+ + + + +

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.

+library(nlme)
+f_parent_nlme_sfo_const <- nlme(f_parent_mkin_const["SFO", ])
+#f_parent_nlme_dfop_const <- nlme(f_parent_mkin_const["DFOP", ])
+# maxIter = 50 reached
+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 here 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 convergence plot for the SFO model using constant variance is shown below.

+library(saemix)
+f_parent_saemix_sfo_const <- mkin::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 <- mkin::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 (see the failure of nlme with the default number of iterations above). Therefore, the number of iterations in the first phase of the algorithm was increased, leading to visually satisfying convergence.

+f_parent_saemix_dfop_const <- mkin::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 more or less stable already after 200 iterations of the first phase.

+f_parent_saemix_dfop_tc_moreiter <- mkin::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$so, f_parent_saemix_dfop_tc_moreiter$so)

Likelihoods calculated by importance sampling

     AIC    BIC
+1 818.37 817.33
+2 820.38 819.14
+3 725.91 724.04
+4 683.64 681.55

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.

+f_parent_saemix_dfop_tc_moreiter$so <-
+  llgq.saemix(f_parent_saemix_dfop_tc_moreiter$so)
+AIC(f_parent_saemix_dfop_tc_moreiter$so)

[1] 683.64

+AIC(f_parent_saemix_dfop_tc_moreiter$so, method = "gq")

[1] 683.7

+AIC(f_parent_saemix_dfop_tc_moreiter$so, method = "lin")

[1] 683.17

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.

+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")

+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 which are repeated below for convenience.

+AIC(
+  f_parent_nlme_sfo_const, f_parent_nlme_sfo_tc, f_parent_nlme_dfop_tc
+)

                        df    AIC
+f_parent_nlme_sfo_const  5 818.63
+f_parent_nlme_sfo_tc     6 820.61
+f_parent_nlme_dfop_tc   10 687.84

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))
+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)
+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))
+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$nm  9 842.84
+f_parent_nlmixr_saem_dfop_tc$nm    10 684.51

The following table gives the AIC values obtained with the three packages.

+AIC_all <- data.frame(
+  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,
+    f_parent_saemix_dfop_const$so, f_parent_saemix_dfop_tc_moreiter$so), AIC),
+  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)

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

nlme	nlmixr_focei	saemix	nlmixr_saem
818.63	818.63	818.37	820.54
820.61	820.61	820.38	835.26
NA	728.11	725.91	842.84
687.84	687.82	683.64	684.51

+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.

+ + + +

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

The remaining trend of the residuals to be higher for higher predicted residues is reduced by using the two-component error model:

@@ -205,7 +205,7 @@ 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)

+plot(f_parent_nlme_dfop_tc)

-- cgit v1.2.1 From 51fab94230e926cec690dc455964bd797a97b7c7 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Wed, 4 Aug 2021 16:37:52 +0200 Subject: Improve AIC table in vignette --- docs/dev/articles/web_only/dimethenamid_2018.html | 14 +++++++++++++- 1 file changed, 13 insertions(+), 1 deletion(-) (limited to 'docs/dev/articles/web_only/dimethenamid_2018.html') diff --git a/docs/dev/articles/web_only/dimethenamid_2018.html b/docs/dev/articles/web_only/dimethenamid_2018.html index 34d882a4..9a6d8388 100644 --- a/docs/dev/articles/web_only/dimethenamid_2018.html +++ b/docs/dev/articles/web_only/dimethenamid_2018.html @@ -101,7 +101,7 @@

Example evaluations of the dimethenamid data from 2018

Johannes Ranke

Last change 27 July 2021, built on 29 Jul 2021

Last change 4 August 2021, built on 04 Aug 2021

Source: vignettes/web_only/dimethenamid_2018.rmd

dimethenamid_2018.rmd

@@ -331,6 +331,8 @@ f_parent_nlmixr_saem_dfop_tc$nm 10 684.51

The following table gives the AIC values obtained with the three packages.

 AIC_all <- data.frame(
+  "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),
@@ -342,6 +344,8 @@ f_parent_nlmixr_saem_dfop_tc$nm    10 684.51

kable(AIC_all)

+ + @@ -349,24 +353,32 @@ f_parent_nlmixr_saem_dfop_tc$nm 10 684.51 + + + + + + + + -- cgit v1.2.1 From c41381a961263c28d60976e68923157916c78b15 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Thu, 16 Sep 2021 15:31:13 +0200 Subject: Adapt and improve the dimethenamid vignette Adapt to the corrected data and unify control parameters for saemix and nlmixr with saem. Update docs --- docs/dev/articles/web_only/dimethenamid_2018.html | 245 +++++++++++----------- 1 file changed, 127 insertions(+), 118 deletions(-) (limited to 'docs/dev/articles/web_only/dimethenamid_2018.html') diff --git a/docs/dev/articles/web_only/dimethenamid_2018.html b/docs/dev/articles/web_only/dimethenamid_2018.html index 9a6d8388..b35d8210 100644 --- a/docs/dev/articles/web_only/dimethenamid_2018.html +++ b/docs/dev/articles/web_only/dimethenamid_2018.html @@ -32,7 +32,7 @@ @@ -95,13 +95,13 @@ -

Example evaluations of the dimethenamid data from 2018

Johannes Ranke

Last change 4 August 2021, built on 04 Aug 2021

Last change 16 September 2021, built on 16 Sep 2021

Source: vignettes/web_only/dimethenamid_2018.rmd

dimethenamid_2018.rmd

@@ -110,31 +110,28 @@ -

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

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.

This vignette is an attempt to satisfy this need.

Data

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) {
+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[["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

@@ -154,20 +151,20 @@ error_model = "tc", quiet = TRUE)

-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", ]))

-plot(mixed(f_parent_mkin_const["DFOP", ]), test_log_parms = TRUE)

+plot(mixed(f_parent_mkin_const["DFOP", ]), test_log_parms = TRUE)

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)

@@ -177,175 +174,184 @@

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. 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.

 library(nlme)
 f_parent_nlme_sfo_const <- nlme(f_parent_mkin_const["SFO", ])
-#f_parent_nlme_dfop_const <- nlme(f_parent_mkin_const["DFOP", ])
-# maxIter = 50 reached
+# 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", ])

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.

-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 here and gives lots of warnings about the LME step not converging

 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

+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)

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

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

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)
-f_parent_saemix_sfo_const <- mkin::saem(f_parent_mkin_const["SFO", ], quiet = TRUE,
-  transformations = "saemix")
+saemix_control <- saemixControl(nbiter.saemix = c(800, 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")

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,
-  transformations = "saemix")
+  control = saemix_control, 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 (see the failure of nlme with the default number of iterations above). Therefore, the number of iterations in the first phase of the algorithm was increased, leading to visually satisfying convergence.
-+ f_parent_saemix_dfop_const <- mkin::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")
+  control = saemix_control, 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 more or less stable already after 200 iterations of the first phase.
--f_parent_saemix_dfop_tc_moreiter <- mkin::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$so, plot.type = "convergence")
-
-The four combinations can be compared using the model comparison function from the saemix package:
+The same applies in the case where the DFOP model is fitted with the two-component error model. Convergence of the variance of k2 is enhanced by using the two-component error, it remains more or less stable already after 200 iterations of the first phase.
 -compare.saemix(f_parent_saemix_sfo_const$so, f_parent_saemix_sfo_tc$so,
-  f_parent_saemix_dfop_const$so, f_parent_saemix_dfop_tc_moreiter$so)
+f_parent_saemix_dfop_tc <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
+  control = saemix_control, transformations = "saemix")
+plot(f_parent_saemix_dfop_tc$so, plot.type = "convergence")
+ The four combinations and including the variations of the DFOP/tc combination 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
-4 683.64 681.55
-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.
+1 796.37 795.33
+2 798.37 797.13
+3 713.16 711.28
+4 666.10 664.01

As in the case of nlme fits, the DFOP model fitted with two-component error (number 4) gives the lowest AIC. Using more iterations and/or more chains does not have a large influence on the final AIC (not shown).

-f_parent_saemix_dfop_tc_moreiter$so <-
-  llgq.saemix(f_parent_saemix_dfop_tc_moreiter$so)
-AIC(f_parent_saemix_dfop_tc_moreiter$so)

[1] 683.64

-AIC(f_parent_saemix_dfop_tc_moreiter$so, method = "gq")

[1] 683.7

-AIC(f_parent_saemix_dfop_tc_moreiter$so, method = "lin")

[1] 683.17

The AIC values based on importance sampling and Gaussian quadrature are quite similar. Using linearisation is less accurate, but still gives a similar value.

+f_parent_saemix_dfop_tc$so <-
+  llgq.saemix(f_parent_saemix_dfop_tc$so)
+AIC(f_parent_saemix_dfop_tc$so)

[1] 666.1

+AIC(f_parent_saemix_dfop_tc$so, method = "gq")

[1] 666.03

+AIC(f_parent_saemix_dfop_tc$so, method = "lin")

[1] 665.48

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.

nlmixr

First, the focei algorithm is used for the four model combinations and the goodness of fit of the results is compared.

+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")
--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
++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.
 -AIC(
-  f_parent_nlme_sfo_const, f_parent_nlme_sfo_tc, f_parent_nlme_dfop_tc
+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
 )

-                        df    AIC
-f_parent_nlme_sfo_const  5 818.63
-f_parent_nlme_sfo_tc     6 820.61
-f_parent_nlme_dfop_tc   10 687.84
-Secondly, we use the SAEM estimation routine and check the convergence plots for SFO with constant variance
+Secondly, we use the SAEM estimation routine and check the convergence plots. The control parameters also used for the saemix fits are defined beforehand.
++nlmixr_saem_control <- saemControl(logLik = TRUE,
+  nBurn = 1000, nEm = 300, nmc = 15)
+The we fit SFO with constant variance
  f_parent_nlmixr_saem_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "saem",
-  control = nlmixr::saemControl(logLik = TRUE))
+  control = nlmixr_saem_control)
 traceplot(f_parent_nlmixr_saem_sfo_const$nm)
 
-for SFO with two-component error
+and SFO with two-component error.
  f_parent_nlmixr_saem_sfo_tc <- nlmixr(f_parent_mkin_tc["SFO", ], est = "saem",
-  control = nlmixr::saemControl(logLik = TRUE))
+  control = nlmixr_saem_control)
 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.
+For DFOP with constant variance, the convergence plots show considerable instability of the fit, which indicates overparameterisation which was already observed earlier for this model combination.
  f_parent_nlmixr_saem_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "saem",
-  control = nlmixr::saemControl(logLik = TRUE, nBurn = 1000), nmc = 15)
+  control = nlmixr_saem_control)
 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.
+For DFOP with two-component error, a less erratic convergence is seen.
  f_parent_nlmixr_saem_dfop_tc <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
-  control = nlmixr::saemControl(logLik = TRUE, nBurn = 1000, nmc = 15))
+  control = nlmixr_saem_control)
 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.
+The AIC values are internally calculated using Gaussian quadrature. For an unknown reason, the AIC value obtained for the DFOP fit using constant error 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$nm  9 842.84
-f_parent_nlmixr_saem_dfop_tc$nm    10 684.51
+f_parent_nlmixr_saem_sfo_const$nm   5 798.68
+f_parent_nlmixr_saem_sfo_tc$nm      6 808.88
+f_parent_nlmixr_saem_dfop_const$nm  9 815.95
+f_parent_nlmixr_saem_dfop_tc$nm    10 669.57

The following table gives the AIC values obtained with the three packages.

 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,
   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,
-    f_parent_saemix_dfop_const$so, f_parent_saemix_dfop_tc_moreiter$so), AIC),
+    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,
   f_parent_nlmixr_saem_dfop_const$nm, f_parent_nlmixr_saem_dfop_tc$nm), AIC)
 )
 kable(AIC_all)

Degradation.model	Error.model	nlme	nlmixr_focei	saemix
SFO	const	818.63	818.63	818.37	820.54
SFO	tc	820.61	820.61	820.38	835.26
DFOP	const	NA	728.11	725.91	842.84
DFOP	tc	687.84	687.82	683.64

- - + + @@ -355,34 +361,34 @@ f_parent_nlmixr_saem_dfop_tc$nm 10 684.51 - - - - + + + + - - - - + + + + - - - + + + - - - - + + + +

Degradation.model	Error.model	Degradation model	Error model	nlme	nlmixr_focei	saemix
SFO	const	818.63	818.63	818.37	820.54	796.60	796.62	796.37	798.68
SFO	tc	820.61	820.61	820.38	835.26	798.60	798.61	798.37	808.88
DFOP	const	NA	728.11	725.91	842.84	750.91	713.16	815.95
DFOP	tc	687.84	687.82	683.64	684.51	671.91	666.60	666.10	669.57

@@ -397,6 +403,9 @@ f_parent_nlmixr_saem_dfop_tc$nm 10 684.51

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.

-- cgit v1.2.1 From 047d048b89e167fb354b45cd7c6b719b9f4cdd28 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Fri, 17 Sep 2021 08:47:09 +0200 Subject: Put the AIC comparison in a subsubsection --- docs/dev/articles/web_only/dimethenamid_2018.html | 46 ++++++++++++----------- 1 file changed, 25 insertions(+), 21 deletions(-) (limited to 'docs/dev/articles/web_only/dimethenamid_2018.html') diff --git a/docs/dev/articles/web_only/dimethenamid_2018.html b/docs/dev/articles/web_only/dimethenamid_2018.html index b35d8210..26b352e1 100644 --- a/docs/dev/articles/web_only/dimethenamid_2018.html +++ b/docs/dev/articles/web_only/dimethenamid_2018.html @@ -101,7 +101,7 @@

Example evaluations of the dimethenamid data from 2018

Johannes Ranke

Last change 16 September 2021, built on 16 Sep 2021

Last change 17 September 2021, built on 17 Sep 2021

Source: vignettes/web_only/dimethenamid_2018.rmd

dimethenamid_2018.rmd

@@ -114,7 +114,7 @@

Introduction

This vignette is an attempt to satisfy this need.

@@ -124,7 +124,7 @@

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

-library(mkin)
+library(mkin, quietly = TRUE)
 dmta_ds <- lapply(1:7, function(i) {
   ds_i <- dimethenamid_2018$ds[[i]]$data
   ds_i[ds_i$name == "DMTAP", "name"] <-  "DMTA"
@@ -258,14 +258,14 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
  f_parent_saemix_dfop_tc$so <-
   llgq.saemix(f_parent_saemix_dfop_tc$so)
-AIC(f_parent_saemix_dfop_tc$so)
-[1] 666.1
--AIC(f_parent_saemix_dfop_tc$so, method = "gq")
-[1] 666.03
--AIC(f_parent_saemix_dfop_tc$so, method = "lin")
-[1] 665.48
+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)


+    is     gq    lin 
+666.10 666.03 665.48 
 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.


 
@@ -273,19 +273,19 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
 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")
-+ 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.
-+ 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))
@@ -297,35 +297,35 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
   check.names = FALSE
 )
 Secondly, we use the SAEM estimation routine and check the convergence plots. The control parameters also used for the saemix fits are defined beforehand.
-+ nlmixr_saem_control <- saemControl(logLik = TRUE,
   nBurn = 1000, nEm = 300, nmc = 15)
 The we fit SFO with constant variance
-+ f_parent_nlmixr_saem_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "saem",
   control = nlmixr_saem_control)
 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",
   control = nlmixr_saem_control)
 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 earlier for this model combination.
-+ f_parent_nlmixr_saem_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "saem",
   control = nlmixr_saem_control)
 traceplot(f_parent_nlmixr_saem_dfop_const$nm)
 
 For DFOP with two-component error, a less erratic convergence is seen.
-+ f_parent_nlmixr_saem_dfop_tc <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
   control = nlmixr_saem_control)
 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 constant error 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
@@ -333,8 +333,12 @@ f_parent_nlmixr_saem_sfo_const$nm   5 798.68
 f_parent_nlmixr_saem_sfo_tc$nm      6 808.88
 f_parent_nlmixr_saem_dfop_const$nm  9 815.95
 f_parent_nlmixr_saem_dfop_tc$nm    10 669.57
+
+
+
+Comparison
 The following table gives the AIC values obtained with the three packages.
-+ AIC_all <- data.frame(
   check.names = FALSE,
   "Degradation model" = c("SFO", "SFO", "DFOP", "DFOP"),
-- 
cgit v1.2.1


From 5c15ef747568b3a9a9c094b6aa546dc80e3aa87a Mon Sep 17 00:00:00 2001
From: Johannes Ranke 
Date: Mon, 27 Sep 2021 20:10:01 +0200
Subject: intervals() methods, more DFOP/tc variants

---
 docs/dev/articles/web_only/dimethenamid_2018.html | 274 ++++++++++++++++++----
 1 file changed, 230 insertions(+), 44 deletions(-)

(limited to 'docs/dev/articles/web_only/dimethenamid_2018.html')

diff --git a/docs/dev/articles/web_only/dimethenamid_2018.html b/docs/dev/articles/web_only/dimethenamid_2018.html
index 26b352e1..aa84435d 100644
--- a/docs/dev/articles/web_only/dimethenamid_2018.html
+++ b/docs/dev/articles/web_only/dimethenamid_2018.html
@@ -101,7 +101,7 @@
       Example evaluations of the dimethenamid data from 2018
                         Johannes Ranke
             
-            Last change 17 September 2021, built on 17 Sep 2021
+            Last change 27 September 2021, built on 27 Sep 2021
       
       Source: vignettes/web_only/dimethenamid_2018.rmd
       dimethenamid_2018.rmd
@@ -174,7 +174,7 @@
 
 
 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. 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.
+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", ])
@@ -182,7 +182,7 @@
 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.
+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(
   f_parent_nlme_sfo_const, f_parent_nlme_sfo_tc, f_parent_nlme_dfop_tc
@@ -216,6 +216,8 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
  library(saemix)
 saemix_control <- saemixControl(nbiter.saemix = c(800, 300), nb.chains = 15,
+    print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
+saemix_control_10k <- saemixControl(nbiter.saemix = c(10000, 1000), 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.
 @@ -229,35 +231,65 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
   control = saemix_control, 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 (see the failure of nlme with the default number of iterations above). Therefore, the number of iterations in the first phase of the algorithm was increased, leading to visually satisfying 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")
 
-The same applies in 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 more or less stable already after 200 iterations of the first phase.
+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$so, plot.type = "convergence")
- The four combinations and including the variations of the DFOP/tc combination can be compared using the model comparison function from the saemix package:
+
+We also check if using many more iterations (10 000 for the first and 1000 for the second phase) improve the result in a significant way. The AIC values obtained are compared further below.
 -compare.saemix(
+f_parent_saemix_dfop_tc_10k <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
+  control = saemix_control_10k, transformations = "saemix")
+plot(f_parent_saemix_dfop_tc_10k$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$so, plot.type = "convergence")
+
+As the convergence plots do not clearly indicate that the algorithm has converged, we again use a much larger number of iterations, which leads to satisfactory convergence (see below).
++f_parent_saemix_dfop_tc_mkin_10k <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
+  control = saemix_control_10k, transformations = "mkin")
+plot(f_parent_saemix_dfop_tc_mkin_10k$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(
   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$so,
+  f_parent_saemix_dfop_tc_10k$so,
+  f_parent_saemix_dfop_tc_mkin$so,
+  f_parent_saemix_dfop_tc_mkin_10k$so)
 Likelihoods calculated by importance sampling
-     AIC    BIC
-1 796.37 795.33
-2 798.37 797.13
-3 713.16 711.28
-4 666.10 664.01
-As in the case of nlme fits, the DFOP model fitted with two-component error (number 4) gives the lowest AIC. Using more iterations and/or more chains does not have a large influence on the final AIC (not shown).
++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                         796.37 795.33
+SFO tc                            798.37 797.13
+DFOP const                        713.16 711.28
+DFOP tc                           666.10 664.01
+DFOP tc more iterations           666.15 664.06
+DFOP tc mkintrans                 682.26 680.17
+DFOP tc mkintrans more iterations 666.12 664.04
+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 improve the fit a lot. When the mkin transformations are used instead of the saemix transformations, this large number of iterations leads to a goodness of fit that is comparable to the result obtained with saemix transformations.
 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$so <-
-  llgq.saemix(f_parent_saemix_dfop_tc$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$so, method = "gq"),
@@ -273,19 +305,19 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
 nlmixr
 In the last years, a lot of effort has been put into the nlmixr package which is designed for pharmacokinetics, where nonlinear mixed-effects models are routinely used, but which can also be used for related data like chemical degradation data. A current development branch of the mkin package provides an interface between mkin and nlmixr. Here, we check if we get equivalent results when using a refined version of the First Order Conditional Estimation (FOCE) algorithm used in nlme, namely the First Order Conditional Estimation with Interaction (FOCEI), and the SAEM algorithm as implemented in nlmixr.
 First, the focei algorithm is used for the four model combinations. A number of warnings are produced with unclear significance.
-+ library(nlmixr)
 f_parent_nlmixr_focei_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "focei")
 f_parent_nlmixr_focei_sfo_tc <- nlmixr(f_parent_mkin_tc["SFO", ], est = "focei")
 f_parent_nlmixr_focei_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "focei")
 f_parent_nlmixr_focei_dfop_tc<- nlmixr(f_parent_mkin_tc["DFOP", ], est = "focei")
-+ aic_nlmixr_focei <- sapply(
   list(f_parent_nlmixr_focei_sfo_const$nm, f_parent_nlmixr_focei_sfo_tc$nm,
     f_parent_nlmixr_focei_dfop_const$nm, f_parent_nlmixr_focei_dfop_tc$nm),
   AIC)
 The AIC values are very close to the ones obtained with nlme which are repeated below for convenience.
-+ aic_nlme <- sapply(
   list(f_parent_nlme_sfo_const, NA, f_parent_nlme_sfo_tc, f_parent_nlme_dfop_tc),
   function(x) if (is.na(x[1])) NA else AIC(x))
@@ -297,48 +329,70 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
   check.names = FALSE
 )
 Secondly, we use the SAEM estimation routine and check the convergence plots. The control parameters also used for the saemix fits are defined beforehand.
--nlmixr_saem_control <- saemControl(logLik = TRUE,
-  nBurn = 1000, nEm = 300, nmc = 15)
++nlmixr_saem_control_800 <- saemControl(logLik = TRUE,
+  nBurn = 800, nEm = 300, nmc = 15)
+nlmixr_saem_control_1000 <- saemControl(logLik = TRUE,
+  nBurn = 1000, nEm = 300, nmc = 15)
+nlmixr_saem_control_10k <- saemControl(logLik = TRUE,
+  nBurn = 10000, nEm = 1000, nmc = 15)
 The we fit SFO with constant variance
-+ f_parent_nlmixr_saem_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "saem",
-  control = nlmixr_saem_control)
+  control = nlmixr_saem_control_800)
 traceplot(f_parent_nlmixr_saem_sfo_const$nm)
 
 and SFO with two-component error.
-+ f_parent_nlmixr_saem_sfo_tc <- nlmixr(f_parent_mkin_tc["SFO", ], est = "saem",
-  control = nlmixr_saem_control)
+  control = nlmixr_saem_control_800)
 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 earlier for this model combination.
-+ f_parent_nlmixr_saem_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "saem",
-  control = nlmixr_saem_control)
+  control = nlmixr_saem_control_800)
 traceplot(f_parent_nlmixr_saem_dfop_const$nm)
 
 For DFOP with two-component error, a less erratic convergence is seen.
-+ f_parent_nlmixr_saem_dfop_tc <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
-  control = nlmixr_saem_control)
+  control = nlmixr_saem_control_800)
 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 constant error is given as Infinity.
-+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$nm)
+
+Here the fit looks very similar, but we will see below that it shows a higher AIC than the fit with 800 iterations in the burn in phase. Next we choose 10 000 iterations for the burn in phase and 1000 iterations for the second phase for comparison with saemix.
++f_parent_nlmixr_saem_dfop_tc_10k <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
+  control = nlmixr_saem_control_10k)
+traceplot(f_parent_nlmixr_saem_dfop_tc_10k$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,
-  f_parent_nlmixr_saem_dfop_const$nm, f_parent_nlmixr_saem_dfop_tc$nm)
-                                   df    AIC
-f_parent_nlmixr_saem_sfo_const$nm   5 798.68
-f_parent_nlmixr_saem_sfo_tc$nm      6 808.88
-f_parent_nlmixr_saem_dfop_const$nm  9 815.95
-f_parent_nlmixr_saem_dfop_tc$nm    10 669.57
+  f_parent_nlmixr_saem_dfop_const$nm, f_parent_nlmixr_saem_dfop_tc$nm,
+  f_parent_nlmixr_saem_dfop_tc_1000$nm,
+  f_parent_nlmixr_saem_dfop_tc_10k$nm)
+                                     df    AIC
+f_parent_nlmixr_saem_sfo_const$nm     5 798.69
+f_parent_nlmixr_saem_sfo_tc$nm        6 810.33
+f_parent_nlmixr_saem_dfop_const$nm    9 736.00
+f_parent_nlmixr_saem_dfop_tc$nm      10 664.85
+f_parent_nlmixr_saem_dfop_tc_1000$nm 10 669.57
+f_parent_nlmixr_saem_dfop_tc_10k$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.
 
 
 
 Comparison
-The following table gives the AIC values obtained with the three packages.
-+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(
   check.names = FALSE,
   "Degradation model" = c("SFO", "SFO", "DFOP", "DFOP"),
@@ -368,7 +422,7 @@ f_parent_nlmixr_saem_dfop_tc$nm    10 669.57
 796.60
 796.62
 796.37
-798.68
+798.69
 
 
 SFO
@@ -376,7 +430,7 @@ f_parent_nlmixr_saem_dfop_tc$nm    10 669.57

 798.60
 798.61
 798.37
-808.88
+810.33
 
 
 DFOP
@@ -384,7 +438,7 @@ f_parent_nlmixr_saem_dfop_tc$nm    10 669.57
 NA
 750.91
 713.16
-815.95
+736.00
 
 
 DFOP
@@ -392,10 +446,142 @@ f_parent_nlmixr_saem_dfop_tc$nm    10 669.57
 671.91
 666.60
 666.10
-669.57
+664.85
 
 
 
++intervals(f_parent_saemix_dfop_tc)
+Approximate 95% confidence intervals
+
+ Fixed effects:
+            lower       est.      upper
+DMTA_0 96.2802274 98.2761977 100.272168
+k1      0.0339753  0.0645487   0.095122
+k2      0.0058977  0.0088887   0.011880
+g       0.9064373  0.9514417   0.996446
+
+ Random effects:
+              lower     est.   upper
+sd(DMTA_0)  0.44404 2.102366 3.76069
+sd(k1)      0.25433 0.589731 0.92514
+sd(k2)     -0.33139 0.099797 0.53099
+sd(g)       0.39606 1.092234 1.78841
+
+ 
+       lower     est.    upper
+a.1 0.863644 1.063021 1.262398
+b.1 0.022555 0.029599 0.036643
++intervals(f_parent_saemix_dfop_tc)
+Approximate 95% confidence intervals
+
+ Fixed effects:
+            lower       est.      upper
+DMTA_0 96.2802274 98.2761977 100.272168
+k1      0.0339753  0.0645487   0.095122
+k2      0.0058977  0.0088887   0.011880
+g       0.9064373  0.9514417   0.996446
+
+ Random effects:
+              lower     est.   upper
+sd(DMTA_0)  0.44404 2.102366 3.76069
+sd(k1)      0.25433 0.589731 0.92514
+sd(k2)     -0.33139 0.099797 0.53099
+sd(g)       0.39606 1.092234 1.78841
+
+ 
+       lower     est.    upper
+a.1 0.863644 1.063021 1.262398
+b.1 0.022555 0.029599 0.036643
++intervals(f_parent_saemix_dfop_tc_10k)
+Approximate 95% confidence intervals
+
+ Fixed effects:
+            lower       est.      upper
+DMTA_0 96.3027896 98.2641150 100.225440
+k1      0.0338214  0.0644055   0.094990
+k2      0.0058857  0.0087896   0.011693
+g       0.9086138  0.9521421   0.995670
+
+ Random effects:
+              lower    est.   upper
+sd(DMTA_0)  0.41448 2.05327 3.69206
+sd(k1)      0.25507 0.59132 0.92758
+sd(k2)     -0.36781 0.09016 0.54813
+sd(g)       0.38585 1.06994 1.75402
+
+ 
+       lower     est.    upper
+a.1 0.866273 1.066115 1.265957
+b.1 0.022501 0.029541 0.036581
++intervals(f_parent_saemix_dfop_tc_mkin_10k)
+Approximate 95% confidence intervals
+
+ Fixed effects:
+            lower       est.      upper
+DMTA_0 96.3021306 98.2736091 100.245088
+k1      0.0401701  0.0645140   0.103611
+k2      0.0064706  0.0089398   0.012351
+g       0.8817692  0.9511605   0.980716
+
+ Random effects:
+                lower     est.   upper
+sd(DMTA_0)    0.42392 2.068018 3.71212
+sd(log_k1)    0.25440 0.589877 0.92536
+sd(log_k2)   -0.38431 0.084334 0.55298
+sd(g_qlogis)  0.39107 1.077303 1.76353
+
+ 
+       lower     est.    upper
+a.1 0.865291 1.064897 1.264504
+b.1 0.022491 0.029526 0.036561
++intervals(f_parent_nlmixr_saem_dfop_tc)
+Approximate 95% confidence intervals
+
+ Fixed effects:
+            lower       est.      upper
+DMTA_0 96.3059406 98.2990616 100.292183
+k1      0.0402306  0.0648255   0.104456
+k2      0.0067864  0.0093097   0.012771
+g       0.8769017  0.9505258   0.981067
+
+ Random effects:
+             lower     est. upper
+sd(DMTA_0)      NA 1.724654    NA
+sd(log_k1)      NA 0.592808    NA
+sd(log_k2)      NA 0.010741    NA
+sd(g_qlogis)    NA 1.087349    NA
+
+ 
+          lower     est. upper
+sigma_low    NA 1.081809    NA
+rsd_high     NA 0.032051    NA
++intervals(f_parent_nlmixr_saem_dfop_tc_10k)
+Approximate 95% confidence intervals
+
+ Fixed effects:
+           lower       est.     upper
+DMTA_0 96.426510 97.8987836 99.371057
+k1      0.040006  0.0644407  0.103799
+k2      0.006748  0.0092476  0.012673
+g       0.879251  0.9511399  0.981147
+
+ Random effects:
+             lower       est. upper
+sd(DMTA_0)      NA 3.7049e-04    NA
+sd(log_k1)      NA 5.9221e-01    NA
+sd(log_k2)      NA 3.8628e-07    NA
+sd(g_qlogis)    NA 1.0694e+00    NA
+
+ 
+          lower     est. upper
+sigma_low    NA 1.082343    NA
+rsd_high     NA 0.034895    NA
 
 
 
-- 
cgit v1.2.1


From ff83d8b2ba623513d92ac90fac4a1b0ec98c2cb5 Mon Sep 17 00:00:00 2001
From: Johannes Ranke 
Date: Tue, 5 Oct 2021 17:33:52 +0200
Subject: Update docs

---
 docs/dev/articles/web_only/dimethenamid_2018.html | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

(limited to 'docs/dev/articles/web_only/dimethenamid_2018.html')

diff --git a/docs/dev/articles/web_only/dimethenamid_2018.html b/docs/dev/articles/web_only/dimethenamid_2018.html
index aa84435d..13b0f98e 100644
--- a/docs/dev/articles/web_only/dimethenamid_2018.html
+++ b/docs/dev/articles/web_only/dimethenamid_2018.html
@@ -101,7 +101,7 @@
       Example evaluations of the dimethenamid data from 2018
                         Johannes Ranke
             
-            Last change 27 September 2021, built on 27 Sep 2021
+            Last change 27 September 2021, built on 05 Okt 2021
       
       Source: vignettes/web_only/dimethenamid_2018.rmd
       dimethenamid_2018.rmd
@@ -151,20 +151,20 @@
   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)
 
 
 
@@ -205,7 +205,7 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
 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)
 
 
 
-- 
cgit v1.2.1


From c0638c84568d475b3b059e2c6e593e6f03b846bc Mon Sep 17 00:00:00 2001
From: Johannes Ranke 
Date: Tue, 11 Jan 2022 19:57:58 +0100
Subject: Update static docs

---
 docs/dev/articles/web_only/dimethenamid_2018.html | 286 +++++++++++-----------
 1 file changed, 137 insertions(+), 149 deletions(-)

(limited to 'docs/dev/articles/web_only/dimethenamid_2018.html')

diff --git a/docs/dev/articles/web_only/dimethenamid_2018.html b/docs/dev/articles/web_only/dimethenamid_2018.html
index 13b0f98e..a2ea5c8d 100644
--- a/docs/dev/articles/web_only/dimethenamid_2018.html
+++ b/docs/dev/articles/web_only/dimethenamid_2018.html
@@ -101,7 +101,7 @@
       Example evaluations of the dimethenamid data from 2018
                         Johannes Ranke
             
-            Last change 27 September 2021, built on 05 Okt 2021
+            Last change 11 January 2022, built on 11 Jan 2022
       
       Source: vignettes/web_only/dimethenamid_2018.rmd
       dimethenamid_2018.rmd
@@ -151,20 +151,20 @@
   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)
 
 
 
@@ -205,7 +205,7 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
 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)
 
 
 
@@ -217,50 +217,54 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
 library(saemix)
 saemix_control <- saemixControl(nbiter.saemix = c(800, 300), nb.chains = 15,
     print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
-saemix_control_10k <- saemixControl(nbiter.saemix = c(10000, 1000), nb.chains = 15,
+saemix_control_moreiter <- saemixControl(nbiter.saemix = c(1600, 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.

When fitting the DFOP model with constant variance (see below), parameter convergence is not as unambiguous.

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.

We also check if using many more iterations (10 000 for the first and 1000 for the second phase) improve the result in a significant way. The AIC values obtained are compared further below.

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.

As the convergence plots do not clearly indicate that the algorithm has converged, we again use a much larger number of iterations, which leads to satisfactory convergence (see below).

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).

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:

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 improve the fit a lot. When the mkin transformations are used instead of the saemix transformations, this large number of iterations leads to a goodness of fit that is comparable to the result obtained with saemix transformations.

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.

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.

@@ -327,72 +331,78 @@ DFOP tc mkintrans more iterations 666.12 664.04 "AIC (nlme)" = aic_nlme, "AIC (nlmixr with FOCEI)" = aic_nlmixr_focei, check.names = FALSE -)

Secondly, we use the SAEM estimation routine and check the convergence plots. The control parameters also used for the saemix fits are defined beforehand.

Example evaluations of the dimethenamid data from 2018

Johannes Ranke

Last change 27 July 2021, built on 27 Jul 2021

+Introduction

+Data

+Parent degradation

+Separate evaluations

+Nonlinear mixed-effects models

+nlme

+saemix

+nlmixr

+References

Example evaluations of the dimethenamid data from 2018

Johannes Ranke

Last change 27 July 2021, built on 27 Jul 2021

Last change 27 July 2021, built on 29 Jul 2021

Example evaluations of the dimethenamid data from 2018

Johannes Ranke

Last change 27 July 2021, built on 29 Jul 2021

Last change 4 August 2021, built on 04 Aug 2021

Example evaluations of the dimethenamid data from 2018

Johannes Ranke

Last change 4 August 2021, built on 04 Aug 2021

Last change 16 September 2021, built on 16 Sep 2021

Introduction

Data

nlme

saemix

nlmixr

Example evaluations of the dimethenamid data from 2018

Johannes Ranke

Last change 16 September 2021, built on 16 Sep 2021

Last change 17 September 2021, built on 17 Sep 2021

Introduction

+Comparison

Example evaluations of the dimethenamid data from 2018

Johannes Ranke

Last change 17 September 2021, built on 17 Sep 2021

Last change 27 September 2021, built on 27 Sep 2021

nlme

Comparison

Example evaluations of the dimethenamid data from 2018

Johannes Ranke

Last change 27 September 2021, built on 27 Sep 2021

Last change 27 September 2021, built on 05 Okt 2021

Example evaluations of the dimethenamid data from 2018

Johannes Ranke

Last change 27 September 2021, built on 05 Okt 2021

Last change 11 January 2022, built on 11 Jan 2022

Comparison