Wissenschaftlicher Berater, Kronacher Str. 12, 79639 Grenzach-Wyhlen, Germany
Privatdozent at the University of Bremen

-Abstract

Wissenschaftlicher Berater, Kronacher Str. 12, 79639 Grenzach-Wyhlen, Germany
Privatdozent at the University of Freiburg

Abstract +

In the regulatory evaluation of chemical substances like plant protection products (pesticides), biocides and other chemicals, degradation data play an important role. For the evaluation of pesticide degradation experiments, detailed guidance has been developed, based on nonlinear optimisation. The R add-on package mkin implements fitting some of the models recommended in this guidance from within R and calculates some statistical measures for data series within one or more compartments, for parent and metabolites.

-library("mkin", quietly = TRUE)
+library("mkin", quietly = TRUE)
 # Define the kinetic model
 m_SFO_SFO_SFO <- mkinmod(parent = mkinsub("SFO", "M1"),
                          M1 = mkinsub("SFO", "M2"),
@@ -125,12 +127,12 @@
 
 
 # Produce model predictions using some arbitrary parameters
-sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
+sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
 d_SFO_SFO_SFO <- mkinpredict(m_SFO_SFO_SFO,
-  c(k_parent = 0.03,
-    f_parent_to_M1 = 0.5, k_M1 = log(2)/100,
-    f_M1_to_M2 = 0.9, k_M2 = log(2)/50),
-  c(parent = 100, M1 = 0, M2 = 0),
+  c(k_parent = 0.03,
+    f_parent_to_M1 = 0.5, k_M1 = log(2)/100,
+    f_M1_to_M2 = 0.9, k_M2 = log(2)/50),
+  c(parent = 100, M1 = 0, M2 = 0),
   sampling_times)
 
 # Generate a dataset by adding normally distributed errors with
@@ -143,31 +145,31 @@
 f_SFO_SFO_SFO <- mkinfit(m_SFO_SFO_SFO, d_SFO_SFO_SFO_err[[1]], quiet = TRUE)
 
 # Plot the results separately for parent and metabolites
-plot_sep(f_SFO_SFO_SFO, lpos = c("topright", "bottomright", "bottomright"))


+plot_sep(f_SFO_SFO_SFO, lpos = c("topright", "bottomright", "bottomright"))

-Background

Background +

The mkin package (Ranke 2021) implements the approach to degradation kinetics recommended in the kinetics report provided by the FOrum for Co-ordination of pesticide fate models and their USe (FOCUS Work Group on Degradation Kinetics 2006, 2014). It covers data series describing the decline of one compound, data series with transformation products (commonly termed metabolites) and data series for more than one compartment. It is possible to include back reactions. Therefore, equilibrium reactions and equilibrium partitioning can be specified, although this often leads to an overparameterisation of the model.

When the first mkin code was published in 2010, the most commonly used tools for fitting more complex kinetic degradation models to experimental data were KinGUI (Schäfer et al. 2007), a MATLAB based tool with a graphical user interface that was specifically tailored to the task and included some output as proposed by the FOCUS Kinetics Workgroup, and ModelMaker, a general purpose compartment based tool providing infrastructure for fitting dynamic simulation models based on differential equations to data.

The ‘mkin’ code was first uploaded to the BerliOS development platform. When this was taken down, the version control history was imported into the R-Forge site (see e.g. the initial commit on 11 May 2010), where the code is still being updated.

At that time, the R package FME (Flexible Modelling Environment) (Soetaert and Petzoldt 2010) was already available, and provided a good basis for developing a package specifically tailored to the task. The remaining challenge was to make it as easy as possible for the users (including the author of this vignette) to specify the system of differential equations and to include the output requested by the FOCUS guidance, such as the \(\chi^2\) error level as defined in this guidance.

Also, mkin introduced using analytical solutions for parent only kinetics for improved optimization speed. Later, Eigenvalue based solutions were introduced to mkin for the case of linear differential equations (i.e. where the FOMC or DFOP models were not used for the parent compound), greatly improving the optimization speed for these cases. This, has become somehow obsolete, as the use of compiled code described below gives even faster execution times.

The possibility to specify back-reactions and a biphasic model (SFORB) for metabolites were present in mkin from the very beginning.

-Derived software tools

Derived software tools +

Soon after the publication of mkin, two derived tools were published, namely KinGUII (developed at Bayer Crop Science) and CAKE (commissioned to Tessella by Syngenta), which added a graphical user interface (GUI), and added fitting by iteratively reweighted least squares (IRLS) and characterisation of likely parameter distributions by Markov Chain Monte Carlo (MCMC) sampling.

CAKE focuses on a smooth use experience, sacrificing some flexibility in the model definition, originally allowing only two primary metabolites in parallel. The current version 3.4 of CAKE released in May 2020 uses a scheme for up to six metabolites in a flexible arrangement and supports biphasic modelling of metabolites, but does not support back-reactions (non-instantaneous equilibria).

KinGUI offers an even more flexible widget for specifying complex kinetic models. Back-reactions (non-instantaneous equilibria) were supported early on, but until 2014, only simple first-order models could be specified for transformation products. Starting with KinGUII version 2.1, biphasic modelling of metabolites was also available in KinGUII.

A further graphical user interface (GUI) that has recently been brought to a decent degree of maturity is the browser based GUI named gmkin. Please see its documentation page and manual for further information.

A comparison of scope, usability and numerical results obtained with these tools has been recently been published by Ranke, Wöltjen, and Meinecke (2018).

-Unique features

Unique features +

Currently, the main unique features available in mkin are

the speed increase by using compiled code when a compiler is present,

The iteratively reweighted least squares fitting of different variances for each variable as introduced by Gao et al. (2011) has been available in mkin since version 0.9-22. With release 0.9.49.5, the IRLS algorithm has been complemented by direct or step-wise maximisation of the likelihood function, which makes it possible not only to fit the variance by variable error model but also a two-component error model inspired by error models developed in analytical chemistry (Ranke and Meinecke 2019).

-Internal parameter transformations

Internal parameter transformations +

For rate constants, the log transformation is used, as proposed by Bates and Watts (1988, 77, 149). Approximate intervals are constructed for the transformed rate constants (compare Bates and Watts 1988, 135), i.e. for their logarithms. Confidence intervals for the rate constants are then obtained using the appropriate backtransformation using the exponential function.

In the first version of mkin allowing for specifying models using formation fractions, a home-made reparameterisation was used in order to ensure that the sum of formation fractions would not exceed unity.

This method is still used in the current version of KinGUII (v2.1 from April 2014), with a modification that allows for fixing the pathway to sink to zero. CAKE uses penalties in the objective function in order to enforce this constraint.

In 2012, an alternative reparameterisation of the formation fractions was proposed together with René Lehmann (Ranke and Lehmann 2012), based on isometric logratio transformation (ILR). The aim was to improve the validity of the linear approximation of the objective function during the parameter estimation procedure as well as in the subsequent calculation of parameter confidence intervals. In the current version of mkin, a logit transformation is used for parameters that are bound between 0 and 1, such as the g parameter of the DFOP model.

-Confidence intervals based on transformed parameters

Confidence intervals based on transformed parameters +

In the first attempt at providing improved parameter confidence intervals introduced to mkin in 2013, confidence intervals obtained from FME on the transformed parameters were simply all backtransformed one by one to yield asymmetric confidence intervals for the backtransformed parameters.

However, while there is a 1:1 relation between the rate constants in the model and the transformed parameters fitted in the model, the parameters obtained by the isometric logratio transformation are calculated from the set of formation fractions that quantify the paths to each of the compounds formed from a specific parent compound, and no such 1:1 relation exists.

Therefore, parameter confidence intervals for formation fractions obtained with this method only appear valid for the case of a single transformation product, where currently the logit transformation is used for the formation fraction.

The confidence intervals obtained by backtransformation for the cases where a 1:1 relation between transformed and original parameter exist are considered by the author of this vignette to be more accurate than those obtained using a re-estimation of the Hessian matrix after backtransformation, as implemented in the FME package.

-Parameter t-test based on untransformed parameters

Parameter t-test based on untransformed parameters +

The standard output of many nonlinear regression software packages includes the results from a test for significant difference from zero for all parameters. Such a test is also recommended to check the validity of rate constants in the FOCUS guidance (FOCUS Work Group on Degradation Kinetics 2014, 96ff).

It has been argued that the precondition for this test, i.e. normal distribution of the estimator for the parameters, is not fulfilled in the case of nonlinear regression (Ranke and Lehmann 2015). However, this test is commonly used by industry, consultants and national authorities in order to decide on the reliability of parameter estimates, based on the FOCUS guidance mentioned above. Therefore, the results of this one-sided t-test are included in the summary output from mkin.

As it is not reasonable to test for significant difference of the transformed parameters (e.g. \(log(k)\)) from zero, the t-test is calculated based on the model definition before parameter transformation, i.e. in a similar way as in packages that do not apply such an internal parameter transformation. A note is included in the mkin output, pointing to the fact that the t-test is based on the unjustified assumption of normal distribution of the parameter estimators.

-References

References +

Bates, D., and D. Watts. 1988. Nonlinear Regression and Its Applications. Wiley-Interscience.

FOCUS Work Group on Degradation Kinetics. 2006. Guidance Document on Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration. Report of the Focus Work Group on Degradation Kinetics. http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics.

———. 2014. Generic Guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration. 1.1 ed. http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics.

Gao, Z., J. W. Green, J. Vanderborght, and W. Schmitt. 2011. “Improving Uncertainty Analysis in Kinetic Evaluations Using Iteratively Reweighted Least Squares.” Journal. Environmental Science and Technology 45: 4429–37.

Ranke, J. 2021. ‘mkin‘: Kinetic Evaluation of Chemical Degradation Data. https://CRAN.R-project.org/package=mkin.

Ranke, J., and R. Lehmann. 2012. “Parameter Reliability in Kinetic Evaluation of Environmental Metabolism Data - Assessment and the Influence of Model Specification.” In SETAC World 20-24 May. Berlin.

———. 2015. “To T-Test or Not to T-Test, That Is the Question.” In XV Symposium on Pesticide Chemistry 2-4 September 2015. Piacenza. http://chem.uft.uni-bremen.de/ranke/posters/piacenza_2015.pdf.

Ranke, Johannes, and Stefan Meinecke. 2019. “Error Models for the Kinetic Evaluation of Chemical Degradation Data.” Environments 6 (12). https://doi.org/10.3390/environments6120124.

Ranke, Johannes, Janina Wöltjen, and Stefan Meinecke. 2018. “Comparison of Software Tools for Kinetic Evaluation of Chemical Degradation Data.” Environmental Sciences Europe 30 (1): 17. https://doi.org/10.1186/s12302-018-0145-1.

Schäfer, D., B. Mikolasch, P. Rainbird, and B. Harvey. 2007. “KinGUI: A New Kinetic Software Tool for Evaluations According to FOCUS Degradation Kinetics.” In Proceedings of the Xiii Symposium Pesticide Chemistry, edited by Del Re A. A. M., Capri E., Fragoulis G., and Trevisan M., 916–23. Piacenza.

Soetaert, Karline, and Thomas Petzoldt. 2010. “Inverse Modelling, Sensitivity and Monte Carlo Analysis in R Using Package FME.” Journal of Statistical Software 33 (3): 1–28. https://www.jstatsoft.org/v33/i03/.

@@ -254,11 +256,13 @@ @@ -267,5 +271,7 @@ + + diff --git a/docs/dev/articles/mkin_files/figure-html/unnamed-chunk-2-1.png b/docs/dev/articles/mkin_files/figure-html/unnamed-chunk-2-1.png index bf38fdd7..63246387 100644 Binary files a/docs/dev/articles/mkin_files/figure-html/unnamed-chunk-2-1.png and b/docs/dev/articles/mkin_files/figure-html/unnamed-chunk-2-1.png differ diff --git a/docs/dev/articles/web_only/dimethenamid_2018.html b/docs/dev/articles/web_only/dimethenamid_2018.html index a2ea5c8d..6b5c8c4e 100644 --- a/docs/dev/articles/web_only/dimethenamid_2018.html +++ b/docs/dev/articles/web_only/dimethenamid_2018.html @@ -20,6 +20,8 @@ + +

Wissenschaftlicher Berater, Kronacher Str. 12, 79639 Grenzach-Wyhlen, Germany

-Introduction

Wissenschaftlicher Berater, Kronacher Str. 12, 79639 Grenzach-Wyhlen, Germany

Introduction +

During the preparation of the journal article on nonlinear mixed-effects models in degradation kinetics (Ranke et al. 2021) and the analysis of the dimethenamid degradation data analysed therein, a need for a more detailed analysis using not only nlme and saemix, but also nlmixr for fitting the mixed-effects models was identified, as many model variants do not converge when fitted with nlme, and not all relevant error models can be fitted with saemix.

This vignette is an attempt to satisfy this need.

-Data

Residue data forming the basis for the endpoints derived in the conclusion on the peer review of the pesticide risk assessment of dimethenamid-P published by the European Food Safety Authority (EFSA) in 2018 (EFSA 2018) were transcribed from the risk assessment report (Rapporteur Member State Germany, Co-Rapporteur Member State Bulgaria 2018) which can be downloaded from the Open EFSA repository https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716.

Data +

The data are available in the mkin package. The following code (hidden by default, please use the button to the right to show it) treats the data available for the racemic mixture dimethenamid (DMTA) and its enantiomer dimethenamid-P (DMTAP) in the same way, as no difference between their degradation behaviour was identified in the EU risk assessment. The observation times of each dataset are multiplied with the corresponding normalisation factor also available in the dataset, in order to make it possible to describe all datasets with a single set of parameters.

Also, datasets observed in the same soil are merged, resulting in dimethenamid (DMTA) data from six soils.

-library(mkin, quietly = TRUE)
-dmta_ds <- lapply(1:7, function(i) {
+library(mkin, quietly = TRUE)
+dmta_ds <- lapply(1:7, function(i) {
   ds_i <- dimethenamid_2018$ds[[i]]$data
   ds_i[ds_i$name == "DMTAP", "name"] <-  "DMTA"
   ds_i$time <- ds_i$time * dimethenamid_2018$f_time_norm[i]
   ds_i
 })
-names(dmta_ds) <- sapply(dimethenamid_2018$ds, function(ds) ds$title)
-dmta_ds[["Elliot"]] <- rbind(dmta_ds[["Elliot 1"]], dmta_ds[["Elliot 2"]])
+names(dmta_ds) <- sapply(dimethenamid_2018$ds, function(ds) ds$title)
+dmta_ds[["Elliot"]] <- rbind(dmta_ds[["Elliot 1"]], dmta_ds[["Elliot 2"]])
 dmta_ds[["Elliot 1"]] <- NULL
 dmta_ds[["Elliot 2"]] <- NULL


-
-
-Parent degradation
+
+Parent degradation
+
 We evaluate the observed degradation of the parent compound using simple exponential decline (SFO) and biexponential decline (DFOP), using constant variance (const) and a two-component variance (tc) as error models.
-
-
-Separate evaluations
+
+Separate evaluations
+
 As a first step, to get a visual impression of the fit of the different models, we do separate evaluations for each soil using the mmkin function from the mkin package:
 -f_parent_mkin_const <- mmkin(c("SFO", "DFOP"), dmta_ds,
+f_parent_mkin_const <- mmkin(c("SFO", "DFOP"), dmta_ds,
   error_model = "const", quiet = TRUE)
-f_parent_mkin_tc <- mmkin(c("SFO", "DFOP"), dmta_ds,
+f_parent_mkin_tc <- mmkin(c("SFO", "DFOP"), dmta_ds,
   error_model = "tc", quiet = TRUE)

 The plot of the individual SFO fits shown below suggests that at least in some datasets the degradation slows down towards later time points, and that the scatter of the residuals error is smaller for smaller values (panel to the right):
 -plot(mixed(f_parent_mkin_const["SFO", ]))
+plot(mixed(f_parent_mkin_const["SFO", ]))

 
 Using biexponential decline (DFOP) results in a slightly more random scatter of the residuals:
 -plot(mixed(f_parent_mkin_const["DFOP", ]))
+plot(mixed(f_parent_mkin_const["DFOP", ]))

 
 The population curve (bold line) in the above plot results from taking the mean of the individual transformed parameters, i.e. of log k1 and log k2, as well as of the logit of the g parameter of the DFOP model). Here, this procedure does not result in parameters that represent the degradation well, because in some datasets the fitted value for k2 is extremely close to zero, leading to a log k2 value that dominates the average. This is alleviated if only rate constants that pass the t-test for significant difference from zero (on the untransformed scale) are considered in the averaging:
 -plot(mixed(f_parent_mkin_const["DFOP", ]), test_log_parms = TRUE)
+plot(mixed(f_parent_mkin_const["DFOP", ]), test_log_parms = TRUE)

 
 While this is visually much more satisfactory, such an average procedure could introduce a bias, as not all results from the individual fits enter the population curve with the same weight. This is where nonlinear mixed-effects models can help out by treating all datasets with equally by fitting a parameter distribution model together with the degradation model and the error model (see below).
 The remaining trend of the residuals to be higher for higher predicted residues is reduced by using the two-component error model:
 -plot(mixed(f_parent_mkin_tc["DFOP", ]), test_log_parms = TRUE)
+plot(mixed(f_parent_mkin_tc["DFOP", ]), test_log_parms = TRUE)

 
+However, note that in the case of using this error model, the fits to the Flaach and BBA 2.3 datasets appear to be ill-defined, indicated by the fact that they did not converge:
++print(f_parent_mkin_tc["DFOP", ])
+<mmkin> object
+Status of individual fits:
+
+      dataset
+model  Calke Borstel Flaach BBA 2.2 BBA 2.3 Elliot
+  DFOP OK    OK      C      OK      C       OK    
+
+OK: No warnings
+C: Optimisation did not converge:
+iteration limit reached without convergence (10)


-
-
-Nonlinear mixed-effects models
+
+Nonlinear mixed-effects models
+
 Instead of taking a model selection decision for each of the individual fits, we fit nonlinear mixed-effects models (using different fitting algorithms as implemented in different packages) and do model selection using all available data at the same time. In order to make sure that these decisions are not unduly influenced by the type of algorithm used, by implementation details or by the use of wrong control parameters, we compare the model selection results obtained with different R packages, with different algorithms and checking control parameters.
-
-
-nlme
+
+nlme
+
 The nlme package was the first R extension providing facilities to fit nonlinear mixed-effects models. We would like to do model selection from all four combinations of degradation models and error models based on the AIC. However, fitting the DFOP model with constant variance and using default control parameters results in an error, signalling that the maximum number of 50 iterations was reached, potentially indicating overparameterisation. Nevertheless, the algorithm converges when the two-component error model is used in combination with the DFOP model. This can be explained by the fact that the smaller residues observed at later sampling times get more weight when using the two-component error model which will counteract the tendency of the algorithm to try parameter combinations unsuitable for fitting these data.
--library(nlme)
-f_parent_nlme_sfo_const <- nlme(f_parent_mkin_const["SFO", ])
++library(nlme)
+f_parent_nlme_sfo_const <- nlme(f_parent_mkin_const["SFO", ])
 # f_parent_nlme_dfop_const <- nlme(f_parent_mkin_const["DFOP", ])
-f_parent_nlme_sfo_tc <- nlme(f_parent_mkin_tc["SFO", ])
-f_parent_nlme_dfop_tc <- nlme(f_parent_mkin_tc["DFOP", ])
+f_parent_nlme_sfo_tc <- nlme(f_parent_mkin_tc["SFO", ])
+f_parent_nlme_dfop_tc <- nlme(f_parent_mkin_tc["DFOP", ])
 Note that a certain degree of overparameterisation is also indicated by a warning obtained when fitting DFOP with the two-component error model (‘false convergence’ in the ‘LME step’ in iteration 3). However, as this warning does not occur in later iterations, and specifically not in the last of the 6 iterations, we can ignore this warning.
 The model comparison function of the nlme package can directly be applied to these fits showing a much lower AIC for the DFOP model fitted with the two-component error model. Also, the likelihood ratio test indicates that this difference is significant as the p-value is below 0.0001.
--anova(
++anova(
   f_parent_nlme_sfo_const, f_parent_nlme_sfo_tc, f_parent_nlme_dfop_tc
 )
                         Model df    AIC    BIC  logLik   Test L.Ratio p-value
@@ -192,227 +207,215 @@ f_parent_nlme_sfo_const     1  5 796.60 811.82 -393.30
 f_parent_nlme_sfo_tc        2  6 798.60 816.86 -393.30 1 vs 2    0.00   0.998
 f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
 In addition to these fits, attempts were also made to include correlations between random effects by using the log Cholesky parameterisation of the matrix specifying them. The code used for these attempts can be made visible below.
--f_parent_nlme_sfo_const_logchol <- nlme(f_parent_mkin_const["SFO", ],
-  random = nlme::pdLogChol(list(DMTA_0 ~ 1, log_k_DMTA ~ 1)))
-anova(f_parent_nlme_sfo_const, f_parent_nlme_sfo_const_logchol)
-f_parent_nlme_sfo_tc_logchol <- nlme(f_parent_mkin_tc["SFO", ],
-  random = nlme::pdLogChol(list(DMTA_0 ~ 1, log_k_DMTA ~ 1)))
-anova(f_parent_nlme_sfo_tc, f_parent_nlme_sfo_tc_logchol)
-f_parent_nlme_dfop_tc_logchol <- nlme(f_parent_mkin_const["DFOP", ],
-  random = nlme::pdLogChol(list(DMTA_0 ~ 1, log_k1 ~ 1, log_k2 ~ 1, g_qlogis ~ 1)))
-anova(f_parent_nlme_dfop_tc, f_parent_nlme_dfop_tc_logchol)
++f_parent_nlme_sfo_const_logchol <- nlme(f_parent_mkin_const["SFO", ],
+  random = nlme::pdLogChol(list(DMTA_0 ~ 1, log_k_DMTA ~ 1)))
+anova(f_parent_nlme_sfo_const, f_parent_nlme_sfo_const_logchol)
+f_parent_nlme_sfo_tc_logchol <- nlme(f_parent_mkin_tc["SFO", ],
+  random = nlme::pdLogChol(list(DMTA_0 ~ 1, log_k_DMTA ~ 1)))
+anova(f_parent_nlme_sfo_tc, f_parent_nlme_sfo_tc_logchol)
+f_parent_nlme_dfop_tc_logchol <- nlme(f_parent_mkin_const["DFOP", ],
+  random = nlme::pdLogChol(list(DMTA_0 ~ 1, log_k1 ~ 1, log_k2 ~ 1, g_qlogis ~ 1)))
+anova(f_parent_nlme_dfop_tc, f_parent_nlme_dfop_tc_logchol)
 While the SFO variants converge fast, the additional parameters introduced by this lead to convergence warnings for the DFOP model. The model comparison clearly show that adding correlations between random effects does not improve the fits.
 The selected model (DFOP with two-component error) fitted to the data assuming no correlations between random effects is shown below.
--plot(f_parent_nlme_dfop_tc)
++plot(f_parent_nlme_dfop_tc)
 
 

-
-
-saemix
+
+saemix
+
 The saemix package provided the first Open Source implementation of the Stochastic Approximation to the Expectation Maximisation (SAEM) algorithm. SAEM fits of degradation models can be conveniently performed using an interface to the saemix package available in current development versions of the mkin package.
 The corresponding SAEM fits of the four combinations of degradation and error models are fitted below. As there is no convergence criterion implemented in the saemix package, the convergence plots need to be manually checked for every fit. As we will compare the SAEM implementation of saemix to the results obtained using the nlmixr package later, we define control settings that work well for all the parent data fits shown in this vignette.
--library(saemix)
-saemix_control <- saemixControl(nbiter.saemix = c(800, 300), nb.chains = 15,
++library(saemix)
+saemix_control <- saemixControl(nbiter.saemix = c(800, 300), nb.chains = 15,
     print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
-saemix_control_moreiter <- saemixControl(nbiter.saemix = c(1600, 300), nb.chains = 15,
+saemix_control_moreiter <- saemixControl(nbiter.saemix = c(1600, 300), nb.chains = 15,
+    print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
+saemix_control_10k <- saemixControl(nbiter.saemix = c(10000, 300), nb.chains = 15,
     print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
 The convergence plot for the SFO model using constant variance is shown below.
-+ f_parent_saemix_sfo_const <- mkin::saem(f_parent_mkin_const["SFO", ], quiet = TRUE,
   control = saemix_control, transformations = "saemix")
-plot(f_parent_saemix_sfo_const$so, plot.type = "convergence")
+plot(f_parent_saemix_sfo_const$so, plot.type = "convergence")
 
 Obviously the default number of iterations is sufficient to reach convergence. This can also be said for the SFO fit using the two-component error model.
-+ f_parent_saemix_sfo_tc <- mkin::saem(f_parent_mkin_tc["SFO", ], quiet = TRUE,
   control = saemix_control, transformations = "saemix")
-plot(f_parent_saemix_sfo_tc$so, plot.type = "convergence")
+plot(f_parent_saemix_sfo_tc$so, plot.type = "convergence")
 
 When fitting the DFOP model with constant variance (see below), parameter convergence is not as unambiguous.
-+ f_parent_saemix_dfop_const <- mkin::saem(f_parent_mkin_const["DFOP", ], quiet = TRUE,
   control = saemix_control, transformations = "saemix")
-plot(f_parent_saemix_dfop_const$so, plot.type = "convergence")
+plot(f_parent_saemix_dfop_const$so, plot.type = "convergence")
 
 This is improved when the DFOP model is fitted with the two-component error model. Convergence of the variance of k2 is enhanced, it remains more or less stable already after 200 iterations of the first phase.
-+ f_parent_saemix_dfop_tc <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
   control = saemix_control, transformations = "saemix")
-plot(f_parent_saemix_dfop_tc$so, plot.type = "convergence")
-
--# The last time I tried (2022-01-11) this gives an error in solve.default(omega.eta)
-# system is computationally singular: reciprocal condition number = 5e-17
-#f_parent_saemix_dfop_tc_10k <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
-#  control = saemix_control_10k, transformations = "saemix")
-# Now we do not get a significant improvement by using twice the number of iterations
 f_parent_saemix_dfop_tc_moreiter <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
   control = saemix_control_moreiter, transformations = "saemix")
-#plot(f_parent_saemix_dfop_tc_moreiter$so, plot.type = "convergence")
-An alternative way to fit DFOP in combination with the two-component error model is to use the model formulation with transformed parameters as used per default in mkin.
--f_parent_saemix_dfop_tc_mkin <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
-  control = saemix_control, transformations = "mkin")
-plot(f_parent_saemix_dfop_tc_mkin$so, plot.type = "convergence")
- As the convergence plots do not clearly indicate that the algorithm has converged, we again use four times the number of iterations, which leads to almost satisfactory convergence (see below).
+plot(f_parent_saemix_dfop_tc$so, plot.type = "convergence")
+
+Doubling the number of iterations in the first phase of the algorithm leads to a slightly lower likelihood, and therefore to slightly higher AIC and BIC values. With even more iterations, the algorithm stops with an error message. This is related to the variance of k2 approximating zero. This has been submitted as a bug to the saemix package, as the algorithm does not converge in this case.
+An alternative way to fit DFOP in combination with the two-component error model is to use the model formulation with transformed parameters as used per default in mkin. When using this option, convergence is slower, but eventually the algorithm stops as well with the same error message.
+The four combinations (SFO/const, SFO/tc, DFOP/const and DFOP/tc) and the version with increased iterations can be compared using the model comparison function of the saemix package:
 -saemix_control_muchmoreiter <- saemixControl(nbiter.saemix = c(3200, 300), nb.chains = 15,
-    print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
-f_parent_saemix_dfop_tc_mkin_muchmoreiter <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
-  control = saemix_control_muchmoreiter, transformations = "mkin")
-plot(f_parent_saemix_dfop_tc_mkin_muchmoreiter$so, plot.type = "convergence")
-
-The four combinations (SFO/const, SFO/tc, DFOP/const and DFOP/tc), including the variations of the DFOP/tc combination can be compared using the model comparison function of the saemix package:
--AIC_parent_saemix <- saemix::compare.saemix(
+AIC_parent_saemix <- saemix::compare.saemix(
   f_parent_saemix_sfo_const$so,
   f_parent_saemix_sfo_tc$so,
   f_parent_saemix_dfop_const$so,
   f_parent_saemix_dfop_tc$so,
-  f_parent_saemix_dfop_tc_moreiter$so,
-  f_parent_saemix_dfop_tc_mkin$so,
-  f_parent_saemix_dfop_tc_mkin_muchmoreiter$so)

+  f_parent_saemix_dfop_tc_moreiter$so)
 Likelihoods calculated by importance sampling
--rownames(AIC_parent_saemix) <- c(
-  "SFO const", "SFO tc", "DFOP const", "DFOP tc", "DFOP tc more iterations",
-  "DFOP tc mkintrans", "DFOP tc mkintrans more iterations")
-print(AIC_parent_saemix)
-                                     AIC    BIC
-SFO const                         796.38 795.34
-SFO tc                            798.38 797.13
-DFOP const                        705.75 703.88
-DFOP tc                           665.65 663.57
-DFOP tc more iterations           665.88 663.80
-DFOP tc mkintrans                 674.02 671.94
-DFOP tc mkintrans more iterations 667.94 665.86
-As in the case of nlme fits, the DFOP model fitted with two-component error (number 4) gives the lowest AIC. Using a much larger number of iterations does not significantly change the AIC. When the mkin transformations are used instead of the saemix transformations, we need four times the number of iterations to obtain a goodness of fit that almost as good as the result obtained with saemix transformations.
++rownames(AIC_parent_saemix) <- c(
+  "SFO const", "SFO tc", "DFOP const", "DFOP tc", "DFOP tc more iterations")
+print(AIC_parent_saemix)
+                           AIC    BIC
+SFO const               796.38 795.34
+SFO tc                  798.38 797.13
+DFOP const              705.75 703.88
+DFOP tc                 665.65 663.57
+DFOP tc more iterations 665.88 663.80
 In order to check the influence of the likelihood calculation algorithms implemented in saemix, the likelihood from Gaussian quadrature is added to the best fit, and the AIC values obtained from the three methods are compared.
-+ f_parent_saemix_dfop_tc$so <-
-  saemix::llgq.saemix(f_parent_saemix_dfop_tc$so)
-AIC_parent_saemix_methods <- c(
-  is = AIC(f_parent_saemix_dfop_tc$so, method = "is"),
-  gq = AIC(f_parent_saemix_dfop_tc$so, method = "gq"),
-  lin = AIC(f_parent_saemix_dfop_tc$so, method = "lin")
+  saemix::llgq.saemix(f_parent_saemix_dfop_tc$so)
+AIC_parent_saemix_methods <- c(
+  is = AIC(f_parent_saemix_dfop_tc$so, method = "is"),
+  gq = AIC(f_parent_saemix_dfop_tc$so, method = "gq"),
+  lin = AIC(f_parent_saemix_dfop_tc$so, method = "lin")
 )
-print(AIC_parent_saemix_methods)
+print(AIC_parent_saemix_methods)
     is     gq    lin 
 665.65 665.68 665.11 
-The AIC values based on importance sampling and Gaussian quadrature are very similar. Using linearisation is known to be less accurate, but still gives a similar value.
+The AIC values based on importance sampling and Gaussian quadrature are very similar. Using linearisation is known to be less accurate, but still gives a similar value. In order to illustrate that the comparison of the three method depends on the degree of convergence obtained in the fit, the same comparison is shown below for the fit using the defaults for the number of iterations and the number of MCMC chains.
++f_parent_saemix_dfop_tc_defaults <- mkin::saem(f_parent_mkin_tc["DFOP", ])
+f_parent_saemix_dfop_tc_defaults$so <-
+  saemix::llgq.saemix(f_parent_saemix_dfop_tc_defaults$so)
+AIC_parent_saemix_methods_defaults <- c(
+  is = AIC(f_parent_saemix_dfop_tc_defaults$so, method = "is"),
+  gq = AIC(f_parent_saemix_dfop_tc_defaults$so, method = "gq"),
+  lin = AIC(f_parent_saemix_dfop_tc_defaults$so, method = "lin")
+)
+print(AIC_parent_saemix_methods_defaults)
+    is     gq    lin 
+668.27 718.36 666.49 
 
-
-
-nlmixr
+
+nlmixr
+
 In the last years, a lot of effort has been put into the nlmixr package which is designed for pharmacokinetics, where nonlinear mixed-effects models are routinely used, but which can also be used for related data like chemical degradation data. A current development branch of the mkin package provides an interface between mkin and nlmixr. Here, we check if we get equivalent results when using a refined version of the First Order Conditional Estimation (FOCE) algorithm used in nlme, namely the First Order Conditional Estimation with Interaction (FOCEI), and the SAEM algorithm as implemented in nlmixr.
-First, the focei algorithm is used for the four model combinations. A number of warnings are produced with unclear significance.
--library(nlmixr)
-f_parent_nlmixr_focei_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "focei")
-f_parent_nlmixr_focei_sfo_tc <- nlmixr(f_parent_mkin_tc["SFO", ], est = "focei")
-f_parent_nlmixr_focei_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "focei")
-f_parent_nlmixr_focei_dfop_tc<- nlmixr(f_parent_mkin_tc["DFOP", ], est = "focei")
+First, the focei algorithm is used for the four model combinations.
 -aic_nlmixr_focei <- sapply(
-  list(f_parent_nlmixr_focei_sfo_const$nm, f_parent_nlmixr_focei_sfo_tc$nm,
-    f_parent_nlmixr_focei_dfop_const$nm, f_parent_nlmixr_focei_dfop_tc$nm),
-  AIC)
-The AIC values are very close to the ones obtained with nlme which are repeated below for convenience.
+library(nlmixr)
+f_parent_nlmixr_focei_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "focei")
+f_parent_nlmixr_focei_sfo_tc <- nlmixr(f_parent_mkin_tc["SFO", ], est = "focei")
+f_parent_nlmixr_focei_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "focei")
+f_parent_nlmixr_focei_dfop_tc<- nlmixr(f_parent_mkin_tc["DFOP", ], est = "focei")
+For the SFO model with constant variance, the AIC values are the same, for the DFOP model, there are significant differences between the AIC values. These may be caused by different solutions that are found, but also by the fact that the AIC values for the nlmixr fits are calculated based on Gaussian quadrature, not on linearisation.
 -aic_nlme <- sapply(
-  list(f_parent_nlme_sfo_const, NA, f_parent_nlme_sfo_tc, f_parent_nlme_dfop_tc),
-  function(x) if (is.na(x[1])) NA else AIC(x))
-aic_nlme_nlmixr_focei <- data.frame(
-  "Degradation model" = c("SFO", "SFO", "DFOP", "DFOP"),
-  "Error model" = rep(c("constant variance", "two-component"), 2),
+aic_nlmixr_focei <- sapply(
+  list(f_parent_nlmixr_focei_sfo_const$nm, f_parent_nlmixr_focei_sfo_tc$nm,
+    f_parent_nlmixr_focei_dfop_const$nm, f_parent_nlmixr_focei_dfop_tc$nm),
+  AIC)
+aic_nlme <- sapply(
+  list(f_parent_nlme_sfo_const, NA, f_parent_nlme_sfo_tc, f_parent_nlme_dfop_tc),
+  function(x) if (is.na(x[1])) NA else AIC(x))
+aic_nlme_nlmixr_focei <- data.frame(
+  "Degradation model" = c("SFO", "SFO", "DFOP", "DFOP"),
+  "Error model" = rep(c("constant variance", "two-component"), 2),
   "AIC (nlme)" = aic_nlme,
   "AIC (nlmixr with FOCEI)" = aic_nlmixr_focei,
   check.names = FALSE
 )
-print(aic_nlme_nlmixr_focei)

+print(aic_nlme_nlmixr_focei)
   Degradation model       Error model AIC (nlme) AIC (nlmixr with FOCEI)
 1               SFO constant variance     796.60                  796.60
 2               SFO     two-component         NA                  798.64
 3              DFOP constant variance     798.60                  745.87
 4              DFOP     two-component     671.91                  740.42
-Secondly, we use the SAEM estimation routine and check the convergence plots. The control parameters also used for the saemix fits are defined beforehand.
+Secondly, we use the SAEM estimation routine and check the convergence plots. The control parameters, which were also used for the saemix fits, are defined beforehand.
 -nlmixr_saem_control_800 <- saemControl(logLik = TRUE,
+nlmixr_saem_control_800 <- saemControl(logLik = TRUE,
   nBurn = 800, nEm = 300, nmc = 15)
-nlmixr_saem_control_1000 <- saemControl(logLik = TRUE,
-  nBurn = 1000, nEm = 300, nmc = 15)
-nlmixr_saem_control_10k <- saemControl(logLik = TRUE,
+nlmixr_saem_control_moreiter <- saemControl(logLik = TRUE,
+  nBurn = 1600, nEm = 300, nmc = 15)
+nlmixr_saem_control_10k <- saemControl(logLik = TRUE,
   nBurn = 10000, nEm = 1000, nmc = 15)

 Then we fit SFO with constant variance
 -f_parent_nlmixr_saem_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "saem",
+f_parent_nlmixr_saem_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "saem",
   control = nlmixr_saem_control_800)
-traceplot(f_parent_nlmixr_saem_sfo_const$nm)

+traceplot(f_parent_nlmixr_saem_sfo_const$nm)

 
 and SFO with two-component error.
 -f_parent_nlmixr_saem_sfo_tc <- nlmixr(f_parent_mkin_tc["SFO", ], est = "saem",
+f_parent_nlmixr_saem_sfo_tc <- nlmixr(f_parent_mkin_tc["SFO", ], est = "saem",
   control = nlmixr_saem_control_800)
-traceplot(f_parent_nlmixr_saem_sfo_tc$nm)

+traceplot(f_parent_nlmixr_saem_sfo_tc$nm)

 
-For DFOP with constant variance, the convergence plots show considerable instability of the fit, which indicates overparameterisation which was already observed above for this model combination.
+For DFOP with constant variance, the convergence plots show considerable instability of the fit, which indicates overparameterisation which was already observed above for this model combination. Also note that the variance of k2 approximates zero, which was already observed in the saemix fits of the DFOP model.
 -f_parent_nlmixr_saem_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "saem",
+f_parent_nlmixr_saem_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "saem",
   control = nlmixr_saem_control_800)
-traceplot(f_parent_nlmixr_saem_dfop_const$nm)

+traceplot(f_parent_nlmixr_saem_dfop_const$nm)

 
-For DFOP with two-component error, a less erratic convergence is seen.
+For DFOP with two-component error, a less erratic convergence is seen, but the variance of k2 again approximates zero.
 -f_parent_nlmixr_saem_dfop_tc <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
+f_parent_nlmixr_saem_dfop_tc <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
   control = nlmixr_saem_control_800)
-traceplot(f_parent_nlmixr_saem_dfop_tc$nm)

+traceplot(f_parent_nlmixr_saem_dfop_tc$nm)

 
 To check if an increase in the number of iterations improves the fit, we repeat the fit with 1000 iterations for the burn in phase and 300 iterations for the second phase.
 -f_parent_nlmixr_saem_dfop_tc_1000 <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
-  control = nlmixr_saem_control_1000)
-traceplot(f_parent_nlmixr_saem_dfop_tc_1000$nm)
+f_parent_nlmixr_saem_dfop_tc_moreiter <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
+  control = nlmixr_saem_control_moreiter)
+traceplot(f_parent_nlmixr_saem_dfop_tc_moreiter$nm)

 
 Here the fit looks very similar, but we will see below that it shows a higher AIC than the fit with 800 iterations in the burn in phase. Next we choose 10 000 iterations for the burn in phase and 1000 iterations for the second phase for comparison with saemix.
 -f_parent_nlmixr_saem_dfop_tc_10k <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
+f_parent_nlmixr_saem_dfop_tc_10k <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
   control = nlmixr_saem_control_10k)
-traceplot(f_parent_nlmixr_saem_dfop_tc_10k$nm)

+traceplot(f_parent_nlmixr_saem_dfop_tc_10k$nm)


 
-In the above convergence plot, the time course of ‘eta.DMTA_0’ and ‘log_k2’ indicate a false convergence.
 The AIC values are internally calculated using Gaussian quadrature.
 -AIC(f_parent_nlmixr_saem_sfo_const$nm, f_parent_nlmixr_saem_sfo_tc$nm,
+AIC(f_parent_nlmixr_saem_sfo_const$nm, f_parent_nlmixr_saem_sfo_tc$nm,
   f_parent_nlmixr_saem_dfop_const$nm, f_parent_nlmixr_saem_dfop_tc$nm,
-  f_parent_nlmixr_saem_dfop_tc_1000$nm,
+  f_parent_nlmixr_saem_dfop_tc_moreiter$nm,
   f_parent_nlmixr_saem_dfop_tc_10k$nm)

-                                     df     AIC
-f_parent_nlmixr_saem_sfo_const$nm     5  798.71
-f_parent_nlmixr_saem_sfo_tc$nm        6  808.64
-f_parent_nlmixr_saem_dfop_const$nm    9 1995.96
-f_parent_nlmixr_saem_dfop_tc$nm      10  664.96
-f_parent_nlmixr_saem_dfop_tc_1000$nm 10  667.39
-f_parent_nlmixr_saem_dfop_tc_10k$nm  10     Inf
-We can see that again, the DFOP/tc model shows the best goodness of fit. However, increasing the number of burn-in iterations from 800 to 1000 results in a higher AIC. If we further increase the number of iterations to 10 000 (burn-in) and 1000 (second phase), the AIC cannot be calculated for the nlmixr/saem fit, supporting that the fit did not converge properly.
+                                         df     AIC
+f_parent_nlmixr_saem_sfo_const$nm         5  798.71
+f_parent_nlmixr_saem_sfo_tc$nm            6  808.64
+f_parent_nlmixr_saem_dfop_const$nm        9 1995.96
+f_parent_nlmixr_saem_dfop_tc$nm          10  664.96
+f_parent_nlmixr_saem_dfop_tc_moreiter$nm 10 4464.93
+f_parent_nlmixr_saem_dfop_tc_10k$nm      10     Inf
+We can see that again, the DFOP/tc model shows the best goodness of fit. However, increasing the number of burn-in iterations from 800 to 1600 results in a higher AIC. If we further increase the number of iterations to 10 000 (burn-in) and 1000 (second phase), the AIC cannot be calculated for the nlmixr/saem fit, confirming that this fit does not converge properly with the SAEM algorithm.


-
-
-Comparison
+
+Comparison
+
 The following table gives the AIC values obtained with the three packages using the same control parameters (800 iterations burn-in, 300 iterations second phase, 15 chains).
 -AIC_all <- data.frame(
+AIC_all <- data.frame(
   check.names = FALSE,
-  "Degradation model" = c("SFO", "SFO", "DFOP", "DFOP"),
-  "Error model" = c("const", "tc", "const", "tc"),
-  nlme = c(AIC(f_parent_nlme_sfo_const), AIC(f_parent_nlme_sfo_tc), NA, AIC(f_parent_nlme_dfop_tc)),
-  nlmixr_focei = sapply(list(f_parent_nlmixr_focei_sfo_const$nm, f_parent_nlmixr_focei_sfo_tc$nm,
+  "Degradation model" = c("SFO", "SFO", "DFOP", "DFOP"),
+  "Error model" = c("const", "tc", "const", "tc"),
+  nlme = c(AIC(f_parent_nlme_sfo_const), AIC(f_parent_nlme_sfo_tc), NA, AIC(f_parent_nlme_dfop_tc)),
+  nlmixr_focei = sapply(list(f_parent_nlmixr_focei_sfo_const$nm, f_parent_nlmixr_focei_sfo_tc$nm,
   f_parent_nlmixr_focei_dfop_const$nm, f_parent_nlmixr_focei_dfop_tc$nm), AIC),
-  saemix = sapply(list(f_parent_saemix_sfo_const$so, f_parent_saemix_sfo_tc$so,
+  saemix = sapply(list(f_parent_saemix_sfo_const$so, f_parent_saemix_sfo_tc$so,
     f_parent_saemix_dfop_const$so, f_parent_saemix_dfop_tc$so), AIC),
-  nlmixr_saem = sapply(list(f_parent_nlmixr_saem_sfo_const$nm, f_parent_nlmixr_saem_sfo_tc$nm,
+  nlmixr_saem = sapply(list(f_parent_nlmixr_saem_sfo_const$nm, f_parent_nlmixr_saem_sfo_tc$nm,
   f_parent_nlmixr_saem_dfop_const$nm, f_parent_nlmixr_saem_dfop_tc$nm), AIC)
 )
 kable(AIC_all)

@@ -460,132 +463,22 @@ f_parent_nlmixr_saem_dfop_tc_10k$nm  10     Inf
 
 
 
--intervals(f_parent_saemix_dfop_tc)
-Approximate 95% confidence intervals
-
- Fixed effects:
-            lower       est.      upper
-DMTA_0 96.3087887 98.2761715 100.243554
-k1      0.0336893  0.0643651   0.095041
-k2      0.0062993  0.0088001   0.011301
-g       0.9100426  0.9524920   0.994941
-
- Random effects:
-               lower      est.    upper
-sd(DMTA_0)   0.41868 2.0607469  3.70281
-sd(k1)       0.25611 0.5935653  0.93102
-sd(k2)     -10.29603 0.0029188 10.30187
-sd(g)        0.38083 1.0572543  1.73368
-
- 
-      lower     est.    upper
-a.1 0.86253 1.061610 1.260690
-b.1 0.02262 0.029666 0.036712
--intervals(f_parent_saemix_dfop_tc)
-Approximate 95% confidence intervals
-
- Fixed effects:
-            lower       est.      upper
-DMTA_0 96.3087887 98.2761715 100.243554
-k1      0.0336893  0.0643651   0.095041
-k2      0.0062993  0.0088001   0.011301
-g       0.9100426  0.9524920   0.994941
-
- Random effects:
-               lower      est.    upper
-sd(DMTA_0)   0.41868 2.0607469  3.70281
-sd(k1)       0.25611 0.5935653  0.93102
-sd(k2)     -10.29603 0.0029188 10.30187
-sd(g)        0.38083 1.0572543  1.73368
-
- 
-      lower     est.    upper
-a.1 0.86253 1.061610 1.260690
-b.1 0.02262 0.029666 0.036712
--intervals(f_parent_saemix_dfop_tc_mkin_muchmoreiter)
-Approximate 95% confidence intervals
-
- Fixed effects:
-            lower       est.      upper
-DMTA_0 96.3402070 98.2789378 100.217669
-k1      0.0397896  0.0641976   0.103578
-k2      0.0041987  0.0084427   0.016977
-g       0.8656257  0.9521509   0.983992
-
- Random effects:
-                lower    est.   upper
-sd(DMTA_0)    0.38907 2.01821 3.64735
-sd(log_k1)    0.25653 0.59512 0.93371
-sd(log_k2)   -0.20501 0.37610 0.95721
-sd(g_qlogis)  0.39712 1.18296 1.96879
-
- 
-       lower     est.    upper
-a.1 0.868558 1.070260 1.271963
-b.1 0.022461 0.029505 0.036548
--intervals(f_parent_nlmixr_saem_dfop_tc)
-Approximate 95% confidence intervals
-
- Fixed effects:
-            lower       est.      upper
-DMTA_0 96.3224806 98.2941093 100.265738
-k1      0.0402270  0.0648200   0.104448
-k2      0.0068547  0.0093928   0.012871
-g       0.8764066  0.9501419   0.980848
-
- Random effects:
-             lower     est. upper
-sd(DMTA_0)      NA 1.686509    NA
-sd(log_k1)      NA 0.592805    NA
-sd(log_k2)      NA 0.009766    NA
-sd(g_qlogis)    NA 1.082616    NA
-
- 
-          lower     est. upper
-sigma_low    NA 1.081677    NA
-rsd_high     NA 0.032073    NA
--intervals(f_parent_nlmixr_saem_dfop_tc_10k)
-Approximate 95% confidence intervals
-
- Fixed effects:
-            lower       est.      upper
-DMTA_0 96.2302085 98.1641090 100.098010
-k1      0.0398514  0.0643909   0.104041
-k2      0.0066292  0.0090784   0.012432
-g       0.8831478  0.9527284   0.981734
-
- Random effects:
-             lower       est. upper
-sd(DMTA_0)      NA 1.6257e+00    NA
-sd(log_k1)      NA 5.9627e-01    NA
-sd(log_k2)      NA 5.8400e-07    NA
-sd(g_qlogis)    NA 1.0676e+00    NA
-
- 
-          lower     est. upper
-sigma_low    NA 1.087722    NA
-rsd_high     NA 0.031883    NA


-
-References
+
+References
+
 
 
 
 EFSA. 2018. “Peer Review of the Pesticide Risk Assessment of the Active Substance Dimethenamid-P.” EFSA Journal 16 (4): 5211.
 
 
-Ranke, Johannes, Janina Wöltjen, Jana Schmidt, and Emmanuelle Comets. 2021. “Taking Kinetic Evaluations of Degradation Data to the Next Level with Nonlinear Mixed-Effects Models.” Environments 8 (8). https://doi.org/10.3390/environments8080071.
+Ranke, Johannes, Janina Wöltjen, Jana Schmidt, and Emmanuelle Comets. 2021. “Taking Kinetic Evaluations of Degradation Data to the Next Level with Nonlinear Mixed-Effects Models.” Environments 8 (8). https://doi.org/10.3390/environments8080071.
 
 
-Rapporteur Member State Germany, Co-Rapporteur Member State Bulgaria. 2018. “Renewal Assessment Report Dimethenamid-P Volume 3 - B.8 Environmental fate and behaviour, Rev. 2 - November 2017.” https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716.
+Rapporteur Member State Germany, Co-Rapporteur Member State Bulgaria. 2018. “Renewal Assessment Report Dimethenamid-P Volume 3 - B.8 Environmental fate and behaviour, Rev. 2 - November 2017.” https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716.
 
 
 
@@ -602,11 +495,13 @@ rsd_high     NA 0.031883    NA

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Articles

All vignettes

Introduction to mkin

Johannes Ranke

Johannes Ranke

Last change 15 February 2021 (rebuilt 2021-02-15)

Last change 15 February 2021 (rebuilt 2022-02-28)

-Abstract

Abstract +

-Background

Background +

-Derived software tools

Derived software tools +

-Unique features

Unique features +

-Internal parameter transformations

Internal parameter transformations +

-Confidence intervals based on transformed parameters

Confidence intervals based on transformed parameters +

-Parameter t-test based on untransformed parameters

Parameter t-test based on untransformed parameters +

-References

References +

Example evaluations of the dimethenamid data from 2018

Johannes Ranke

Johannes Ranke

Last change 11 January 2022, built on 11 Jan 2022

Last change 10 February 2022, built on 28 Feb 2022

-Introduction

Introduction +

-Data

Data +

-Parent degradation

Parent degradation +

-Separate evaluations

Separate evaluations +

-Nonlinear mixed-effects models

Nonlinear mixed-effects models +

-nlme

nlme +

-saemix

saemix +

-nlmixr

nlmixr +

-Comparison

Comparison +

-References

References +