Introduction

+ + +

Introduction +

The purpose of this document is to test demonstrate how nonlinear hierarchical models (NLHM) based on the parent degradation models SFO, FOMC, DFOP and HS, with serial formation of two or more metabolites can @@ -377,7 +103,7 @@ be fitted with the mkin package.

173340 (Application of nonlinear hierarchical models to the kinetic evaluation of chemical degradation data) of the German Environment Agency carried out in 2022 and 2023.

The mkin package is used in version 1.2.9 which is currently under +

The mkin package is used in version 1.2.10 which is currently under development. The newly introduced functionality that is used here is a simplification of excluding random effects for a set of fits based on a related set of fits with a reduced model, and the documentation of the @@ -389,47 +115,49 @@ but is also loaded to make the convergence plot function available.

also provides the kable function that is used to improve the display of tabular data in R markdown documents. For parallel processing, the parallel package is used.

library(mkin)
-library(knitr)
-library(saemix)
-library(parallel)
-n_cores <- detectCores()
-
-# We need to start a new cluster after defining a compiled model that is
-# saved as a DLL to the user directory, therefore we define a function
-# This is used again after defining the pathway model
-start_cluster <- function(n_cores) {
-  if (Sys.info()["sysname"] == "Windows") {
-    ret <- makePSOCKcluster(n_cores)
-  } else {
-    ret <- makeForkCluster(n_cores)
-  }
-  return(ret)
-}
-cl <- start_cluster(n_cores)

Test data

+library(mkin)
+library(knitr)
+library(saemix)
+library(parallel)
+n_cores <- detectCores()
+
+# We need to start a new cluster after defining a compiled model that is
+# saved as a DLL to the user directory, therefore we define a function
+# This is used again after defining the pathway model
+start_cluster <- function(n_cores) {
+  if (Sys.info()["sysname"] == "Windows") {
+    ret <- makePSOCKcluster(n_cores)
+  } else {
+    ret <- makeForkCluster(n_cores)
+  }
+  return(ret)
+}
+cl <- start_cluster(n_cores)

Test data +

The example data are taken from the final addendum to the DAR from 2014 and are distributed with the mkin package. Residue data and time step normalisation factors are read in using the function read_spreadsheet from the mkin package. This function also performs the time step normalisation.

data_file <- system.file(
-  "testdata", "cyantraniliprole_soil_efsa_2014.xlsx",
-  package = "mkin")
-cyan_ds <- read_spreadsheet(data_file, parent_only = FALSE)

+data_file <- system.file(
+  "testdata", "cyantraniliprole_soil_efsa_2014.xlsx",
+  package = "mkin")
+cyan_ds <- read_spreadsheet(data_file, parent_only = FALSE)

The following tables show the covariate data and the 5 datasets that were read in from the spreadsheet file.

pH <- attr(cyan_ds, "covariates")
-kable(pH, caption = "Covariate data")

- +

+pH <- attr(cyan_ds, "covariates")
+kable(pH, caption = "Covariate data")

- - + - - + @@ -453,25 +181,24 @@ kable(pH, caption = "Covariate data")

Covariate data
	pH
Nambsheim

for (ds_name in names(cyan_ds)) {
-  print(
-    kable(mkin_long_to_wide(cyan_ds[[ds_name]]),
-      caption = paste("Dataset", ds_name),
-      booktabs = TRUE, row.names = FALSE))
-    cat("\n\\clearpage\n")
-}

- +

+for (ds_name in names(cyan_ds)) {
+  print(
+    kable(mkin_long_to_wide(cyan_ds[[ds_name]]),
+      caption = paste("Dataset", ds_name),
+      booktabs = TRUE, row.names = FALSE))
+    cat("\n\\clearpage\n")
+}

- - + - - + @@ -683,17 +410,15 @@ kable(pH, caption = "Covariate data")

Dataset Nambsheim
time	cyan	JCZ38	J9C38	JSE76	J9Z38
0.000000

- +

- - + - - + @@ -879,17 +604,15 @@ kable(pH, caption = "Covariate data")

Dataset Tama
time	cyan	JCZ38	J9Z38	JSE76
0.000000

- +

- - + - - + @@ -1145,17 +868,15 @@ kable(pH, caption = "Covariate data")

Dataset Gross-Umstadt
time	cyan	JCZ38	J9Z38	JSE76
0.0000000

- +

- - + - - + @@ -1285,17 +1006,15 @@ kable(pH, caption = "Covariate data")

Dataset Sassafras
time	cyan	JCZ38	J9Z38	JSE76
0.000000

- +

- - + - - + @@ -1427,25 +1146,25 @@ kable(pH, caption = "Covariate data")

Dataset Lleida
time	cyan	JCZ38	J9Z38	JSE76
0.000000

Parent only evaluations

Parent only evaluations +

As the pathway fits have very long run times, evaluations of the parent data are performed first, in order to determine for each hierarchical parent degradation model which random effects on the degradation model parameters are ill-defined.

cyan_sep_const <- mmkin(c("SFO", "FOMC", "DFOP", "SFORB", "HS"),
-  cyan_ds, quiet = TRUE, cores = n_cores)
-cyan_sep_tc <- update(cyan_sep_const, error_model = "tc")
-cyan_saem_full <- mhmkin(list(cyan_sep_const, cyan_sep_tc))
-status(cyan_saem_full) |> kable()

- - - +

+cyan_sep_const <- mmkin(c("SFO", "FOMC", "DFOP", "SFORB", "HS"),
+  cyan_ds, quiet = TRUE, cores = n_cores)
+cyan_sep_tc <- update(cyan_sep_const, error_model = "tc")
+cyan_saem_full <- mhmkin(list(cyan_sep_const, cyan_sep_tc))
+status(cyan_saem_full) |> kable()

+ - - + @@ -1475,15 +1194,14 @@ status(cyan_saem_full) |> kable()

	const	tc
SFO

All fits converged successfully.

illparms(cyan_saem_full) |> kable()

- - - +

+illparms(cyan_saem_full) |> kable()

+ - - + @@ -1516,17 +1234,16 @@ status(cyan_saem_full) |> kable() of the parent compound is ill-defined. For the biexponential models DFOP and SFORB, the random effect of one additional parameter is ill-defined when the two-component error model is used.

anova(cyan_saem_full) |> kable(digits = 1)

	const	tc
SFO

- - +

+anova(cyan_saem_full) |> kable(digits = 1)

+ - - + @@ -1604,71 +1321,74 @@ when the two-component error model is used.

two-component error model is preferable for all parent models with the exception of DFOP. The lowest AIC and BIC values are are obtained with the FOMC model, followed by SFORB and DFOP.

stopCluster(cl)

+stopCluster(cl)

Pathway fits

Evaluations with pathway established previously

Pathway fits +

Evaluations with pathway established previously +

To test the technical feasibility of coupling the relevant parent degradation models with different transformation pathway models, a list of mkinmod models is set up below. As in the EU evaluation, parallel formation of metabolites JCZ38 and J9Z38 and secondary formation of metabolite JSE76 from JCZ38 is used.

if (!dir.exists("cyan_dlls")) dir.create("cyan_dlls")
-cyan_path_1 <- list(
-  sfo_path_1 = mkinmod(
-    cyan = mkinsub("SFO", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO"), quiet = TRUE,
-    name = "sfo_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
-  fomc_path_1 = mkinmod(
-    cyan = mkinsub("FOMC", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO"), quiet = TRUE,
-    name = "fomc_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
-  dfop_path_1 = mkinmod(
-    cyan = mkinsub("DFOP", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO"), quiet = TRUE,
-    name = "dfop_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
-  sforb_path_1 = mkinmod(
-    cyan = mkinsub("SFORB", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO"), quiet = TRUE,
-    name = "sforb_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
-  hs_path_1 = mkinmod(
-    cyan = mkinsub("HS", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO"), quiet = TRUE,
-    name = "hs_path_1", dll_dir = "cyan_dlls", overwrite = TRUE)
-)
-cl_path_1 <- start_cluster(n_cores)

+if (!dir.exists("cyan_dlls")) dir.create("cyan_dlls")
+cyan_path_1 <- list(
+  sfo_path_1 = mkinmod(
+    cyan = mkinsub("SFO", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO"), quiet = TRUE,
+    name = "sfo_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
+  fomc_path_1 = mkinmod(
+    cyan = mkinsub("FOMC", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO"), quiet = TRUE,
+    name = "fomc_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
+  dfop_path_1 = mkinmod(
+    cyan = mkinsub("DFOP", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO"), quiet = TRUE,
+    name = "dfop_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
+  sforb_path_1 = mkinmod(
+    cyan = mkinsub("SFORB", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO"), quiet = TRUE,
+    name = "sforb_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
+  hs_path_1 = mkinmod(
+    cyan = mkinsub("HS", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO"), quiet = TRUE,
+    name = "hs_path_1", dll_dir = "cyan_dlls", overwrite = TRUE)
+)
+cl_path_1 <- start_cluster(n_cores)

To obtain suitable starting values for the NLHM fits, separate pathway fits are performed for all datasets.

f_sep_1_const <- mmkin(
-  cyan_path_1,
-  cyan_ds,
-  error_model = "const",
-  cluster = cl_path_1,
-  quiet = TRUE)
-status(f_sep_1_const) |> kable()

	npar	AIC	BIC	Lik
SFO const

- - +

+f_sep_1_const <- mmkin(
+  cyan_path_1,
+  cyan_ds,
+  error_model = "const",
+  cluster = cl_path_1,
+  quiet = TRUE)
+status(f_sep_1_const) |> kable()

+ - - + @@ -1712,19 +1432,18 @@ status(f_sep_1_const) |> kable()

	Nambsheim	Tama	Gross-Umstadt	Sassafras	Lleida
sfo_path_1

f_sep_1_tc <- update(f_sep_1_const, error_model = "tc")
-status(f_sep_1_tc) |> kable()

- - - +

+f_sep_1_tc <- update(f_sep_1_const, error_model = "tc")
+status(f_sep_1_tc) |> kable()

+ - - + @@ -1778,18 +1497,18 @@ for the parent only fits is used as an argument no_random_effect to the mhmkin function. The possibility to do so was introduced in mkin version 1.2.2 which is currently under development.

f_saem_1 <- mhmkin(list(f_sep_1_const, f_sep_1_tc),
-  no_random_effect = illparms(cyan_saem_full),
-  cluster = cl_path_1)

status(f_saem_1) |> kable()

	Nambsheim	Tama	Gross-Umstadt	Sassafras	Lleida
sfo_path_1

- - +

+f_saem_1 <- mhmkin(list(f_sep_1_const, f_sep_1_tc),
+  no_random_effect = illparms(cyan_saem_full),
+  cluster = cl_path_1)

+status(f_saem_1) |> kable()

+ - - + @@ -1825,20 +1544,19 @@ Fisher Information Matrix could not be inverted for the fixed effects fits, ill-defined parameters cannot be determined using the illparms function, because it relies on the Fisher Information Matrix.

illparms(f_saem_1) |> kable()

	const	tc
sfo_path_1

+illparms(f_saem_1) |> kable()

---+++ - - + - - + @@ -1870,17 +1588,16 @@ sd(f_JCZ38_qlogis)

	const	tc
sfo_path_1

The model comparisons below suggest that the pathway fits using DFOP or SFORB for the parent compound provide the best fit.

anova(f_saem_1[, "const"]) |> kable(digits = 1)

- - - +

+anova(f_saem_1[, "const"]) |> kable(digits = 1)

+ - - + @@ -1919,17 +1636,16 @@ or SFORB for the parent compound provide the best fit.

	npar	AIC	BIC	Lik
sfo_path_1 const

anova(f_saem_1[1:4, ]) |> kable(digits = 1)

- - - +

+anova(f_saem_1[1:4, ]) |> kable(digits = 1)

+ - - + @@ -1991,27 +1707,29 @@ or SFORB for the parent compound provide the best fit.

	npar	AIC	BIC	Lik
sfo_path_1 const

For these two parent model, successful fits are shown below. Plots of the fits with the other parent models are shown in the Appendix.

plot(f_saem_1[["dfop_path_1", "tc"]])

+plot(f_saem_1[["dfop_path_1", "tc"]])

+ DFOP pathway fit with two-component error

DFOP pathway fit with two-component error

plot(f_saem_1[["sforb_path_1", "tc"]])

+plot(f_saem_1[["sforb_path_1", "tc"]])

+ SFORB pathway fit with two-component error

SFORB pathway fit with two-component error

A closer graphical analysis of these Figures shows that the residues of transformation product JCZ38 in the soils Tama and Nambsheim observed at later time points are strongly and systematically underestimated.

stopCluster(cl_path_1)

+stopCluster(cl_path_1)

Alternative pathway fits

Alternative pathway fits +

To improve the fit for JCZ38, a back-reaction from JSE76 to JCZ38 was introduced in an alternative version of the transformation pathway, in analogy to the back-reaction from K5A78 to K5A77. Both pairs of @@ -2020,56 +1738,55 @@ corresponding amide (Addendum 2014, p. 109). As FOMC provided the best fit for the parent, and the biexponential models DFOP and SFORB provided the best initial pathway fits, these three parent models are used in the alternative pathway fits.

cyan_path_2 <- list(
-  fomc_path_2 = mkinmod(
-    cyan = mkinsub("FOMC", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO", "JCZ38"),
-    name = "fomc_path_2", quiet = TRUE,
-    dll_dir = "cyan_dlls",
-    overwrite = TRUE
-  ),
-  dfop_path_2 = mkinmod(
-    cyan = mkinsub("DFOP", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO", "JCZ38"),
-    name = "dfop_path_2", quiet = TRUE,
-    dll_dir = "cyan_dlls",
-    overwrite = TRUE
-  ),
-  sforb_path_2 = mkinmod(
-    cyan = mkinsub("SFORB", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO", "JCZ38"),
-    name = "sforb_path_2", quiet = TRUE,
-    dll_dir = "cyan_dlls",
-    overwrite = TRUE
-  )
-)
-
-cl_path_2 <- start_cluster(n_cores)
-f_sep_2_const <- mmkin(
-  cyan_path_2,
-  cyan_ds,
-  error_model = "const",
-  cluster = cl_path_2,
-  quiet = TRUE)
-
-status(f_sep_2_const) |> kable()

- - - +

+cyan_path_2 <- list(
+  fomc_path_2 = mkinmod(
+    cyan = mkinsub("FOMC", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO", "JCZ38"),
+    name = "fomc_path_2", quiet = TRUE,
+    dll_dir = "cyan_dlls",
+    overwrite = TRUE
+  ),
+  dfop_path_2 = mkinmod(
+    cyan = mkinsub("DFOP", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO", "JCZ38"),
+    name = "dfop_path_2", quiet = TRUE,
+    dll_dir = "cyan_dlls",
+    overwrite = TRUE
+  ),
+  sforb_path_2 = mkinmod(
+    cyan = mkinsub("SFORB", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO", "JCZ38"),
+    name = "sforb_path_2", quiet = TRUE,
+    dll_dir = "cyan_dlls",
+    overwrite = TRUE
+  )
+)
+
+cl_path_2 <- start_cluster(n_cores)
+f_sep_2_const <- mmkin(
+  cyan_path_2,
+  cyan_ds,
+  error_model = "const",
+  cluster = cl_path_2,
+  quiet = TRUE)
+
+status(f_sep_2_const) |> kable()

+ - - + @@ -2099,19 +1816,18 @@ status(f_sep_2_const) |> kable()

	Nambsheim	Tama	Gross-Umstadt	Sassafras	Lleida
fomc_path_2

Using constant variance, separate fits converge with the exception of the fits to the Sassafras soil data.

f_sep_2_tc <- update(f_sep_2_const, error_model = "tc")
-status(f_sep_2_tc) |> kable()

- - - +

+f_sep_2_tc <- update(f_sep_2_const, error_model = "tc")
+status(f_sep_2_tc) |> kable()

+ - - + @@ -2142,18 +1858,18 @@ status(f_sep_2_tc) |> kable()

Using the two-component error model, all separate fits converge with the exception of the alternative pathway fit with DFOP used for the parent and the Sassafras dataset.

f_saem_2 <- mhmkin(list(f_sep_2_const, f_sep_2_tc),
-  no_random_effect = illparms(cyan_saem_full[2:4, ]),
-  cluster = cl_path_2)

status(f_saem_2) |> kable()

	Nambsheim	Tama	Gross-Umstadt	Sassafras	Lleida
fomc_path_2

- - +

+f_saem_2 <- mhmkin(list(f_sep_2_const, f_sep_2_tc),
+  no_random_effect = illparms(cyan_saem_full[2:4, ]),
+  cluster = cl_path_2)

+status(f_saem_2) |> kable()

+ - - + @@ -2175,20 +1891,19 @@ parent and the Sassafras dataset.

The hierarchical fits for the alternative pathway completed successfully, with the exception of the model using FOMC for the parent compound and constant variance as the error model.

illparms(f_saem_2) |> kable()

	const	tc
fomc_path_2

+illparms(f_saem_2) |> kable()

---+++ - - + - - + @@ -2211,17 +1926,16 @@ compound and constant variance as the error model.

random effects for the formation fractions for the pathways from JCZ38 to JSE76, and for the reverse pathway from JSE76 to JCZ38 are ill-defined.

anova(f_saem_2[, "tc"]) |> kable(digits = 1)

	const	tc
fomc_path_2

- - +

+anova(f_saem_2[, "tc"]) |> kable(digits = 1)

+ - - + @@ -2246,17 +1960,16 @@ ill-defined.

	npar	AIC	BIC	Lik
fomc_path_2 tc

anova(f_saem_2[2:3,]) |> kable(digits = 1)

- - - +

+anova(f_saem_2[2:3,]) |> kable(digits = 1)

+ - - + @@ -2294,30 +2007,31 @@ and BIC values and are plotted below. Compared with the original pathway, the AIC and BIC values indicate a large improvement. This is confirmed by the plots, which show that the metabolite JCZ38 is fitted much better with this model.

plot(f_saem_2[["fomc_path_2", "tc"]])

+plot(f_saem_2[["fomc_path_2", "tc"]])

+ FOMC pathway fit with two-component error, alternative pathway

FOMC pathway fit with two-component error, alternative pathway

plot(f_saem_2[["dfop_path_2", "tc"]])

+plot(f_saem_2[["dfop_path_2", "tc"]])

+ DFOP pathway fit with two-component error, alternative pathway

DFOP pathway fit with two-component error, alternative pathway

plot(f_saem_2[["sforb_path_2", "tc"]])

+plot(f_saem_2[["sforb_path_2", "tc"]])

+ SFORB pathway fit with two-component error, alternative pathway

SFORB pathway fit with two-component error, alternative pathway

Refinement of alternative pathway fits

All ill-defined random effects that were identified in the parent only fits and in the above pathway fits, are excluded for the final evaluations below. For this purpose, a list of character vectors is @@ -2325,29 +2039,29 @@ created below that can be indexed by row and column indices, and which contains the degradation parameter names for which random effects should be excluded for each of the hierarchical fits contained in f_saem_2.

no_ranef <- matrix(list(), nrow = 3, ncol = 2, dimnames = dimnames(f_saem_2))
-no_ranef[["fomc_path_2", "const"]] <- c("log_beta", "f_JCZ38_qlogis", "f_JSE76_qlogis")
-no_ranef[["fomc_path_2", "tc"]] <- c("cyan_0", "f_JCZ38_qlogis", "f_JSE76_qlogis")
-no_ranef[["dfop_path_2", "const"]] <- c("cyan_0", "f_JCZ38_qlogis", "f_JSE76_qlogis")
-no_ranef[["dfop_path_2", "tc"]] <- c("cyan_0", "log_k1", "f_JCZ38_qlogis", "f_JSE76_qlogis")
-no_ranef[["sforb_path_2", "const"]] <- c("cyan_free_0",
-  "f_JCZ38_qlogis", "f_JSE76_qlogis")
-no_ranef[["sforb_path_2", "tc"]] <- c("cyan_free_0", "log_k_cyan_free_bound",
-  "f_JCZ38_qlogis", "f_JSE76_qlogis")
-clusterExport(cl_path_2, "no_ranef")
-
-f_saem_3 <- update(f_saem_2,
-  no_random_effect = no_ranef,
-  cluster = cl_path_2)

status(f_saem_3) |> kable()

	npar	AIC	BIC	Lik
dfop_path_2 const

- - +

+no_ranef <- matrix(list(), nrow = 3, ncol = 2, dimnames = dimnames(f_saem_2))
+no_ranef[["fomc_path_2", "const"]] <- c("log_beta", "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["fomc_path_2", "tc"]] <- c("cyan_0", "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["dfop_path_2", "const"]] <- c("cyan_0", "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["dfop_path_2", "tc"]] <- c("cyan_0", "log_k1", "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["sforb_path_2", "const"]] <- c("cyan_free_0",
+  "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["sforb_path_2", "tc"]] <- c("cyan_free_0", "log_k_cyan_free_bound",
+  "f_JCZ38_qlogis", "f_JSE76_qlogis")
+clusterExport(cl_path_2, "no_ranef")
+
+f_saem_3 <- update(f_saem_2,
+  no_random_effect = no_ranef,
+  cluster = cl_path_2)

+status(f_saem_3) |> kable()

+ - - + @@ -2370,15 +2084,14 @@ f_saem_3 <- update(f_saem_2, all updated fits completed successfully. However, the Fisher Information Matrix for the fixed effects (Fth) could not be inverted, so no confidence intervals for the optimised parameters are available.

illparms(f_saem_3) |> kable()

	const	tc
fomc_path_2

- - +

+illparms(f_saem_3) |> kable()

+ - - + @@ -2397,17 +2110,16 @@ confidence intervals for the optimised parameters are available.

	const	tc
fomc_path_2

anova(f_saem_3[, "tc"]) |> kable(digits = 1)

- - - +

+anova(f_saem_3[, "tc"]) |> kable(digits = 1)

+ - - + @@ -2432,17 +2144,16 @@ confidence intervals for the optimised parameters are available.

	npar	AIC	BIC	Lik
fomc_path_2 tc

anova(f_saem_3[2:3,]) |> kable(digits = 1)

- - - +

+anova(f_saem_3[2:3,]) |> kable(digits = 1)

+ - - + @@ -2478,11 +2189,13 @@ confidence intervals for the optimised parameters are available.

two-component error) are lower than in the previous fits with the alternative pathway, the practical value of these refined evaluations is limited as no confidence intervals are obtained.

stopCluster(cl_path_2)

+stopCluster(cl_path_2)

Conclusion

Conclusion +

It was demonstrated that a relatively complex transformation pathway with parallel formation of two primary metabolites and one secondary metabolite can be fitted even if the data in the individual datasets are @@ -2492,50 +2205,55 @@ practical feasibility of iterative refinements based on ill-defined parameters and of alternative checks of parameter identifiability based on multistart runs.

Acknowledgements

Acknowledgements +

The helpful comments by Janina Wöltjen of the German Environment Agency are gratefully acknowledged.

Appendix

Plots of fits that were not refined further

plot(f_saem_1[["sfo_path_1", "tc"]])

Appendix +

Plots of fits that were not refined further +

+plot(f_saem_1[["sfo_path_1", "tc"]])

+ SFO pathway fit with two-component error

SFO pathway fit with two-component error

plot(f_saem_1[["fomc_path_1", "tc"]])

+plot(f_saem_1[["fomc_path_1", "tc"]])

+ FOMC pathway fit with two-component error

FOMC pathway fit with two-component error

plot(f_saem_1[["sforb_path_1", "tc"]])

+plot(f_saem_1[["sforb_path_1", "tc"]])

+ HS pathway fit with two-component error

HS pathway fit with two-component error

Hierarchical fit listings

Pathway 1

Hierarchical fit listings +

Pathway 1 +


 saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.9 
-R version used for fitting:         4.4.2 
-Date of fit:     Thu Feb 13 18:31:33 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:35:03 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - k_cyan * cyan
@@ -2548,7 +2266,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 480.873 s
+Fitted in 445.08 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -2653,17 +2371,17 @@ JCZ38  14.46  48.05
 J9Z38 103.86 345.00
 JSE76 143.91 478.04
 
-

+ +


 saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.9 
-R version used for fitting:         4.4.2 
-Date of fit:     Thu Feb 13 18:32:28 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:34:47 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - k_cyan * cyan
@@ -2676,7 +2394,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 534.75 s
+Fitted in 428.46 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -2783,17 +2501,17 @@ JCZ38  15.81  52.52
 J9Z38 107.97 358.68
 JSE76 114.20 379.35
 
-

+ +


 saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.9 
-R version used for fitting:         4.4.2 
-Date of fit:     Thu Feb 13 18:33:51 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:35:21 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
@@ -2808,7 +2526,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 618.676 s
+Fitted in 462.739 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -2928,17 +2646,17 @@ JCZ38  20.53   68.19       NA
 J9Z38 140.07  465.32       NA
 JSE76 318.86 1059.22       NA
 
-

+ +


 saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.9 
-R version used for fitting:         4.4.2 
-Date of fit:     Thu Feb 13 18:34:01 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:35:31 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
@@ -2953,7 +2671,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 627.822 s
+Fitted in 472.067 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -3066,17 +2784,17 @@ JCZ38  22.01  73.1       NA
 J9Z38 130.09 432.2       NA
 JSE76 210.98 700.9       NA
 
-

+ +


 saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.9 
-R version used for fitting:         4.4.2 
-Date of fit:     Thu Feb 13 18:33:18 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:36:02 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -3095,7 +2813,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 584.724 s
+Fitted in 503.671 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -3212,17 +2930,17 @@ JCZ38  22.34  74.22       NA      NA      NA
 J9Z38 119.92 398.36       NA      NA      NA
 JSE76 200.41 665.76       NA      NA      NA
 
-

+ +


 saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.9 
-R version used for fitting:         4.4.2 
-Date of fit:     Thu Feb 13 18:35:43 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:38:54 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -3241,7 +2959,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 729.575 s
+Fitted in 674.81 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -3358,17 +3076,17 @@ JCZ38  22.20  73.75       NA      NA      NA
 J9Z38 108.23 359.53       NA      NA      NA
 JSE76 179.30 595.62       NA      NA      NA
 
-

+ +


 saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.9 
-R version used for fitting:         4.4.2 
-Date of fit:     Thu Feb 13 18:34:05 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:36:26 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
@@ -3386,7 +3104,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 632.71 s
+Fitted in 527.639 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -3523,17 +3241,17 @@ JCZ38  22.98  76.33       NA           NA           NA
 J9Z38 116.28 386.29       NA           NA           NA
 JSE76 193.42 642.53       NA           NA           NA
 
-

+ +


 saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.9 
-R version used for fitting:         4.4.2 
-Date of fit:     Thu Feb 13 18:37:01 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:38:31 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
@@ -3551,7 +3269,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 807.852 s
+Fitted in 651.67 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -3688,17 +3406,17 @@ JCZ38  22.34  74.2       NA           NA           NA
 J9Z38 110.14 365.9       NA           NA           NA
 JSE76 177.11 588.3       NA           NA           NA
 
-

+ +


 saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.9 
-R version used for fitting:         4.4.2 
-Date of fit:     Thu Feb 13 18:33:29 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:36:13 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - ifelse(time <= tb, k1, k2) * cyan
@@ -3713,7 +3431,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 596.235 s
+Fitted in 514.353 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -3830,20 +3548,21 @@ JCZ38  22.27  73.98       NA      NA      NA
 J9Z38 113.09 375.69       NA      NA      NA
 JSE76 187.01 621.23       NA      NA      NA
 
-

+ +

Pathway 2

Pathway 2 +


 saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.9 
-R version used for fitting:         4.4.2 
-Date of fit:     Thu Feb 13 18:46:08 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:47:30 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
@@ -3858,7 +3577,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 536.687 s
+Fitted in 505.533 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -3999,17 +3718,17 @@ JCZ38   7.075  23.50       NA
 J9Z38 117.249 389.49       NA
 JSE76  14.169  47.07       NA
 
-

+ +


 saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.9 
-R version used for fitting:         4.4.2 
-Date of fit:     Thu Feb 13 18:47:06 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:48:20 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -4029,7 +3748,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 594.209 s
+Fitted in 555.413 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -4190,17 +3909,17 @@ JCZ38  12.50  41.53       NA      NA      NA
 J9Z38 118.69 394.27       NA      NA      NA
 JSE76  24.32  80.78       NA      NA      NA
 
-

+ +


 saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.9 
-R version used for fitting:         4.4.2 
-Date of fit:     Thu Feb 13 18:49:43 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:51:02 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -4220,7 +3939,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 751.883 s
+Fitted in 717.675 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -4381,17 +4100,17 @@ JCZ38   8.93  29.66       NA      NA      NA
 J9Z38 110.45 366.89       NA      NA      NA
 JSE76  17.96  59.66       NA      NA      NA
 
-

+ +


 saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.9 
-R version used for fitting:         4.4.2 
-Date of fit:     Thu Feb 13 18:46:57 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:48:15 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
@@ -4409,7 +4128,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 585.771 s
+Fitted in 550.772 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -4577,17 +4296,17 @@ JCZ38   7.203  23.93       NA           NA           NA
 J9Z38 131.918 438.22       NA           NA           NA
 JSE76  14.287  47.46       NA           NA           NA
 
-

+ +


 saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.9 
-R version used for fitting:         4.4.2 
-Date of fit:     Thu Feb 13 18:50:00 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:50:59 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
@@ -4605,7 +4324,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 767.874 s
+Fitted in 714.48 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -4773,21 +4492,22 @@ JCZ38   8.535  28.35       NA           NA           NA
 J9Z38 105.517 350.52       NA           NA           NA
 JSE76  17.837  59.25       NA           NA           NA
 
-

+ +

Pathway 2, refined fits

Pathway 2, refined fits +


 saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.9 
-R version used for fitting:         4.4.2 
-Date of fit:     Thu Feb 13 19:03:52 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 21:04:10 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
@@ -4802,7 +4522,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 830.375 s
+Fitted in 786.038 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -4919,18 +4639,18 @@ JCZ38  12.03  39.96       NA
 J9Z38 111.14 369.19       NA
 JSE76  23.77  78.98       NA
 
-

+ +


 saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.9 
-R version used for fitting:         4.4.2 
-Date of fit:     Thu Feb 13 19:05:47 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 21:05:56 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -4950,7 +4670,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 945.728 s
+Fitted in 892.139 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -5085,18 +4805,18 @@ JCZ38  13.04  43.33       NA      NA      NA
 J9Z38 120.93 401.73       NA      NA      NA
 JSE76  26.39  87.68       NA      NA      NA
 
-

+ +


 saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.9 
-R version used for fitting:         4.4.2 
-Date of fit:     Thu Feb 13 19:05:49 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 21:06:02 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -5116,7 +4836,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 947.743 s
+Fitted in 898.534 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -5251,18 +4971,18 @@ JCZ38  11.49  38.18       NA      NA      NA
 J9Z38 107.55 357.28       NA      NA      NA
 JSE76  27.20  90.36       NA      NA      NA
 
-

+ +


 saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.9 
-R version used for fitting:         4.4.2 
-Date of fit:     Thu Feb 13 19:05:38 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 21:05:52 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
@@ -5280,7 +5000,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 936.368 s
+Fitted in 888.333 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -5422,18 +5142,18 @@ JCZ38  12.92  42.93       NA           NA           NA
 J9Z38 114.71 381.07       NA           NA           NA
 JSE76  26.04  86.51       NA           NA           NA
 
-

+ +


 saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.9 
-R version used for fitting:         4.4.2 
-Date of fit:     Thu Feb 13 19:05:52 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 21:06:21 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
@@ -5451,7 +5171,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 950.661 s
+Fitted in 916.619 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -5593,19 +5313,20 @@ JCZ38  11.06  36.75       NA           NA           NA
 J9Z38 106.71 354.49       NA           NA           NA
 JSE76  25.44  84.51       NA           NA           NA
 
-

+ +

Session info

R version 4.4.2 (2024-10-31)
+
+Session info
+
+R version 4.5.0 (2025-04-11)
 Platform: x86_64-pc-linux-gnu
 Running under: Debian GNU/Linux 12 (bookworm)
 
 Matrix products: default
 BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0 
-LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0
+LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0  LAPACK version 3.11.0
 
 locale:
  [1] LC_CTYPE=de_DE.UTF-8       LC_NUMERIC=C              
@@ -5623,75 +5344,52 @@ attached base packages:
 [8] base     
 
 other attached packages:
-[1] saemix_3.3      npde_3.5        knitr_1.49      mkin_1.2.9     
-[5] rmarkdown_2.29  nvimcom_0.9-167
+[1] rmarkdown_2.29  nvimcom_0.9-167 saemix_3.3      npde_3.5       
+[5] knitr_1.49      mkin_1.2.10    
 
 loaded via a namespace (and not attached):
- [1] sass_0.4.9        utf8_1.2.4        generics_0.1.3    lattice_0.22-6   
- [5] digest_0.6.37     magrittr_2.0.3    evaluate_1.0.1    grid_4.4.2       
- [9] fastmap_1.2.0     cellranger_1.1.0  jsonlite_1.8.9    processx_3.8.4   
-[13] pkgbuild_1.4.5    deSolve_1.40      mclust_6.1.1      ps_1.8.1         
-[17] gridExtra_2.3     fansi_1.0.6       scales_1.3.0      codetools_0.2-20 
-[21] jquerylib_0.1.4   cli_3.6.3         rlang_1.1.4       munsell_0.5.1    
-[25] cachem_1.1.0      yaml_2.3.10       inline_0.3.20     tools_4.4.2      
-[29] colorout_1.3-2    dplyr_1.1.4       colorspace_2.1-1  ggplot2_3.5.1    
-[33] vctrs_0.6.5       R6_2.5.1          zoo_1.8-12        lifecycle_1.0.4  
-[37] MASS_7.3-61       pkgconfig_2.0.3   callr_3.7.6       pillar_1.9.0     
-[41] bslib_0.8.0       gtable_0.3.6      glue_1.8.0        xfun_0.49        
-[45] tibble_3.2.1      lmtest_0.9-40     tidyselect_1.2.1  htmltools_0.5.8.1
-[49] nlme_3.1-166      compiler_4.4.2    readxl_1.4.3     
+ [1] sass_0.4.9        generics_0.1.3    lattice_0.22-6    digest_0.6.37    
+ [5] magrittr_2.0.3    evaluate_1.0.3    grid_4.5.0        fastmap_1.2.0    
+ [9] cellranger_1.1.0  jsonlite_1.9.0    processx_3.8.6    pkgbuild_1.4.6   
+[13] deSolve_1.40      mclust_6.1.1      ps_1.9.0          gridExtra_2.3    
+[17] scales_1.3.0      codetools_0.2-20  textshaping_1.0.0 jquerylib_0.1.4  
+[21] cli_3.6.4         rlang_1.1.5       munsell_0.5.1     cachem_1.1.0     
+[25] yaml_2.3.10       inline_0.3.21     tools_4.5.0       dplyr_1.1.4      
+[29] colorspace_2.1-1  ggplot2_3.5.1     vctrs_0.6.5       R6_2.6.1         
+[33] zoo_1.8-13        lifecycle_1.0.4   fs_1.6.5          htmlwidgets_1.6.4
+[37] MASS_7.3-65       ragg_1.3.3        pkgconfig_2.0.3   desc_1.4.3       
+[41] callr_3.7.6       pkgdown_2.1.1     pillar_1.10.1     bslib_0.9.0      
+[45] gtable_0.3.6      glue_1.8.0        systemfonts_1.2.1 xfun_0.51        
+[49] tibble_3.2.1      lmtest_0.9-40     tidyselect_1.2.1  htmltools_0.5.8.1
+[53] nlme_3.1-168      compiler_4.5.0    readxl_1.4.4

Hardware info

Hardware info +

CPU model: AMD Ryzen 9 7950X 16-Core Processor

MemTotal:       64927788 kB

MemTotal:       64927780 kB

- - - - + - +

Hierarchical SFO path 1 fit with constant variance
	npar	AIC	BIC	Lik
dfop_path_2 const

Testing hierarchical pathway kinetics with -residue data on cyantraniliprole

Johannes Ranke

Last change on 13 February 2023, last compiled on 13 -Februar 2025

Testing hierarchical pathway kinetics with residue data on cyantraniliprole

Johannes +Ranke

Last change on 13 February +2023, last compiled on 12 Mai 2025

Introduction

Introduction +

Test data

Test data +

Parent only evaluations

Parent only evaluations +

Pathway fits

Evaluations with pathway established previously

Pathway fits +

Evaluations with pathway established previously +

Alternative pathway fits

Alternative pathway fits +

Refinement of alternative pathway fits

Refinement of alternative pathway fits +

Conclusion

Conclusion +

Acknowledgements

Acknowledgements +

Appendix

Plots of fits that were not refined further

Appendix +

Plots of fits that were not refined further +

Hierarchical fit listings

Pathway 1

Hierarchical fit listings +

Pathway 1 +

Pathway 2

Pathway 2 +

Pathway 2, refined fits

Pathway 2, refined fits +

Session info

Session info +

Hardware info

Hardware info +