From 40b78bed232798ecbeb72759cdf8d400ea35b31f Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Fri, 23 Jul 2021 13:55:34 +0200 Subject: Some example evaluations of dimethenamid data Evaluations with nlme, saemix and nlmixr are included --- DESCRIPTION | 4 +- R/dimethenamid_2018.R | 33 +- R/mkinsub.R | 5 - vignettes/references.bib | 23 +- vignettes/web_only/.build.timestamp | 0 vignettes/web_only/dimethenamid_2018.R | 66 + vignettes/web_only/dimethenamid_2018.html | 1864 ++++++++++++++++++++ vignettes/web_only/dimethenamid_2018.rmd | 374 ++++ .../figure-html/f_parent_mkin_dfop_const-1.png | Bin 0 -> 60693 bytes .../f_parent_mkin_dfop_const_test-1.png | Bin 0 -> 60929 bytes .../figure-html/f_parent_mkin_dfop_tc_test-1.png | Bin 0 -> 62234 bytes .../figure-html/f_parent_mkin_sfo_const-1.png | Bin 0 -> 58445 bytes .../f_parent_nlmixr_saem_dfop_const-1.png | Bin 0 -> 92167 bytes .../figure-html/f_parent_nlmixr_saem_dfop_tc-1.png | Bin 0 -> 76934 bytes .../f_parent_nlmixr_saem_sfo_const-1.png | Bin 0 -> 62426 bytes .../figure-html/f_parent_nlmixr_saem_sfo_tc-1.png | Bin 0 -> 70230 bytes .../figure-html/f_parent_saemix_dfop_const-1.png | Bin 0 -> 41208 bytes .../f_parent_saemix_dfop_const_moreiter-1.png | Bin 0 -> 39456 bytes .../figure-html/f_parent_saemix_dfop_tc-1.png | Bin 0 -> 31646 bytes .../f_parent_saemix_dfop_tc_moreiter-1.png | Bin 0 -> 32077 bytes .../figure-html/f_parent_saemix_sfo_const-1.png | Bin 0 -> 35758 bytes .../figure-html/f_parent_saemix_sfo_tc-1.png | Bin 0 -> 30708 bytes .../f_parent_saemix_sfo_tc_moreiter-1.png | Bin 0 -> 30416 bytes .../figure-html/plot_parent_nlme-1.png | Bin 0 -> 60491 bytes 24 files changed, 2349 insertions(+), 20 deletions(-) create mode 100644 vignettes/web_only/.build.timestamp create mode 100644 vignettes/web_only/dimethenamid_2018.R create mode 100644 vignettes/web_only/dimethenamid_2018.html create mode 100644 vignettes/web_only/dimethenamid_2018.rmd create mode 100644 vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const-1.png create mode 100644 vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const_test-1.png create mode 100644 vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_tc_test-1.png create mode 100644 vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_sfo_const-1.png create mode 100644 vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_const-1.png create mode 100644 vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_tc-1.png create mode 100644 vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_sfo_const-1.png create mode 100644 vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_sfo_tc-1.png create mode 100644 vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_const-1.png create mode 100644 vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_const_moreiter-1.png create mode 100644 vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc-1.png create mode 100644 vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_moreiter-1.png create mode 100644 vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_const-1.png create mode 100644 vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc-1.png create mode 100644 vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc_moreiter-1.png create mode 100644 vignettes/web_only/dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png diff --git a/DESCRIPTION b/DESCRIPTION index c6151839..4689cb2a 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,8 +1,8 @@ Package: mkin Type: Package Title: Kinetic Evaluation of Chemical Degradation Data -Version: 1.0.5 -Date: 2021-06-11 +Version: 1.1.0 +Date: 2021-06-23 Authors@R: c( person("Johannes", "Ranke", role = c("aut", "cre", "cph"), email = "jranke@uni-bremen.de", diff --git a/R/dimethenamid_2018.R b/R/dimethenamid_2018.R index 6e0bda0c..770649e2 100644 --- a/R/dimethenamid_2018.R +++ b/R/dimethenamid_2018.R @@ -15,7 +15,7 @@ #' @source 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 -#' \url{http://registerofquestions.efsa.europa.eu/roqFrontend/outputLoader?output=ON-5211} +#' \url{https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716} #' @examples #' print(dimethenamid_2018) #' dmta_ds <- lapply(1:8, function(i) { @@ -43,15 +43,30 @@ #' list("DFOP-SFO3+" = dfop_sfo3_plus), #' dmta_ds, quiet = TRUE, error_model = "tc") #' nlmixr_model(f_dmta_mkin_tc) -#' f_dmta_nlmixr_focei <- nlmixr(f_dmta_mkin_tc, est = "focei", -#' control = nlmixr::foceiControl(print = 500)) +#' # The focei fit takes about four minutes on my system +#' system.time( +#' f_dmta_nlmixr_focei <- nlmixr(f_dmta_mkin_tc, est = "focei", +#' control = nlmixr::foceiControl(print = 500)) +#' ) #' summary(f_dmta_nlmixr_focei) #' plot(f_dmta_nlmixr_focei) -#' # saem has a problem with this model/data combination, maybe because of the -#' # overparameterised error model, to be investigated -#' #f_dmta_nlmixr_saem <- nlmixr(f_dmta_mkin_tc, est = "saem", -#' # control = saemControl(print = 500)) -#' #summary(f_dmta_nlmixr_saem) -#' #plot(f_dmta_nlmixr_saem) +#' # Using saemix takes about 18 minutes +#' system.time( +#' f_dmta_saemix <- saem(f_dmta_mkin_tc, test_log_parms = TRUE) +#' ) +#' +#' # nlmixr with est = "saem" is pretty fast with default iteration numbers, most +#' # of the time (about 2.5 minutes) is spent for calculating the log likelihood at the end +#' # The likelihood calculated for the nlmixr fit is much lower than that found by saemix +#' # Also, the trace plot and the plot of the individual predictions is not +#' # convincing for the parent. It seems we are fitting an overparameterised +#' # model, so the result we get strongly depends on starting parameters and control settings. +#' system.time( +#' f_dmta_nlmixr_saem <- nlmixr(f_dmta_mkin_tc, est = "saem", +#' control = nlmixr::saemControl(print = 500, logLik = TRUE, nmc = 9)) +#' ) +#' traceplot(f_dmta_nlmixr_saem$nm) +#' summary(f_dmta_nlmixr_saem) +#' plot(f_dmta_nlmixr_saem) #' } "dimethenamid_2018" diff --git a/R/mkinsub.R b/R/mkinsub.R index 886f712c..93af3f16 100644 --- a/R/mkinsub.R +++ b/R/mkinsub.R @@ -1,8 +1,3 @@ -#' Function to set up a kinetic submodel for one state variable -#' -#' This is a convenience function to set up the lists used as arguments for -#' \code{\link{mkinmod}}. -#' #' @rdname mkinmod #' @param submodel Character vector of length one to specify the submodel type. #' See \code{\link{mkinmod}} for the list of allowed submodel names. diff --git a/vignettes/references.bib b/vignettes/references.bib index 18b93fd3..f7eb4692 100644 --- a/vignettes/references.bib +++ b/vignettes/references.bib @@ -1,6 +1,3 @@ -% This file was originally created with JabRef 2.7b. -% Encoding: ISO8859_1 - @BOOK{bates1988, title = {Nonlinear regression and its applications}, publisher = {Wiley-Interscience}, @@ -97,7 +94,7 @@ @Techreport{ranke2014, title = {{Prüfung und Validierung von Modellierungssoftware als Alternative zu ModelMaker 4.0}}, - author = {J. Ranke}, + author = {J. Ranke}, year = 2014, institution = {Umweltbundesamt}, volume = {Projektnummer 27452} @@ -146,3 +143,21 @@ Volume = {45}, Type = {Journal} } + + +@article{efsa_2018_dimethenamid, + author = {EFSA}, + issue = {4}, + journal = {EFSA Journal}, + pages = {5211}, + title = {Peer review of the pesticide risk assessment of the active substance dimethenamid-P}, + volume = {16}, + year = {2018} +} + +@techreport{dimethenamid_rar_2018_b8, + author = {{Rapporteur Member State Germany, Co-Rapporteur Member State Bulgaria}}, + year = {2018}, + title = {{Renewal Assessment Report Dimethenamid-P Volume 3 - B.8 Environmental fate and behaviour, Rev. 2 - November 2017}}, + url = {https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716} +} diff --git a/vignettes/web_only/.build.timestamp b/vignettes/web_only/.build.timestamp new file mode 100644 index 00000000..e69de29b diff --git a/vignettes/web_only/dimethenamid_2018.R b/vignettes/web_only/dimethenamid_2018.R new file mode 100644 index 00000000..625cceb8 --- /dev/null +++ b/vignettes/web_only/dimethenamid_2018.R @@ -0,0 +1,66 @@ +## ---- include = FALSE--------------------------------------------------------- +require(knitr) +options(digits = 5) +opts_chunk$set( + comment = "", + tidy = FALSE, + cache = TRUE +) + +## ----dimethenamid_data-------------------------------------------------------- +library(mkin) +dmta_ds <- lapply(1:8, 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[["Borstel"]] <- rbind(dmta_ds[["Borstel 1"]], dmta_ds[["Borstel 2"]]) +dmta_ds[["Borstel 1"]] <- NULL +dmta_ds[["Borstel 2"]] <- NULL +dmta_ds[["Elliot"]] <- rbind(dmta_ds[["Elliot 1"]], dmta_ds[["Elliot 2"]]) +dmta_ds[["Elliot 1"]] <- NULL +dmta_ds[["Elliot 2"]] <- NULL + +## ----f_parent_mkin------------------------------------------------------------ +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, + error_model = "tc", quiet = TRUE) + +## ----f_parent_mkin_sfo_const-------------------------------------------------- +plot(mixed(f_parent_mkin_const["SFO", ])) + +## ----f_parent_mkin_dfop_const------------------------------------------------- +plot(mixed(f_parent_mkin_const["DFOP", ])) + +## ----f_parent_mkin_dfop_const_test-------------------------------------------- +plot(mixed(f_parent_mkin_const["DFOP", ]), test_log_parms = TRUE) + +## ----f_parent_mkin_dfop_tc_test----------------------------------------------- +plot(mixed(f_parent_mkin_tc["DFOP", ]), test_log_parms = TRUE) + +## ----f_parent_nlme, warning = FALSE------------------------------------------- +f_parent_nlme_sfo_const <- nlme(f_parent_mkin_const["SFO", ]) +#f_parent_nlme_dfop_const <- nlme(f_parent_mkin_const["DFOP", ]) # error +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_logchol, warning = FALSE, eval = FALSE--------------------- +# f_parent_nlme_sfo_const_logchol <- nlme(f_parent_mkin_const["SFO", ], +# random = pdLogChol(list(DMTA_0 ~ 1, log_k_DMTA ~ 1))) +# anova(f_parent_nlme_sfo_const, f_parent_nlme_sfo_const_logchol) # not better +# f_parent_nlme_dfop_tc_logchol <- update(f_parent_nlme_dfop_tc, +# random = pdLogChol(list(DMTA_0 ~ 1, log_k1 ~ 1, log_k2 ~ 1, g_qlogis ~ 1))) +# # using log Cholesky parameterisation for random effects (nlme default) does +# # not converge and gives lots of warnings about the LME step not converging + +## ----AIC_parent_nlme---------------------------------------------------------- +anova( + f_parent_nlme_sfo_const, f_parent_nlme_sfo_tc, f_parent_nlme_dfop_tc +) + +## ----plot_parent_nlme--------------------------------------------------------- +plot(f_parent_nlme_dfop_tc) + diff --git a/vignettes/web_only/dimethenamid_2018.html b/vignettes/web_only/dimethenamid_2018.html new file mode 100644 index 00000000..e84a435c --- /dev/null +++ b/vignettes/web_only/dimethenamid_2018.html @@ -0,0 +1,1864 @@ + + + + + + + + + + + + + + +Example evaluations of the dimethenamid data from 2018 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + +
+
+
+
+
+ +
+ + + + + + + +

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

+
+

Introduction

+

During the preparation of the journal article on nonlinear mixed-effects models in degradation kinetics (submitted) 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.

+

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 EFSA register of questions.

+

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)
+dmta_ds <- lapply(1:8, 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[["Borstel"]] <- rbind(dmta_ds[["Borstel 1"]], dmta_ds[["Borstel 2"]])
+dmta_ds[["Borstel 1"]] <- NULL
+dmta_ds[["Borstel 2"]] <- NULL
+dmta_ds[["Elliot"]] <- rbind(dmta_ds[["Elliot 1"]], dmta_ds[["Elliot 2"]])
+dmta_ds[["Elliot 1"]] <- NULL
+dmta_ds[["Elliot 2"]] <- NULL
+
+
+

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

+

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,
+  error_model = "const", quiet = TRUE)
+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", ]))
+

+

Using biexponential decline (DFOP) results in a slightly more random scatter of the residuals:

+
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)
+

+

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)
+

+
+
+

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

+

The nlme package was the first R extension providing facilities to fit nonlinear mixed-effects models. We use 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. However, 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.

+
f_parent_nlme_sfo_const <- nlme(f_parent_mkin_const["SFO", ])
+#f_parent_nlme_dfop_const <- nlme(f_parent_mkin_const["DFOP", ]) # error
+f_parent_nlme_sfo_tc <- nlme(f_parent_mkin_tc["SFO", ])
+f_parent_nlme_dfop_tc <- nlme(f_parent_mkin_tc["DFOP", ])
+

Note that overparameterisation is also indicated by warnings obtained when fitting SFO or DFOP with the two-component error model (‘false convergence’ in the ‘LME step’ in some iterations). 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 = pdLogChol(list(DMTA_0 ~ 1, log_k_DMTA ~ 1)))
+anova(f_parent_nlme_sfo_const, f_parent_nlme_sfo_const_logchol) # not better
+f_parent_nlme_dfop_tc_logchol <- update(f_parent_nlme_dfop_tc,
+  random = pdLogChol(list(DMTA_0 ~ 1, log_k1 ~ 1, log_k2 ~ 1, g_qlogis ~ 1)))
+# using log Cholesky parameterisation for random effects (nlme default) does
+# not converge and gives lots of warnings about the LME step not converging
+

The model comparison function of the nlme package can directly be applied to these fits showing a similar goodness-of-fit of the SFO model, but 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(
+  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
+f_parent_nlme_sfo_const     1  5 818.63 834.00 -404.31                       
+f_parent_nlme_sfo_tc        2  6 820.61 839.06 -404.31 1 vs 2   0.014  0.9049
+f_parent_nlme_dfop_tc       3 10 687.84 718.59 -333.92 2 vs 3 140.771  <.0001
+

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)
+

+
+
+

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 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.

+

The convergence plot for the SFO model using constant variance is shown below.

+
library(saemix)
+f_parent_saemix_sfo_const <- saem(f_parent_mkin_const["SFO", ], quiet = TRUE,
+  transformations = "saemix")
+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 <- saem(f_parent_mkin_tc["SFO", ], quiet = TRUE,
+  transformations = "saemix")
+plot(f_parent_saemix_sfo_tc$so, plot.type = "convergence")
+

+

When fitting the DFOP model with constant variance, parameter convergence is not as unambiguous. Therefore, the number of iterations in the first phase of the algorithm was increased, leading to visually satisfying convergence.

+
f_parent_saemix_dfop_const <- saem(f_parent_mkin_const["DFOP", ], quiet = TRUE,
+  control = saemixControl(nbiter.saemix = c(800, 200), print = FALSE,
+    save = FALSE, save.graphs = FALSE, displayProgress = FALSE),
+  transformations = "saemix")
+plot(f_parent_saemix_dfop_const$so, plot.type = "convergence")
+

+

The same applies to the case where the DFOP model is fitted with the two-component error model.

+
f_parent_saemix_dfop_tc_moreiter <- saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
+  control = saemixControl(nbiter.saemix = c(800, 200), print = FALSE,
+    save = FALSE, save.graphs = FALSE, displayProgress = FALSE),
+  transformations = "saemix")
+plot(f_parent_saemix_dfop_tc_moreiter$so, plot.type = "convergence")
+

+

The four combinations can be compared using the model comparison function from the saemix package:

+
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)
+
Likelihoods calculated by importance sampling
+
     AIC    BIC
+1 818.37 817.33
+2 820.38 819.14
+3 725.91 724.04
+4 688.09 686.01
+

As in the case of nlme fits, the DFOP model fitted with two-component error (number 4) gives the lowest AIC. The numeric values are reasonably close to the ones obtained using nlme, considering that the algorithms for fitting the model and for the likelihood calculation are quite different.

+
+
+

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 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 and the goodness of fit of the results is compared.

+
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")
+
AIC(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)
+
                                    df    AIC
+f_parent_nlmixr_focei_sfo_const$nm   5 818.63
+f_parent_nlmixr_focei_sfo_tc$nm      6 820.61
+f_parent_nlmixr_focei_dfop_const$nm  9 728.11
+f_parent_nlmixr_focei_dfop_tc$nm    10 687.82
+

The AIC values are very close to the ones obtained with nlme.

+

Secondly, we use the SAEM estimation routine and check the convergence plots for SFO with constant variance

+
f_parent_nlmixr_saem_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "saem",
+  control = nlmixr::saemControl(logLik = TRUE))
+traceplot(f_parent_nlmixr_saem_sfo_const$nm)
+

+

for SFO with two-component error

+
f_parent_nlmixr_saem_sfo_tc <- nlmixr(f_parent_mkin_tc["SFO", ], est = "saem",
+  control = nlmixr::saemControl(logLik = TRUE))
+nlmixr::traceplot(f_parent_nlmixr_saem_sfo_tc$nm)
+

+

For DFOP with constant variance, the convergence plots show considerable instability of the fit, which can be alleviated by increasing the number of iterations and the number of parallel chains for the first phase of algorithm.

+
f_parent_nlmixr_saem_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "saem",
+  control = nlmixr::saemControl(logLik = TRUE, nBurn = 1000), nmc = 15)
+nlmixr::traceplot(f_parent_nlmixr_saem_dfop_const$nm)
+

+

For DFOP with two-component error, the same increase in iterations and parallel chains was used, but using the two-component error appears to lead to a less erratic convergence, so this may not be necessary to this degree.

+
f_parent_nlmixr_saem_dfop_tc <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
+  control = nlmixr::saemControl(logLik = TRUE, nBurn = 1000, nmc = 15))
+nlmixr::traceplot(f_parent_nlmixr_saem_dfop_tc$nm)
+

+

The AIC values are internally calculated using Gaussian quadrature. For an unknown reason, the AIC value obtained for the DFOP fit using the two-component error model is given as Infinity.

+
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)
+
                                   df    AIC
+f_parent_nlmixr_saem_sfo_const$nm   5 820.54
+f_parent_nlmixr_saem_sfo_tc$nm      6 835.26
+f_parent_nlmixr_saem_dfop_const$nm  9 850.72
+f_parent_nlmixr_saem_dfop_tc$nm    10    Inf
+
+
+
+
+

References

+ +
+
+

EFSA. 2018. “Peer Review of the Pesticide Risk Assessment of the Active Substance Dimethenamid-P.” EFSA Journal 16 (4): 5211.

+
+
+

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.

+
+
+
+ + + +
+
+ +
+ + + + + + + + + + + + + + + + + diff --git a/vignettes/web_only/dimethenamid_2018.rmd b/vignettes/web_only/dimethenamid_2018.rmd new file mode 100644 index 00000000..d3541a34 --- /dev/null +++ b/vignettes/web_only/dimethenamid_2018.rmd @@ -0,0 +1,374 @@ +--- +title: Example evaluations of the dimethenamid data from 2018 +author: Johannes Ranke +date: Last change 23 June 2021, built on `r format(Sys.Date(), format = "%d %b %Y")` +output: + html_document: + toc: true + toc_float: true + code_folding: hide + fig_retina: null +bibliography: ../references.bib +vignette: > + %\VignetteEngine{knitr::rmarkdown} + %\VignetteEncoding{UTF-8} +--- + +[Wissenschaftlicher Berater, Kronacher Str. 12, 79639 Grenzach-Wyhlen, Germany](http://www.jrwb.de)
+[Privatdozent at the University of Bremen](http://chem.uft.uni-bremen.de/ranke) + +```{r, include = FALSE} +require(knitr) +options(digits = 5) +opts_chunk$set( + comment = "", + tidy = FALSE, + cache = TRUE +) +``` + +# Introduction + +During the preparation of the journal article on nonlinear mixed-effects models in +degradation kinetics (submitted) and the analysis of the dimethenamid degradation +data analysed therein, a need for a more detailed analysis using not only nlme and saemix, +but also nlmixr for fitting the mixed-effects models was identified. + +This vignette is an attempt to satisfy this need. + +# Data + +Residue data forming the basis for the endpoints derived in the conclusion on +the peer review of the pesticide risk assessment of dimethenamid-P published by +the European Food Safety Authority (EFSA) in 2018 [@efsa_2018_dimethenamid] +were transcribed from the risk assessment report [@dimethenamid_rar_2018_b8] +which can be downloaded from the +[EFSA register of questions](https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716). + +The data are [available in the mkin +package](https://pkgdown.jrwb.de/mkin/reference/dimethenamid_2018.html). The +following code (hidden by default, please use the button to the right to show +it) treats the data available for the racemic mixture dimethenamid (DMTA) and +its enantiomer dimethenamid-P (DMTAP) in the same way, as no difference between +their degradation behaviour was identified in the EU risk assessment. The +observation times of each dataset are multiplied with the corresponding +normalisation factor also available in the dataset, in order to make it +possible to describe all datasets with a single set of parameters. + +Also, datasets observed in the same soil are merged, resulting in dimethenamid +(DMTA) data from six soils. + +```{r dimethenamid_data} +library(mkin) +dmta_ds <- lapply(1:8, function(i) { + ds_i <- dimethenamid_2018$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[["Borstel"]] <- rbind(dmta_ds[["Borstel 1"]], dmta_ds[["Borstel 2"]]) +dmta_ds[["Borstel 1"]] <- NULL +dmta_ds[["Borstel 2"]] <- NULL +dmta_ds[["Elliot"]] <- rbind(dmta_ds[["Elliot 1"]], dmta_ds[["Elliot 2"]]) +dmta_ds[["Elliot 1"]] <- NULL +dmta_ds[["Elliot 2"]] <- NULL +``` + +# 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 + +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: + +```{r f_parent_mkin} +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, + 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): + +```{r f_parent_mkin_sfo_const} +plot(mixed(f_parent_mkin_const["SFO", ])) +``` + +Using biexponential decline (DFOP) results in a slightly more random +scatter of the residuals: + +```{r f_parent_mkin_dfop_const} +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: + +```{r f_parent_mkin_dfop_const_test} +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: + +```{r f_parent_mkin_dfop_tc_test} +plot(mixed(f_parent_mkin_tc["DFOP", ]), test_log_parms = TRUE) +``` + +## 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 + +The nlme package was the first R extension providing facilities to fit nonlinear +mixed-effects models. We use 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. +However, 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. + +```{r f_parent_nlme, warning = FALSE} +f_parent_nlme_sfo_const <- nlme(f_parent_mkin_const["SFO", ]) +#f_parent_nlme_dfop_const <- nlme(f_parent_mkin_const["DFOP", ]) # error +f_parent_nlme_sfo_tc <- nlme(f_parent_mkin_tc["SFO", ]) +f_parent_nlme_dfop_tc <- nlme(f_parent_mkin_tc["DFOP", ]) +``` + +Note that overparameterisation is also indicated by warnings obtained when +fitting SFO or DFOP with the two-component error model ('false convergence' in +the 'LME step' in some iterations). 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. + +```{r f_parent_nlme_logchol, warning = FALSE, eval = FALSE} +f_parent_nlme_sfo_const_logchol <- nlme(f_parent_mkin_const["SFO", ], + random = pdLogChol(list(DMTA_0 ~ 1, log_k_DMTA ~ 1))) +anova(f_parent_nlme_sfo_const, f_parent_nlme_sfo_const_logchol) # not better +f_parent_nlme_dfop_tc_logchol <- update(f_parent_nlme_dfop_tc, + random = pdLogChol(list(DMTA_0 ~ 1, log_k1 ~ 1, log_k2 ~ 1, g_qlogis ~ 1))) +# using log Cholesky parameterisation for random effects (nlme default) does +# not converge and gives lots of warnings about the LME step not converging +``` + +The model comparison function of the nlme package can directly be applied +to these fits showing a similar goodness-of-fit of the SFO model, but 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. + +```{r AIC_parent_nlme} +anova( + f_parent_nlme_sfo_const, f_parent_nlme_sfo_tc, f_parent_nlme_dfop_tc +) +``` + +The selected model (DFOP with two-component error) fitted to the data assuming +no correlations between random effects is shown below. + +```{r plot_parent_nlme} +plot(f_parent_nlme_dfop_tc) +``` + +### 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 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. + +The convergence plot for the SFO model using constant variance is shown below. + +```{r f_parent_saemix_sfo_const, results = 'hide'} +library(saemix) +f_parent_saemix_sfo_const <- saem(f_parent_mkin_const["SFO", ], quiet = TRUE, + transformations = "saemix") +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. + +```{r f_parent_saemix_sfo_tc, results = 'hide'} +f_parent_saemix_sfo_tc <- saem(f_parent_mkin_tc["SFO", ], quiet = TRUE, + transformations = "saemix") +plot(f_parent_saemix_sfo_tc$so, plot.type = "convergence") +``` + +When fitting the DFOP model with constant variance, parameter convergence +is not as unambiguous. Therefore, the number of iterations in the first +phase of the algorithm was increased, leading to visually satisfying +convergence. + +```{r f_parent_saemix_dfop_const, results = 'hide'} +f_parent_saemix_dfop_const <- saem(f_parent_mkin_const["DFOP", ], quiet = TRUE, + control = saemixControl(nbiter.saemix = c(800, 200), print = FALSE, + save = FALSE, save.graphs = FALSE, displayProgress = FALSE), + transformations = "saemix") +plot(f_parent_saemix_dfop_const$so, plot.type = "convergence") +``` + +The same applies to the case where the DFOP model is fitted with the +two-component error model. Convergence of the variance of k2 is enhanced +by using the two-component error, it remains pretty stable already after 200 +iterations of the first phase. + +```{r f_parent_saemix_dfop_tc_moreiter, results = 'hide'} +f_parent_saemix_dfop_tc_moreiter <- saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE, + control = saemixControl(nbiter.saemix = c(800, 200), print = FALSE, + save = FALSE, save.graphs = FALSE, displayProgress = FALSE), + transformations = "saemix") +plot(f_parent_saemix_dfop_tc_moreiter$so, plot.type = "convergence") +``` + +The four combinations can be compared using the model comparison function from the +saemix package: + +```{r AIC_parent_saemix} +compare.saemix(f_parent_saemix_sfo_const$so, f_parent_saemix_sfo_tc$so, + f_parent_saemix_dfop_const$so, f_parent_saemix_dfop_tc_moreiter$so) +``` + +As in the case of nlme fits, the DFOP model fitted with two-component error +(number 4) gives the lowest AIC. The numeric values are reasonably close to +the ones obtained using nlme, considering that the algorithms for fitting the +model and for the likelihood calculation are quite different. + +In order to check the influence of the likelihood calculation algorithms +implemented in saemix, the likelihood from Gaussian quadrature is added +to the best fit, and the AIC values obtained from the three methods +are compared. + +```{r AIC_parent_saemix_methods} +f_parent_saemix_dfop_tc_moreiter$so <- + llgq.saemix(f_parent_saemix_dfop_tc_moreiter$so) +AIC(f_parent_saemix_dfop_tc_moreiter$so) +AIC(f_parent_saemix_dfop_tc_moreiter$so, method = "gq") +AIC(f_parent_saemix_dfop_tc_moreiter$so, method = "lin") +``` + +The AIC values based on importance sampling and Gaussian quadrature are quite +similar. Using linearisation is less accurate, but still gives a similar value. + + +### 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 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 and the +goodness of fit of the results is compared. + +```{r f_parent_nlmixr_focei, results = "hide", message = FALSE, warning = FALSE} +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") +``` + +```{r AIC_parent_nlmixr_focei} +AIC(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) +``` + +The AIC values are very close to the ones obtained with nlme. + +Secondly, we use the SAEM estimation routine and check the convergence plots for +SFO with constant variance + +```{r f_parent_nlmixr_saem_sfo_const, results = "hide", warning = FALSE, message = FALSE} +f_parent_nlmixr_saem_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "saem", + control = nlmixr::saemControl(logLik = TRUE)) +traceplot(f_parent_nlmixr_saem_sfo_const$nm) +``` + +for SFO with two-component error + +```{r f_parent_nlmixr_saem_sfo_tc, results = "hide", warning = FALSE, message = FALSE} +f_parent_nlmixr_saem_sfo_tc <- nlmixr(f_parent_mkin_tc["SFO", ], est = "saem", + control = nlmixr::saemControl(logLik = TRUE)) +nlmixr::traceplot(f_parent_nlmixr_saem_sfo_tc$nm) +``` + +For DFOP with constant variance, the convergence plots show considerable instability +of the fit, which can be alleviated by increasing the number of iterations and +the number of parallel chains for the first phase of algorithm. + +```{r f_parent_nlmixr_saem_dfop_const, results = "hide", warning = FALSE, message = FALSE} +f_parent_nlmixr_saem_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "saem", + control = nlmixr::saemControl(logLik = TRUE, nBurn = 1000), nmc = 15) +nlmixr::traceplot(f_parent_nlmixr_saem_dfop_const$nm) +``` + +For DFOP with two-component error, the same increase in iterations and parallel +chains was used, but using the two-component error appears to lead to a less +erratic convergence, so this may not be necessary to this degree. + + +```{r f_parent_nlmixr_saem_dfop_tc, results = "hide", warning = FALSE, message = FALSE} +f_parent_nlmixr_saem_dfop_tc <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem", + control = nlmixr::saemControl(logLik = TRUE, nBurn = 1000, nmc = 15)) +nlmixr::traceplot(f_parent_nlmixr_saem_dfop_tc$nm) +``` + +The AIC values are internally calculated using Gaussian quadrature. For an +unknown reason, the AIC value obtained for the DFOP fit using the two-component +error model is given as Infinity. + +```{r AIC_parent_nlmixr_saem} +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) +``` + + + + +# References + + diff --git a/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const-1.png b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const-1.png new file mode 100644 index 00000000..de699f30 Binary files /dev/null and b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const-1.png differ diff --git a/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const_test-1.png b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const_test-1.png new file mode 100644 index 00000000..5f752168 Binary files /dev/null and b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const_test-1.png differ diff --git a/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_tc_test-1.png b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_tc_test-1.png new file mode 100644 index 00000000..0265c22f Binary files /dev/null and b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_tc_test-1.png differ diff --git a/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_sfo_const-1.png b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_sfo_const-1.png new file mode 100644 index 00000000..9bbb57c7 Binary files /dev/null and b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_sfo_const-1.png differ diff --git a/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_const-1.png b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_const-1.png new file mode 100644 index 00000000..043a1fca Binary files /dev/null and b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_const-1.png differ diff --git a/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_tc-1.png b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_tc-1.png new file mode 100644 index 00000000..7d2aea59 Binary files /dev/null and b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_tc-1.png differ diff --git a/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_sfo_const-1.png b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_sfo_const-1.png new file mode 100644 index 00000000..032d6043 Binary files /dev/null and b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_sfo_const-1.png differ diff --git a/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_sfo_tc-1.png b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_sfo_tc-1.png new file mode 100644 index 00000000..a602715c Binary files /dev/null and b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_sfo_tc-1.png differ diff --git a/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_const-1.png b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_const-1.png new file mode 100644 index 00000000..621d34f2 Binary files /dev/null and b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_const-1.png differ diff --git a/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_const_moreiter-1.png b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_const_moreiter-1.png new file mode 100644 index 00000000..e127b354 Binary files /dev/null and b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_const_moreiter-1.png differ diff --git a/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc-1.png b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc-1.png new file mode 100644 index 00000000..ecc6ccf3 Binary files /dev/null and b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc-1.png differ diff --git a/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_moreiter-1.png b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_moreiter-1.png new file mode 100644 index 00000000..1337ea8f Binary files /dev/null and b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_moreiter-1.png differ diff --git a/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_const-1.png b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_const-1.png new file mode 100644 index 00000000..492a7888 Binary files /dev/null and b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_const-1.png differ diff --git a/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc-1.png b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc-1.png new file mode 100644 index 00000000..5e3b9c13 Binary files /dev/null and b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc-1.png differ diff --git a/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc_moreiter-1.png b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc_moreiter-1.png new file mode 100644 index 00000000..3ca2804d Binary files /dev/null and b/vignettes/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc_moreiter-1.png differ diff --git a/vignettes/web_only/dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png b/vignettes/web_only/dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png new file mode 100644 index 00000000..a48f41b2 Binary files /dev/null and b/vignettes/web_only/dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png differ -- cgit v1.2.1