_dfop_sfo_deSolve <- saem(f_mmkin["DFOP-SFO", ], solution_type = "deSolve",</span>
<span class='co'># control = list(nbiter.saemix = c(200, 80), nbdisplay = 10))</span>
<span class='co'>#saemix::compare.saemix(list(</span>
<span class='co'># f_saem_dfop_sfo$so,</span>
<span class='co'># f_saem_dfop_sfo_deSolve$so))</span>
<span class='co'># If the model supports it, we can also use eigenvalue based solutions, which</span>
<span class='co'># take a similar amount of time</span>
<span class='co'>#f_saem_sfo_sfo_eigen <- saem(f_mmkin["SFO-SFO", ], solution_type = "eigen",</span>
<span class='co'># control = list(nbiter.saemix = c(200, 80), nbdisplay = 10))</span>
<span class='co'># }</span>
</div></pre>
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