From 2bb59c88d49b193f278916ad9cc4de83c0de9604 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Wed, 2 Mar 2022 18:03:54 +0100 Subject: Make tests more platform independent, update docs --- docs/articles/web_only/FOCUS_Z.html | 250 ++-- .../figure-html/FOCUS_2006_Z_fits_1-1.png | Bin 66566 -> 66689 bytes .../figure-html/FOCUS_2006_Z_fits_10-1.png | Bin 105728 -> 105896 bytes .../figure-html/FOCUS_2006_Z_fits_11-1.png | Bin 104598 -> 104793 bytes .../figure-html/FOCUS_2006_Z_fits_11a-1.png | Bin 75131 -> 75230 bytes .../figure-html/FOCUS_2006_Z_fits_11b-1.png | Bin 36162 -> 36314 bytes .../figure-html/FOCUS_2006_Z_fits_2-1.png | Bin 66566 -> 66689 bytes .../figure-html/FOCUS_2006_Z_fits_3-1.png | Bin 66341 -> 66448 bytes .../figure-html/FOCUS_2006_Z_fits_5-1.png | Bin 80289 -> 80373 bytes .../figure-html/FOCUS_2006_Z_fits_6-1.png | Bin 104958 -> 105210 bytes .../figure-html/FOCUS_2006_Z_fits_7-1.png | Bin 104309 -> 104538 bytes .../figure-html/FOCUS_2006_Z_fits_9-1.png | Bin 88640 -> 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+

Example evaluation of FOCUS dataset Z

-

Johannes Ranke

+

Johannes Ranke

-

Last change 16 January 2018 (rebuilt 2021-03-31)

+

Last change 16 January 2018 (rebuilt 2022-03-02)

- Source: vignettes/web_only/FOCUS_Z.rmd + Source: vignettes/web_only/FOCUS_Z.rmd
-

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

-
-

-The data

+

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

+
+

The data +

The following code defines the example dataset from Appendix 7 to the FOCUS kinetics report (FOCUS Work Group on Degradation Kinetics 2014, 354).

-library(mkin, quietly = TRUE)
+library(mkin, quietly = TRUE)
 LOD = 0.5
-FOCUS_2006_Z = data.frame(
-  t = c(0, 0.04, 0.125, 0.29, 0.54, 1, 2, 3, 4, 7, 10, 14, 21,
+FOCUS_2006_Z = data.frame(
+  t = c(0, 0.04, 0.125, 0.29, 0.54, 1, 2, 3, 4, 7, 10, 14, 21,
         42, 61, 96, 124),
-  Z0 = c(100, 81.7, 70.4, 51.1, 41.2, 6.6, 4.6, 3.9, 4.6, 4.3, 6.8,
+  Z0 = c(100, 81.7, 70.4, 51.1, 41.2, 6.6, 4.6, 3.9, 4.6, 4.3, 6.8,
          2.9, 3.5, 5.3, 4.4, 1.2, 0.7),
-  Z1 = c(0, 18.3, 29.6, 46.3, 55.1, 65.7, 39.1, 36, 15.3, 5.6, 1.1,
+  Z1 = c(0, 18.3, 29.6, 46.3, 55.1, 65.7, 39.1, 36, 15.3, 5.6, 1.1,
          1.6, 0.6, 0.5 * LOD, NA, NA, NA),
-  Z2 = c(0, NA, 0.5 * LOD, 2.6, 3.8, 15.3, 37.2, 31.7, 35.6, 14.5,
+  Z2 = c(0, NA, 0.5 * LOD, 2.6, 3.8, 15.3, 37.2, 31.7, 35.6, 14.5,
          0.8, 2.1, 1.9, 0.5 * LOD, NA, NA, NA),
-  Z3 = c(0, NA, NA, NA, NA, 0.5 * LOD, 9.2, 13.1, 22.3, 28.4, 32.5,
+  Z3 = c(0, NA, NA, NA, NA, 0.5 * LOD, 9.2, 13.1, 22.3, 28.4, 32.5,
          25.2, 17.2, 4.8, 4.5, 2.8, 4.4))
 
 FOCUS_2006_Z_mkin <- mkin_wide_to_long(FOCUS_2006_Z)
-
-

-Parent and one metabolite

+
+

Parent and one metabolite +

The next step is to set up the models used for the kinetic analysis. As the simultaneous fit of parent and the first metabolite is usually straightforward, Step 1 (SFO for parent only) is skipped here. We start with the model 2a, with formation and decline of metabolite Z1 and the pathway from parent directly to sink included (default in mkin).

 Z.2a <- mkinmod(Z0 = mkinsub("SFO", "Z1"),
                 Z1 = mkinsub("SFO"))
-
## Temporary DLL for differentials generated and loaded
+
## Temporary DLL for differentials generated and loaded
 m.Z.2a <- mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE)
-
## Warning in mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
-## value of zero were removed from the data
+
## Warning in mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
+## value of zero were removed from the data
 plot_sep(m.Z.2a)

-summary(m.Z.2a, data = FALSE)$bpar
-
##            Estimate se_notrans t value     Pr(>t)    Lower    Upper
-## Z0_0       97.01488   3.301084 29.3888 3.2971e-21 91.66556 102.3642
-## k_Z0        2.23601   0.207078 10.7979 3.3309e-11  1.95303   2.5600
-## k_Z1        0.48212   0.063265  7.6207 2.8154e-08  0.40341   0.5762
-## f_Z0_to_Z1  1.00000   0.094764 10.5525 5.3560e-11  0.00000   1.0000
-## sigma       4.80411   0.635638  7.5579 3.2592e-08  3.52677   6.0815
+summary(m.Z.2a, data = FALSE)$bpar
+
##            Estimate se_notrans t value     Pr(>t)    Lower    Upper
+## Z0_0       97.01488   3.301084 29.3888 3.2971e-21 91.66556 102.3642
+## k_Z0        2.23601   0.207078 10.7979 3.3309e-11  1.95303   2.5600
+## k_Z1        0.48212   0.063265  7.6207 2.8154e-08  0.40341   0.5762
+## f_Z0_to_Z1  1.00000   0.094764 10.5525 5.3560e-11  0.00000   1.0000
+## sigma       4.80411   0.635638  7.5579 3.2592e-08  3.52677   6.0815

As obvious from the parameter summary (the component of the summary), the kinetic rate constant from parent compound Z to sink is very small and the t-test for this parameter suggests that it is not significantly different from zero. This suggests, in agreement with the analysis in the FOCUS kinetics report, to simplify the model by removing the pathway to sink.

A similar result can be obtained when formation fractions are used in the model formulation:

 Z.2a.ff <- mkinmod(Z0 = mkinsub("SFO", "Z1"),
                    Z1 = mkinsub("SFO"),
                    use_of_ff = "max")
-
## Temporary DLL for differentials generated and loaded
+
## Temporary DLL for differentials generated and loaded
 m.Z.2a.ff <- mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE)
-
## Warning in mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
-## value of zero were removed from the data
+
## Warning in mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
+## value of zero were removed from the data
 plot_sep(m.Z.2a.ff)

-summary(m.Z.2a.ff, data = FALSE)$bpar
-
##            Estimate se_notrans t value     Pr(>t)    Lower    Upper
-## Z0_0       97.01488   3.301084 29.3888 3.2971e-21 91.66556 102.3642
-## k_Z0        2.23601   0.207078 10.7979 3.3309e-11  1.95303   2.5600
-## k_Z1        0.48212   0.063265  7.6207 2.8154e-08  0.40341   0.5762
-## f_Z0_to_Z1  1.00000   0.094764 10.5525 5.3560e-11  0.00000   1.0000
-## sigma       4.80411   0.635638  7.5579 3.2592e-08  3.52677   6.0815
+summary(m.Z.2a.ff, data = FALSE)$bpar
+
##            Estimate se_notrans t value     Pr(>t)    Lower    Upper
+## Z0_0       97.01488   3.301084 29.3888 3.2971e-21 91.66556 102.3642
+## k_Z0        2.23601   0.207078 10.7979 3.3309e-11  1.95303   2.5600
+## k_Z1        0.48212   0.063265  7.6207 2.8154e-08  0.40341   0.5762
+## f_Z0_to_Z1  1.00000   0.094764 10.5525 5.3560e-11  0.00000   1.0000
+## sigma       4.80411   0.635638  7.5579 3.2592e-08  3.52677   6.0815

Here, the ilr transformed formation fraction fitted in the model takes a very large value, and the backtransformed formation fraction from parent Z to Z1 is practically unity. Here, the covariance matrix used for the calculation of confidence intervals is not returned as the model is overparameterised.

A simplified model is obtained by removing the pathway to the sink.

In the following, we use the parameterisation with formation fractions in order to be able to compare with the results in the FOCUS guidance, and as it makes it easier to use parameters obtained in a previous fit when adding a further metabolite.

 Z.3 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
                Z1 = mkinsub("SFO"), use_of_ff = "max")
-
## Temporary DLL for differentials generated and loaded
+
## Temporary DLL for differentials generated and loaded
 m.Z.3 <- mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE)
-
## Warning in mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
-## value of zero were removed from the data
+
## Warning in mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
+## value of zero were removed from the data
 plot_sep(m.Z.3)

-summary(m.Z.3, data = FALSE)$bpar
-
##       Estimate se_notrans t value     Pr(>t)    Lower    Upper
-## Z0_0  97.01488   2.597342  37.352 2.0106e-24 91.67597 102.3538
-## k_Z0   2.23601   0.146904  15.221 9.1477e-15  1.95354   2.5593
-## k_Z1   0.48212   0.041727  11.554 4.8268e-12  0.40355   0.5760
-## sigma  4.80411   0.620208   7.746 1.6110e-08  3.52925   6.0790
+summary(m.Z.3, data = FALSE)$bpar
+
##       Estimate se_notrans t value     Pr(>t)    Lower    Upper
+## Z0_0  97.01488   2.597342  37.352 2.0106e-24 91.67597 102.3538
+## k_Z0   2.23601   0.146904  15.221 9.1477e-15  1.95354   2.5593
+## k_Z1   0.48212   0.041727  11.554 4.8268e-12  0.40355   0.5760
+## sigma  4.80411   0.620208   7.746 1.6110e-08  3.52925   6.0790

As there is only one transformation product for Z0 and no pathway to sink, the formation fraction is internally fixed to unity.

-
-

-Metabolites Z2 and Z3

+
+

Metabolites Z2 and Z3 +

As suggested in the FOCUS report, the pathway to sink was removed for metabolite Z1 as well in the next step. While this step appears questionable on the basis of the above results, it is followed here for the purpose of comparison. Also, in the FOCUS report, it is assumed that there is additional empirical evidence that Z1 quickly and exclusively hydrolyses to Z2.

 Z.5 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
                Z1 = mkinsub("SFO", "Z2", sink = FALSE),
                Z2 = mkinsub("SFO"), use_of_ff = "max")
-
## Temporary DLL for differentials generated and loaded
+
## Temporary DLL for differentials generated and loaded
 m.Z.5 <- mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE)
-
## Warning in mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
-## value of zero were removed from the data
+
## Warning in mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
+## value of zero were removed from the data
 plot_sep(m.Z.5)

@@ -222,45 +227,45 @@ Z2 = mkinsub("SFO", "Z3"), Z3 = mkinsub("SFO"), use_of_ff = "max")
-
## Temporary DLL for differentials generated and loaded
+
## Temporary DLL for differentials generated and loaded
 m.Z.FOCUS <- mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin,
                      parms.ini = m.Z.5$bparms.ode,
                      quiet = TRUE)
-
## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, :
-## Observations with value of zero were removed from the data
-
## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, : Optimisation did not converge:
-## false convergence (8)
+
## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, :
+## Observations with value of zero were removed from the data
+
## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, : Optimisation did not converge:
+## false convergence (8)
 plot_sep(m.Z.FOCUS)

-summary(m.Z.FOCUS, data = FALSE)$bpar
-
##             Estimate se_notrans t value     Pr(>t)     Lower      Upper
-## Z0_0       96.838822   1.994274 48.5584 4.0280e-42 92.826981 100.850664
-## k_Z0        2.215393   0.118458 18.7019 1.0413e-23  1.989456   2.466989
-## k_Z1        0.478305   0.028258 16.9266 6.2418e-22  0.424708   0.538666
-## k_Z2        0.451627   0.042139 10.7176 1.6314e-14  0.374339   0.544872
-## k_Z3        0.058692   0.015245  3.8499 1.7803e-04  0.034808   0.098965
-## f_Z2_to_Z3  0.471502   0.058351  8.0805 9.6608e-11  0.357769   0.588274
-## sigma       3.984431   0.383402 10.3923 4.5575e-14  3.213126   4.755736
+summary(m.Z.FOCUS, data = FALSE)$bpar
+
##             Estimate se_notrans t value     Pr(>t)     Lower      Upper
+## Z0_0       96.838822   1.994274 48.5584 4.0280e-42 92.826981 100.850664
+## k_Z0        2.215393   0.118458 18.7019 1.0413e-23  1.989456   2.466989
+## k_Z1        0.478305   0.028258 16.9266 6.2418e-22  0.424708   0.538666
+## k_Z2        0.451627   0.042139 10.7176 1.6314e-14  0.374339   0.544872
+## k_Z3        0.058692   0.015245  3.8499 1.7803e-04  0.034808   0.098965
+## f_Z2_to_Z3  0.471502   0.058351  8.0805 9.6608e-11  0.357769   0.588274
+## sigma       3.984431   0.383402 10.3923 4.5575e-14  3.213126   4.755736
 endpoints(m.Z.FOCUS)
-
## $ff
-##   Z2_Z3 Z2_sink 
-##  0.4715  0.5285 
-## 
-## $distimes
-##        DT50    DT90
-## Z0  0.31288  1.0394
-## Z1  1.44917  4.8141
-## Z2  1.53478  5.0984
-## Z3 11.80986 39.2315
+
## $ff
+##   Z2_Z3 Z2_sink 
+##  0.4715  0.5285 
+## 
+## $distimes
+##        DT50    DT90
+## Z0  0.31288  1.0394
+## Z1  1.44917  4.8141
+## Z2  1.53478  5.0984
+## Z3 11.80986 39.2315

This fit corresponds to the final result chosen in Appendix 7 of the FOCUS report. Confidence intervals returned by mkin are based on internally transformed parameters, however.

-
-

-Using the SFORB model

+
+

Using the SFORB model +

As the FOCUS report states, there is a certain tailing of the time course of metabolite Z3. Also, the time course of the parent compound is not fitted very well using the SFO model, as residues at a certain low level remain.

Therefore, an additional model is offered here, using the single first-order reversible binding (SFORB) model for metabolite Z3. As expected, the \(\chi^2\) error level is lower for metabolite Z3 using this model and the graphical fit for Z3 is improved. However, the covariance matrix is not returned.

@@ -268,27 +273,27 @@
                     Z1 = mkinsub("SFO", "Z2", sink = FALSE),
                     Z2 = mkinsub("SFO", "Z3"),
                     Z3 = mkinsub("SFORB"))
-
## Temporary DLL for differentials generated and loaded
+
## Temporary DLL for differentials generated and loaded
 m.Z.mkin.1 <- mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE)
-
## Warning in mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
-## value of zero were removed from the data
+
## Warning in mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
+## value of zero were removed from the data
 plot_sep(m.Z.mkin.1)

-summary(m.Z.mkin.1, data = FALSE)$cov.unscaled
-
## NULL
+summary(m.Z.mkin.1, data = FALSE)$cov.unscaled
+
## NULL

Therefore, a further stepwise model building is performed starting from the stage of parent and two metabolites, starting from the assumption that the model fit for the parent compound can be improved by using the SFORB model.

 Z.mkin.3 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
                     Z1 = mkinsub("SFO", "Z2", sink = FALSE),
                     Z2 = mkinsub("SFO"))
-
## Temporary DLL for differentials generated and loaded
+
## Temporary DLL for differentials generated and loaded
 m.Z.mkin.3 <- mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE)
-
## Warning in mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
-## value of zero were removed from the data
+
## Warning in mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
+## value of zero were removed from the data
 plot_sep(m.Z.mkin.3)

@@ -299,13 +304,14 @@ Z1 = mkinsub("SFO", "Z2", sink = FALSE), Z2 = mkinsub("SFO", "Z3"), Z3 = mkinsub("SFO"))
-
## Temporary DLL for differentials generated and loaded
+
## Temporary DLL for differentials generated and loaded
 m.Z.mkin.4 <- mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin,
                       parms.ini = m.Z.mkin.3$bparms.ode,
                       quiet = TRUE)
-
## Warning in mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, parms.ini = m.Z.mkin.
-## 3$bparms.ode, : Observations with value of zero were removed from the data
+
## Warning in mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, parms.ini =
+## m.Z.mkin.3$bparms.ode, : Observations with value of zero were removed from the
+## data
 plot_sep(m.Z.mkin.4)

@@ -315,25 +321,27 @@ Z1 = mkinsub("SFO", "Z2", sink = FALSE), Z2 = mkinsub("SFO", "Z3"), Z3 = mkinsub("SFORB"))
-
## Temporary DLL for differentials generated and loaded
+
## Temporary DLL for differentials generated and loaded
 m.Z.mkin.5 <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin,
                       parms.ini = m.Z.mkin.4$bparms.ode[1:4],
                       quiet = TRUE)
-
## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini = m.Z.mkin.
-## 4$bparms.ode[1:4], : Observations with value of zero were removed from the data
+
## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini =
+## m.Z.mkin.4$bparms.ode[1:4], : Observations with value of zero were removed from
+## the data
 plot_sep(m.Z.mkin.5)

The summary view of the backtransformed parameters shows that we get no confidence intervals due to overparameterisation. As the optimized is excessively small, it seems reasonable to fix it to zero.

 m.Z.mkin.5a <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin,
-                       parms.ini = c(m.Z.mkin.5$bparms.ode[1:7],
+                       parms.ini = c(m.Z.mkin.5$bparms.ode[1:7],
                                      k_Z3_bound_free = 0),
                        fixed_parms = "k_Z3_bound_free",
                        quiet = TRUE)
-
## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini = c(m.Z.mkin.
-## 5$bparms.ode[1:7], : Observations with value of zero were removed from the data
+
## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini =
+## c(m.Z.mkin.5$bparms.ode[1:7], : Observations with value of zero were removed
+## from the data
 plot_sep(m.Z.mkin.5a)

@@ -345,29 +353,29 @@

The endpoints obtained with this model are

 endpoints(m.Z.mkin.5a)
-
## $ff
-## Z0_free   Z2_Z3 Z2_sink Z3_free 
-## 1.00000 0.53656 0.46344 1.00000 
-## 
-## $SFORB
-##     Z0_b1     Z0_b2     Z3_b1     Z3_b2 
-## 2.4471322 0.0075125 0.0800069 0.0000000 
-## 
-## $distimes
-##      DT50   DT90 DT50back DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2
-## Z0 0.3043 1.1848  0.35666    0.28325     92.266         NA         NA
-## Z1 1.5148 5.0320       NA         NA         NA         NA         NA
-## Z2 1.6414 5.4526       NA         NA         NA         NA         NA
-## Z3     NA     NA       NA         NA         NA     8.6636        Inf
+
## $ff
+## Z0_free   Z2_Z3 Z2_sink Z3_free 
+## 1.00000 0.53656 0.46344 1.00000 
+## 
+## $SFORB
+##     Z0_b1     Z0_b2     Z3_b1     Z3_b2 
+## 2.4471322 0.0075125 0.0800069 0.0000000 
+## 
+## $distimes
+##      DT50   DT90 DT50back DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2
+## Z0 0.3043 1.1848  0.35666    0.28325     92.266         NA         NA
+## Z1 1.5148 5.0320       NA         NA         NA         NA         NA
+## Z2 1.6414 5.4526       NA         NA         NA         NA         NA
+## Z3     NA     NA       NA         NA         NA     8.6636        Inf

It is clear the degradation rate of Z3 towards the end of the experiment is very low as DT50_Z3_b2 (the second Eigenvalue of the system of two differential equations representing the SFORB system for Z3, corresponding to the slower rate constant of the DFOP model) is reported to be infinity. However, this appears to be a feature of the data.

-
-

-References

+
+

References +

-

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

+

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

@@ -384,11 +392,13 @@
-

Developed by Johannes Ranke.

+

+

Developed by Johannes Ranke.

-

Site built with pkgdown 1.6.1.

+

+

Site built with pkgdown 2.0.2.

@@ -397,5 +407,7 @@ + + diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png index 2e70b207..be652d31 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png differ diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png index 4a205020..bc6efaf7 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png differ diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png index 8b07d497..55c1b645 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png differ diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png index 4765c9fe..8e63cd04 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png differ diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png index e005446b..3902e059 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png differ diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png index 2e70b207..be652d31 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png differ diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png index f06ee667..59524035 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png differ diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png index b8e0e900..d95cac25 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png differ diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png index 14dd7805..cb333a1c 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png differ diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png index 414bc941..d87105fb 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png differ diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png index 0a83f8ea..db807f14 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png differ diff --git a/docs/articles/web_only/NAFTA_examples.html b/docs/articles/web_only/NAFTA_examples.html index 65a71b56..996e5d49 100644 --- a/docs/articles/web_only/NAFTA_examples.html +++ b/docs/articles/web_only/NAFTA_examples.html @@ -19,6 +19,8 @@ + +
+

Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance

-

Johannes Ranke

+

Johannes Ranke

-

26 February 2019 (rebuilt 2021-03-31)

+

26 February 2019 (rebuilt 2022-03-02)

- Source: vignettes/web_only/NAFTA_examples.rmd + Source: vignettes/web_only/NAFTA_examples.rmd
-
-

-Introduction

+
+

Introduction +

In this document, the example evaluations provided in Attachment 1 to the SOP of US EPA for using the NAFTA guidance (US EPA 2015) are repeated using mkin. The original evaluations reported in the attachment were performed using PestDF in version 0.8.4. Note that PestDF 0.8.13 is the version distributed at the US EPA website today (2019-02-26).

The datasets are now distributed with the mkin package.

-
-

-Examples where DFOP did not converge with PestDF 0.8.4

+
+

Examples where DFOP did not converge with PestDF 0.8.4 +

In attachment 1, it is reported that the DFOP model does not converge for these datasets when PestDF 0.8.4 was used. For all four datasets, the DFOP model can be fitted with mkin (see below). The negative half-life given by PestDF 0.8.4 for these fits appears to be the result of a bug. The results for the other two models (SFO and IORE) are the same.

-
-

-Example on page 5, upper panel

+
+

Example on page 5, upper panel +

 p5a <- nafta(NAFTA_SOP_Attachment[["p5a"]])
-
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
-
## The half-life obtained from the IORE model may be used
+
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
+
## The half-life obtained from the IORE model may be used
-plot(p5a)
+plot(p5a)

-print(p5a)
-
## Sums of squares:
-##       SFO      IORE      DFOP 
-## 465.21753  56.27506  32.06401 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 64.4304
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)  Lower   Upper
-## parent_0  95.8401 4.67e-21 92.245 99.4357
-## k_parent   0.0102 3.92e-12  0.009  0.0117
-## sigma      4.8230 3.81e-06  3.214  6.4318
-## 
-## $IORE
-##                Estimate Pr(>t)    Lower    Upper
-## parent_0       1.01e+02     NA 9.91e+01 1.02e+02
-## k__iore_parent 1.54e-05     NA 4.08e-06 5.84e-05
-## N_parent       2.57e+00     NA 2.25e+00 2.89e+00
-## sigma          1.68e+00     NA 1.12e+00 2.24e+00
-## 
-## $DFOP
-##          Estimate   Pr(>t)   Lower    Upper
-## parent_0 9.99e+01 1.41e-26 98.8116 101.0810
-## k1       2.67e-02 5.05e-06  0.0243   0.0295
-## k2       2.26e-12 5.00e-01  0.0000      Inf
-## g        6.47e-01 3.67e-06  0.6248   0.6677
-## sigma    1.27e+00 8.91e-06  0.8395   1.6929
-## 
-## 
-## DTx values:
-##      DT50     DT90 DT50_rep
-## SFO  67.7 2.25e+02 6.77e+01
-## IORE 58.2 1.07e+03 3.22e+02
-## DFOP 55.5 5.59e+11 3.07e+11
-## 
-## Representative half-life:
-## [1] 321.51
+print(p5a)
+
## Sums of squares:
+##       SFO      IORE      DFOP 
+## 465.21753  56.27506  32.06401 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 64.4304
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)  Lower   Upper
+## parent_0  95.8401 4.67e-21 92.245 99.4357
+## k_parent   0.0102 3.92e-12  0.009  0.0117
+## sigma      4.8230 3.81e-06  3.214  6.4318
+## 
+## $IORE
+##                Estimate Pr(>t)    Lower    Upper
+## parent_0       1.01e+02     NA 9.91e+01 1.02e+02
+## k__iore_parent 1.54e-05     NA 4.08e-06 5.84e-05
+## N_parent       2.57e+00     NA 2.25e+00 2.89e+00
+## sigma          1.68e+00     NA 1.12e+00 2.24e+00
+## 
+## $DFOP
+##          Estimate   Pr(>t)   Lower    Upper
+## parent_0 9.99e+01 1.41e-26 98.8116 101.0810
+## k1       2.67e-02 5.05e-06  0.0243   0.0295
+## k2       2.26e-12 5.00e-01  0.0000      Inf
+## g        6.47e-01 3.67e-06  0.6248   0.6677
+## sigma    1.27e+00 8.91e-06  0.8395   1.6929
+## 
+## 
+## DTx values:
+##      DT50     DT90 DT50_rep
+## SFO  67.7 2.25e+02 6.77e+01
+## IORE 58.2 1.07e+03 3.22e+02
+## DFOP 55.5 5.59e+11 3.07e+11
+## 
+## Representative half-life:
+## [1] 321.51
-
-

-Example on page 5, lower panel

+
+

Example on page 5, lower panel +

 p5b <- nafta(NAFTA_SOP_Attachment[["p5b"]])
-
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
-
## The half-life obtained from the IORE model may be used
+
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
+
## The half-life obtained from the IORE model may be used
-plot(p5b)
+plot(p5b)

-print(p5b)
-
## Sums of squares:
-##      SFO     IORE     DFOP 
-## 94.81123 10.10936  7.55871 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 11.77879
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0   96.497 2.32e-24 94.85271 98.14155
-## k_parent    0.008 3.42e-14  0.00737  0.00869
-## sigma       2.295 1.22e-05  1.47976  3.11036
-## 
-## $IORE
-##                Estimate   Pr(>t)    Lower    Upper
-## parent_0       9.85e+01 1.17e-28 9.79e+01 9.92e+01
-## k__iore_parent 1.53e-04 6.50e-03 7.21e-05 3.26e-04
-## N_parent       1.94e+00 5.88e-13 1.76e+00 2.12e+00
-## sigma          7.49e-01 1.63e-05 4.82e-01 1.02e+00
-## 
-## $DFOP
-##          Estimate   Pr(>t)   Lower   Upper
-## parent_0 9.84e+01 1.24e-27 97.8078 98.9187
-## k1       1.55e-02 4.10e-04  0.0143  0.0167
-## k2       8.63e-12 5.00e-01  0.0000     Inf
-## g        6.89e-01 2.92e-03  0.6626  0.7142
-## sigma    6.48e-01 2.38e-05  0.4147  0.8813
-## 
-## 
-## DTx values:
-##      DT50     DT90 DT50_rep
-## SFO  86.6 2.88e+02 8.66e+01
-## IORE 85.5 7.17e+02 2.16e+02
-## DFOP 83.6 1.32e+11 8.04e+10
-## 
-## Representative half-life:
-## [1] 215.87
+print(p5b)
+
## Sums of squares:
+##      SFO     IORE     DFOP 
+## 94.81123 10.10936  7.55871 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 11.77879
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0   96.497 2.32e-24 94.85271 98.14155
+## k_parent    0.008 3.42e-14  0.00737  0.00869
+## sigma       2.295 1.22e-05  1.47976  3.11036
+## 
+## $IORE
+##                Estimate   Pr(>t)    Lower    Upper
+## parent_0       9.85e+01 1.17e-28 9.79e+01 9.92e+01
+## k__iore_parent 1.53e-04 6.50e-03 7.21e-05 3.26e-04
+## N_parent       1.94e+00 5.88e-13 1.76e+00 2.12e+00
+## sigma          7.49e-01 1.63e-05 4.82e-01 1.02e+00
+## 
+## $DFOP
+##          Estimate   Pr(>t)   Lower   Upper
+## parent_0 9.84e+01 1.24e-27 97.8078 98.9187
+## k1       1.55e-02 4.10e-04  0.0143  0.0167
+## k2       8.63e-12 5.00e-01  0.0000     Inf
+## g        6.89e-01 2.92e-03  0.6626  0.7142
+## sigma    6.48e-01 2.38e-05  0.4147  0.8813
+## 
+## 
+## DTx values:
+##      DT50     DT90 DT50_rep
+## SFO  86.6 2.88e+02 8.66e+01
+## IORE 85.5 7.17e+02 2.16e+02
+## DFOP 83.6 1.32e+11 8.04e+10
+## 
+## Representative half-life:
+## [1] 215.87
-
-

-Example on page 6

+
+

Example on page 6 +

 p6 <- nafta(NAFTA_SOP_Attachment[["p6"]])
-
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
-
## The half-life obtained from the IORE model may be used
+
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
+
## The half-life obtained from the IORE model may be used
-plot(p6)
+plot(p6)

-print(p6)
-
## Sums of squares:
-##       SFO      IORE      DFOP 
-## 188.45361  51.00699  42.46931 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 58.39888
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)   Lower   Upper
-## parent_0  94.7759 7.29e-24 92.3478 97.2039
-## k_parent   0.0179 8.02e-16  0.0166  0.0194
-## sigma      3.0696 3.81e-06  2.0456  4.0936
-## 
-## $IORE
-##                Estimate   Pr(>t)    Lower    Upper
-## parent_0       97.12446 2.63e-26 95.62461 98.62431
-## k__iore_parent  0.00252 1.95e-03  0.00134  0.00472
-## N_parent        1.49587 4.07e-13  1.33896  1.65279
-## sigma           1.59698 5.05e-06  1.06169  2.13227
-## 
-## $DFOP
-##          Estimate   Pr(>t)   Lower   Upper
-## parent_0 9.66e+01 1.57e-25 95.3476 97.8979
-## k1       2.55e-02 7.33e-06  0.0233  0.0278
-## k2       3.22e-11 5.00e-01  0.0000     Inf
-## g        8.61e-01 7.55e-06  0.8314  0.8867
-## sigma    1.46e+00 6.93e-06  0.9661  1.9483
-## 
-## 
-## DTx values:
-##      DT50     DT90 DT50_rep
-## SFO  38.6 1.28e+02 3.86e+01
-## IORE 34.0 1.77e+02 5.32e+01
-## DFOP 34.1 1.01e+10 2.15e+10
-## 
-## Representative half-life:
-## [1] 53.17
+print(p6)
+
## Sums of squares:
+##       SFO      IORE      DFOP 
+## 188.45361  51.00699  42.46931 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 58.39888
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)   Lower   Upper
+## parent_0  94.7759 7.29e-24 92.3478 97.2039
+## k_parent   0.0179 8.02e-16  0.0166  0.0194
+## sigma      3.0696 3.81e-06  2.0456  4.0936
+## 
+## $IORE
+##                Estimate   Pr(>t)    Lower    Upper
+## parent_0       97.12446 2.63e-26 95.62461 98.62431
+## k__iore_parent  0.00252 1.95e-03  0.00134  0.00472
+## N_parent        1.49587 4.07e-13  1.33896  1.65279
+## sigma           1.59698 5.05e-06  1.06169  2.13227
+## 
+## $DFOP
+##          Estimate   Pr(>t)   Lower   Upper
+## parent_0 9.66e+01 1.57e-25 95.3476 97.8979
+## k1       2.55e-02 7.33e-06  0.0233  0.0278
+## k2       3.22e-11 5.00e-01  0.0000     Inf
+## g        8.61e-01 7.55e-06  0.8314  0.8867
+## sigma    1.46e+00 6.93e-06  0.9661  1.9483
+## 
+## 
+## DTx values:
+##      DT50     DT90 DT50_rep
+## SFO  38.6 1.28e+02 3.86e+01
+## IORE 34.0 1.77e+02 5.32e+01
+## DFOP 34.1 1.01e+10 2.15e+10
+## 
+## Representative half-life:
+## [1] 53.17
-
-

-Example on page 7

+
+

Example on page 7 +

 p7 <- nafta(NAFTA_SOP_Attachment[["p7"]])
-
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
-
## The half-life obtained from the IORE model may be used
+
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
+
## The half-life obtained from the IORE model may be used
-plot(p7)
+plot(p7)

-print(p7)
-
## Sums of squares:
-##      SFO     IORE     DFOP 
-## 3661.661 3195.030 3174.145 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 3334.194
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 96.41796 4.80e-53 93.32245 99.51347
-## k_parent  0.00735 7.64e-21  0.00641  0.00843
-## sigma     7.94557 1.83e-15  6.46713  9.42401
-## 
-## $IORE
-##                Estimate Pr(>t)    Lower    Upper
-## parent_0       9.92e+01     NA 9.55e+01 1.03e+02
-## k__iore_parent 1.60e-05     NA 1.45e-07 1.77e-03
-## N_parent       2.45e+00     NA 1.35e+00 3.54e+00
-## sigma          7.42e+00     NA 6.04e+00 8.80e+00
-## 
-## $DFOP
-##          Estimate   Pr(>t)   Lower    Upper
-## parent_0 9.89e+01 9.44e-49 95.4640 102.2573
-## k1       1.81e-02 1.75e-01  0.0116   0.0281
-## k2       3.63e-10 5.00e-01  0.0000      Inf
-## g        6.06e-01 2.19e-01  0.4826   0.7178
-## sigma    7.40e+00 2.97e-15  6.0201   8.7754
-## 
-## 
-## DTx values:
-##      DT50     DT90 DT50_rep
-## SFO  94.3 3.13e+02 9.43e+01
-## IORE 96.7 1.51e+03 4.55e+02
-## DFOP 96.4 3.77e+09 1.91e+09
-## 
-## Representative half-life:
-## [1] 454.55
+print(p7)
+
## Sums of squares:
+##      SFO     IORE     DFOP 
+## 3661.661 3195.030 3174.145 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 3334.194
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 96.41796 4.80e-53 93.32245 99.51347
+## k_parent  0.00735 7.64e-21  0.00641  0.00843
+## sigma     7.94557 1.83e-15  6.46713  9.42401
+## 
+## $IORE
+##                Estimate Pr(>t)    Lower    Upper
+## parent_0       9.92e+01     NA 9.55e+01 1.03e+02
+## k__iore_parent 1.60e-05     NA 1.45e-07 1.77e-03
+## N_parent       2.45e+00     NA 1.35e+00 3.54e+00
+## sigma          7.42e+00     NA 6.04e+00 8.80e+00
+## 
+## $DFOP
+##          Estimate   Pr(>t)   Lower    Upper
+## parent_0 9.89e+01 9.44e-49 95.4640 102.2573
+## k1       1.81e-02 1.75e-01  0.0116   0.0281
+## k2       3.63e-10 5.00e-01  0.0000      Inf
+## g        6.06e-01 2.19e-01  0.4826   0.7178
+## sigma    7.40e+00 2.97e-15  6.0201   8.7754
+## 
+## 
+## DTx values:
+##      DT50     DT90 DT50_rep
+## SFO  94.3 3.13e+02 9.43e+01
+## IORE 96.7 1.51e+03 4.55e+02
+## DFOP 96.4 3.77e+09 1.91e+09
+## 
+## Representative half-life:
+## [1] 454.55
-
-

-Examples where the representative half-life deviates from the observed DT50

-
-

-Example on page 8

+
+

Examples where the representative half-life deviates from the observed DT50 +

+
+

Example on page 8 +

For this dataset, the IORE fit does not converge when the default starting values used by mkin for the IORE model are used. Therefore, a lower value for the rate constant is used here.

-p8 <- nafta(NAFTA_SOP_Attachment[["p8"]], parms.ini = c(k__iore_parent = 1e-3))
-
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
-
## The half-life obtained from the IORE model may be used
+p8 <- nafta(NAFTA_SOP_Attachment[["p8"]], parms.ini = c(k__iore_parent = 1e-3))
+
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
+
## The half-life obtained from the IORE model may be used
-plot(p8)
+plot(p8)

-print(p8)
-
## Sums of squares:
-##       SFO      IORE      DFOP 
-## 1996.9408  444.9237  547.5616 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 477.4924
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 88.16549 6.53e-29 83.37344 92.95754
-## k_parent  0.00803 1.67e-13  0.00674  0.00957
-## sigma     7.44786 4.17e-10  5.66209  9.23363
-## 
-## $IORE
-##                Estimate   Pr(>t)    Lower    Upper
-## parent_0       9.77e+01 7.03e-35 9.44e+01 1.01e+02
-## k__iore_parent 6.14e-05 3.20e-02 2.12e-05 1.78e-04
-## N_parent       2.27e+00 4.23e-18 2.00e+00 2.54e+00
-## sigma          3.52e+00 5.36e-10 2.67e+00 4.36e+00
-## 
-## $DFOP
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 95.70619 8.99e-32 91.87941 99.53298
-## k1        0.02500 5.25e-04  0.01422  0.04394
-## k2        0.00273 6.84e-03  0.00125  0.00597
-## g         0.58835 2.84e-06  0.36595  0.77970
-## sigma     3.90001 6.94e-10  2.96260  4.83741
-## 
-## 
-## DTx values:
-##      DT50 DT90 DT50_rep
-## SFO  86.3  287     86.3
-## IORE 53.4  668    201.0
-## DFOP 55.6  517    253.0
-## 
-## Representative half-life:
-## [1] 201.03
+print(p8)
+
## Sums of squares:
+##       SFO      IORE      DFOP 
+## 1996.9408  444.9237  547.5616 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 477.4924
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 88.16549 6.53e-29 83.37344 92.95754
+## k_parent  0.00803 1.67e-13  0.00674  0.00957
+## sigma     7.44786 4.17e-10  5.66209  9.23363
+## 
+## $IORE
+##                Estimate   Pr(>t)    Lower    Upper
+## parent_0       9.77e+01 7.03e-35 9.44e+01 1.01e+02
+## k__iore_parent 6.14e-05 3.20e-02 2.12e-05 1.78e-04
+## N_parent       2.27e+00 4.23e-18 2.00e+00 2.54e+00
+## sigma          3.52e+00 5.36e-10 2.67e+00 4.36e+00
+## 
+## $DFOP
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 95.70619 8.99e-32 91.87941 99.53298
+## k1        0.02500 5.25e-04  0.01422  0.04394
+## k2        0.00273 6.84e-03  0.00125  0.00597
+## g         0.58835 2.84e-06  0.36595  0.77970
+## sigma     3.90001 6.94e-10  2.96260  4.83741
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  86.3  287     86.3
+## IORE 53.4  668    201.0
+## DFOP 55.6  517    253.0
+## 
+## Representative half-life:
+## [1] 201.03
-
-

-Examples where SFO was not selected for an abiotic study

-
-

-Example on page 9, upper panel

+
+

Examples where SFO was not selected for an abiotic study +

+
+

Example on page 9, upper panel +

 p9a <- nafta(NAFTA_SOP_Attachment[["p9a"]])
-
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
-
## The half-life obtained from the IORE model may be used
+
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
+
## The half-life obtained from the IORE model may be used
-plot(p9a)
+plot(p9a)

-print(p9a)
-
## Sums of squares:
-##       SFO      IORE      DFOP 
-## 839.35238  88.57064   9.93363 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 105.5678
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)   Lower   Upper
-## parent_0  88.1933 3.06e-12 79.9447 96.4419
-## k_parent   0.0409 2.07e-07  0.0324  0.0516
-## sigma      7.2429 3.92e-05  4.4768 10.0090
-## 
-## $IORE
-##                Estimate   Pr(>t)    Lower    Upper
-## parent_0       9.89e+01 1.12e-16 9.54e+01 1.02e+02
-## k__iore_parent 1.93e-05 1.13e-01 3.49e-06 1.06e-04
-## N_parent       2.91e+00 1.45e-09 2.50e+00 3.32e+00
-## sigma          2.35e+00 5.31e-05 1.45e+00 3.26e+00
-## 
-## $DFOP
-##          Estimate   Pr(>t)  Lower  Upper
-## parent_0 9.85e+01 2.54e-20 97.390 99.672
-## k1       1.38e-01 3.52e-05  0.131  0.146
-## k2       9.02e-13 5.00e-01  0.000    Inf
-## g        6.52e-01 8.13e-06  0.642  0.661
-## sigma    7.88e-01 6.13e-02  0.481  1.095
-## 
-## 
-## DTx values:
-##      DT50     DT90 DT50_rep
-## SFO  16.9 5.63e+01 1.69e+01
-## IORE 11.6 3.37e+02 1.01e+02
-## DFOP 10.5 1.38e+12 7.69e+11
-## 
-## Representative half-life:
-## [1] 101.43
+print(p9a)
+
## Sums of squares:
+##       SFO      IORE      DFOP 
+## 839.35238  88.57064   9.93363 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 105.5678
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)   Lower   Upper
+## parent_0  88.1933 3.06e-12 79.9447 96.4419
+## k_parent   0.0409 2.07e-07  0.0324  0.0516
+## sigma      7.2429 3.92e-05  4.4768 10.0090
+## 
+## $IORE
+##                Estimate   Pr(>t)    Lower    Upper
+## parent_0       9.89e+01 1.12e-16 9.54e+01 1.02e+02
+## k__iore_parent 1.93e-05 1.13e-01 3.49e-06 1.06e-04
+## N_parent       2.91e+00 1.45e-09 2.50e+00 3.32e+00
+## sigma          2.35e+00 5.31e-05 1.45e+00 3.26e+00
+## 
+## $DFOP
+##          Estimate   Pr(>t)  Lower  Upper
+## parent_0 9.85e+01 2.54e-20 97.390 99.672
+## k1       1.38e-01 3.52e-05  0.131  0.146
+## k2       9.02e-13 5.00e-01  0.000    Inf
+## g        6.52e-01 8.13e-06  0.642  0.661
+## sigma    7.88e-01 6.13e-02  0.481  1.095
+## 
+## 
+## DTx values:
+##      DT50     DT90 DT50_rep
+## SFO  16.9 5.63e+01 1.69e+01
+## IORE 11.6 3.37e+02 1.01e+02
+## DFOP 10.5 1.38e+12 7.69e+11
+## 
+## Representative half-life:
+## [1] 101.43

In this example, the residuals of the SFO indicate a lack of fit of this model, so even if it was an abiotic experiment, the data do not suggest a simple exponential decline.

-
-

-Example on page 9, lower panel

+
+

Example on page 9, lower panel +

 p9b <- nafta(NAFTA_SOP_Attachment[["p9b"]])
-
## Warning in sqrt(diag(covar)): NaNs produced
-
## Warning in sqrt(diag(covar_notrans)): NaNs produced
-
## Warning in sqrt(1/diag(V)): NaNs produced
-
## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
-## doubtful
-
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
-
## The half-life obtained from the IORE model may be used
+
## Warning in sqrt(diag(covar)): NaNs produced
+
## Warning in sqrt(diag(covar_notrans)): NaNs produced
+
## Warning in sqrt(1/diag(V)): NaNs produced
+
## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful
+
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
+
## The half-life obtained from the IORE model may be used
-plot(p9b)
+plot(p9b)

-print(p9b)
-
## Sums of squares:
-##      SFO     IORE     DFOP 
-## 35.64867 23.22334 35.64867 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 28.54188
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)  Lower   Upper
-## parent_0  94.7123 2.15e-19 93.178 96.2464
-## k_parent   0.0389 4.47e-14  0.037  0.0408
-## sigma      1.5957 1.28e-04  0.932  2.2595
-## 
-## $IORE
-##                Estimate   Pr(>t)   Lower  Upper
-## parent_0         93.863 2.32e-18 92.4565 95.269
-## k__iore_parent    0.127 1.85e-02  0.0504  0.321
-## N_parent          0.711 1.88e-05  0.4843  0.937
-## sigma             1.288 1.76e-04  0.7456  1.830
-## 
-## $DFOP
-##          Estimate   Pr(>t)   Lower   Upper
-## parent_0  94.7123 1.61e-16 93.1355 96.2891
-## k1         0.0389 1.08e-04  0.0266  0.0569
-## k2         0.0389 2.23e-04  0.0255  0.0592
-## g          0.5256      NaN      NA      NA
-## sigma      1.5957 2.50e-04  0.9135  2.2779
-## 
-## 
-## DTx values:
-##      DT50 DT90 DT50_rep
-## SFO  17.8 59.2     17.8
-## IORE 18.4 49.2     14.8
-## DFOP 17.8 59.2     17.8
-## 
-## Representative half-life:
-## [1] 14.8
+print(p9b)
+
## Sums of squares:
+##      SFO     IORE     DFOP 
+## 35.64867 23.22334 35.64867 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 28.54188
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)  Lower   Upper
+## parent_0  94.7123 2.15e-19 93.178 96.2464
+## k_parent   0.0389 4.47e-14  0.037  0.0408
+## sigma      1.5957 1.28e-04  0.932  2.2595
+## 
+## $IORE
+##                Estimate   Pr(>t)   Lower  Upper
+## parent_0         93.863 2.32e-18 92.4565 95.269
+## k__iore_parent    0.127 1.85e-02  0.0504  0.321
+## N_parent          0.711 1.88e-05  0.4843  0.937
+## sigma             1.288 1.76e-04  0.7456  1.830
+## 
+## $DFOP
+##          Estimate   Pr(>t)   Lower   Upper
+## parent_0  94.7123 1.61e-16 93.1355 96.2891
+## k1         0.0389 1.08e-04  0.0266  0.0569
+## k2         0.0389 2.23e-04  0.0255  0.0592
+## g          0.5256      NaN      NA      NA
+## sigma      1.5957 2.50e-04  0.9135  2.2779
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  17.8 59.2     17.8
+## IORE 18.4 49.2     14.8
+## DFOP 17.8 59.2     17.8
+## 
+## Representative half-life:
+## [1] 14.8

Here, mkin gives a longer slow DT50 for the DFOP model (17.8 days) than PestDF (13.5 days). Presumably, this is related to the fact that PestDF gives a negative value for the proportion of the fast degradation which should be between 0 and 1, inclusive. This parameter is called f in PestDF and g in mkin. In mkin, it is restricted to the interval from 0 to 1.

-
-

-Example on page 10

+
+

Example on page 10 +

 p10 <- nafta(NAFTA_SOP_Attachment[["p10"]])
-
## Warning in sqrt(diag(covar)): NaNs produced
-
## Warning in sqrt(1/diag(V)): NaNs produced
-
## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
-## doubtful
-
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
-
## The half-life obtained from the IORE model may be used
+
## Warning in sqrt(diag(covar)): NaNs produced
+
## Warning in sqrt(1/diag(V)): NaNs produced
+
## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful
+
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
+
## The half-life obtained from the IORE model may be used
-plot(p10)
+plot(p10)

-print(p10)
-
## Sums of squares:
-##      SFO     IORE     DFOP 
-## 899.4089 336.4348 899.4089 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 413.4841
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)   Lower    Upper
-## parent_0 101.7315 6.42e-11 91.9259 111.5371
-## k_parent   0.0495 1.70e-07  0.0404   0.0607
-## sigma      8.0152 1.28e-04  4.6813  11.3491
-## 
-## $IORE
-##                Estimate   Pr(>t)  Lower   Upper
-## parent_0          96.86 3.32e-12 90.848 102.863
-## k__iore_parent     2.96 7.91e-02  0.687  12.761
-## N_parent           0.00 5.00e-01 -0.372   0.372
-## sigma              4.90 1.77e-04  2.837   6.968
-## 
-## $DFOP
-##          Estimate   Pr(>t)   Lower    Upper
-## parent_0 101.7315 1.41e-09 91.6534 111.8097
-## k1         0.0495 6.58e-03  0.0303   0.0809
-## k2         0.0495 2.60e-03  0.0410   0.0598
-## g          0.4487 5.00e-01      NA       NA
-## sigma      8.0152 2.50e-04  4.5886  11.4418
-## 
-## 
-## DTx values:
-##      DT50 DT90 DT50_rep
-## SFO  14.0 46.5    14.00
-## IORE 16.4 29.4     8.86
-## DFOP 14.0 46.5    14.00
-## 
-## Representative half-life:
-## [1] 8.86
+print(p10)
+
## Sums of squares:
+##      SFO     IORE     DFOP 
+## 899.4089 336.4348 899.4089 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 413.4841
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)   Lower    Upper
+## parent_0 101.7315 6.42e-11 91.9259 111.5371
+## k_parent   0.0495 1.70e-07  0.0404   0.0607
+## sigma      8.0152 1.28e-04  4.6813  11.3491
+## 
+## $IORE
+##                Estimate   Pr(>t)  Lower   Upper
+## parent_0          96.86 3.32e-12 90.848 102.863
+## k__iore_parent     2.96 7.91e-02  0.687  12.761
+## N_parent           0.00 5.00e-01 -0.372   0.372
+## sigma              4.90 1.77e-04  2.837   6.968
+## 
+## $DFOP
+##          Estimate   Pr(>t)   Lower    Upper
+## parent_0 101.7315 1.41e-09 91.6534 111.8097
+## k1         0.0495 6.58e-03  0.0303   0.0809
+## k2         0.0495 2.60e-03  0.0410   0.0598
+## g          0.4487 5.00e-01      NA       NA
+## sigma      8.0152 2.50e-04  4.5886  11.4418
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  14.0 46.5    14.00
+## IORE 16.4 29.4     8.86
+## DFOP 14.0 46.5    14.00
+## 
+## Representative half-life:
+## [1] 8.86

Here, a value below N is given for the IORE model, because the data suggests a faster decline towards the end of the experiment, which appears physically rather unlikely in the case of a photolysis study. It seems PestDF does not constrain N to values above zero, thus the slight difference in IORE model parameters between PestDF and mkin.

-
-

-The DT50 was not observed during the study

-
-

-Example on page 11

+
+

The DT50 was not observed during the study +

+
+

Example on page 11 +

 p11 <- nafta(NAFTA_SOP_Attachment[["p11"]])
-
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
-
## The half-life obtained from the IORE model may be used
+
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
+
## The half-life obtained from the IORE model may be used
-plot(p11)
+plot(p11)

-print(p11)
-
## Sums of squares:
-##      SFO     IORE     DFOP 
-## 579.6805 204.7932 144.7783 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 251.6944
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 96.15820 4.83e-13 90.24934 1.02e+02
-## k_parent  0.00321 4.71e-05  0.00222 4.64e-03
-## sigma     6.43473 1.28e-04  3.75822 9.11e+00
-## 
-## $IORE
-##                Estimate Pr(>t)    Lower    Upper
-## parent_0       1.05e+02     NA 9.90e+01 1.10e+02
-## k__iore_parent 3.11e-17     NA 1.35e-20 7.18e-14
-## N_parent       8.36e+00     NA 6.62e+00 1.01e+01
-## sigma          3.82e+00     NA 2.21e+00 5.44e+00
-## 
-## $DFOP
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 1.05e+02 9.47e-13  99.9990 109.1224
-## k1       4.41e-02 5.95e-03   0.0296   0.0658
-## k2       9.94e-13 5.00e-01   0.0000      Inf
-## g        3.22e-01 1.45e-03   0.2814   0.3650
-## sigma    3.22e+00 3.52e-04   1.8410   4.5906
-## 
-## 
-## DTx values:
-##          DT50     DT90 DT50_rep
-## SFO  2.16e+02 7.18e+02 2.16e+02
-## IORE 9.73e+02 1.37e+08 4.11e+07
-## DFOP 3.07e+11 1.93e+12 6.98e+11
-## 
-## Representative half-life:
-## [1] 41148170
+print(p11)
+
## Sums of squares:
+##      SFO     IORE     DFOP 
+## 579.6805 204.7932 144.7783 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 251.6944
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 96.15820 4.83e-13 90.24934 1.02e+02
+## k_parent  0.00321 4.71e-05  0.00222 4.64e-03
+## sigma     6.43473 1.28e-04  3.75822 9.11e+00
+## 
+## $IORE
+##                Estimate Pr(>t)    Lower    Upper
+## parent_0       1.05e+02     NA 9.90e+01 1.10e+02
+## k__iore_parent 3.11e-17     NA 1.35e-20 7.18e-14
+## N_parent       8.36e+00     NA 6.62e+00 1.01e+01
+## sigma          3.82e+00     NA 2.21e+00 5.44e+00
+## 
+## $DFOP
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 1.05e+02 9.47e-13  99.9990 109.1224
+## k1       4.41e-02 5.95e-03   0.0296   0.0658
+## k2       9.94e-13 5.00e-01   0.0000      Inf
+## g        3.22e-01 1.45e-03   0.2814   0.3650
+## sigma    3.22e+00 3.52e-04   1.8410   4.5906
+## 
+## 
+## DTx values:
+##          DT50     DT90 DT50_rep
+## SFO  2.16e+02 7.18e+02 2.16e+02
+## IORE 9.73e+02 1.37e+08 4.11e+07
+## DFOP 3.07e+11 1.93e+12 6.98e+11
+## 
+## Representative half-life:
+## [1] 41148170

In this case, the DFOP fit reported for PestDF resulted in a negative value for the slower rate constant, which is not possible in mkin. The other results are in agreement.

-
-

-N is less than 1 and the DFOP rate constants are like the SFO rate constant

+
+

N is less than 1 and the DFOP rate constants are like the SFO rate constant +

In the following three examples, the same results are obtained with mkin as reported for PestDF. As in the case on page 10, the N values below 1 are deemed unrealistic and appear to be the result of an overparameterisation.

-
-

-Example on page 12, upper panel

+
+

Example on page 12, upper panel +

 p12a <- nafta(NAFTA_SOP_Attachment[["p12a"]])
-
## Warning in summary.mkinfit(x): Could not calculate correlation; no covariance
-## matrix
-
## Warning in sqrt(diag(covar)): NaNs produced
-
## Warning in sqrt(diag(covar_notrans)): NaNs produced
-
## Warning in sqrt(1/diag(V)): NaNs produced
-
## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
-## doubtful
-
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
-
## The half-life obtained from the IORE model may be used
+
## Warning in summary.mkinfit(x): Could not calculate correlation; no covariance
+## matrix
+
## Warning in sqrt(diag(covar)): NaNs produced
+
## Warning in sqrt(diag(covar_notrans)): NaNs produced
+
## Warning in sqrt(1/diag(V)): NaNs produced
+
## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful
+
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
+
## The half-life obtained from the IORE model may be used
-plot(p12a)
+plot(p12a)

-print(p12a)
-
## Sums of squares:
-##      SFO     IORE     DFOP 
-## 695.4440 220.0685 695.4440 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 270.4679
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)  Lower   Upper
-## parent_0  100.521 8.75e-12 92.461 108.581
-## k_parent    0.124 3.61e-08  0.104   0.148
-## sigma       7.048 1.28e-04  4.116   9.980
-## 
-## $IORE
-##                Estimate Pr(>t) Lower Upper
-## parent_0         96.823     NA    NA    NA
-## k__iore_parent    2.436     NA    NA    NA
-## N_parent          0.263     NA    NA    NA
-## sigma             3.965     NA    NA    NA
-## 
-## $DFOP
-##          Estimate   Pr(>t)   Lower   Upper
-## parent_0  100.521 2.74e-10 92.2366 108.805
-## k1          0.124 2.53e-05  0.0908   0.170
-## k2          0.124 2.52e-02  0.0456   0.339
-## g           0.793      NaN      NA      NA
-## sigma       7.048 2.50e-04  4.0349  10.061
-## 
-## 
-## DTx values:
-##      DT50 DT90 DT50_rep
-## SFO  5.58 18.5     5.58
-## IORE 6.49 13.2     3.99
-## DFOP 5.58 18.5     5.58
-## 
-## Representative half-life:
-## [1] 3.99
+print(p12a)
+
## Sums of squares:
+##      SFO     IORE     DFOP 
+## 695.4440 220.0685 695.4440 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 270.4679
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)  Lower   Upper
+## parent_0  100.521 8.75e-12 92.461 108.581
+## k_parent    0.124 3.61e-08  0.104   0.148
+## sigma       7.048 1.28e-04  4.116   9.980
+## 
+## $IORE
+##                Estimate Pr(>t) Lower Upper
+## parent_0         96.823     NA    NA    NA
+## k__iore_parent    2.436     NA    NA    NA
+## N_parent          0.263     NA    NA    NA
+## sigma             3.965     NA    NA    NA
+## 
+## $DFOP
+##          Estimate   Pr(>t)   Lower   Upper
+## parent_0  100.521 2.74e-10 92.2366 108.805
+## k1          0.124 2.53e-05  0.0908   0.170
+## k2          0.124 2.52e-02  0.0456   0.339
+## g           0.793      NaN      NA      NA
+## sigma       7.048 2.50e-04  4.0349  10.061
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  5.58 18.5     5.58
+## IORE 6.49 13.2     3.99
+## DFOP 5.58 18.5     5.58
+## 
+## Representative half-life:
+## [1] 3.99
-
-

-Example on page 12, lower panel

+
+

Example on page 12, lower panel +

 p12b <- nafta(NAFTA_SOP_Attachment[["p12b"]])
-
## Warning in qt(alpha/2, rdf): NaNs produced
-
## Warning in qt(1 - alpha/2, rdf): NaNs produced
-
## Warning in sqrt(diag(covar_notrans)): NaNs produced
-
## Warning in pt(abs(tval), rdf, lower.tail = FALSE): NaNs produced
-
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
-
## The half-life obtained from the IORE model may be used
+
## Warning in qt(alpha/2, rdf): NaNs produced
+
## Warning in qt(1 - alpha/2, rdf): NaNs produced
+
## Warning in sqrt(diag(covar_notrans)): NaNs produced
+
## Warning in pt(abs(tval), rdf, lower.tail = FALSE): NaNs produced
+
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
+
## The half-life obtained from the IORE model may be used
-plot(p12b)
+plot(p12b)

-print(p12b)
-
## Sums of squares:
-##      SFO     IORE     DFOP 
-## 58.90242 19.06353 58.90242 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 51.51756
-## 
-## Parameters:
-## $SFO
-##          Estimate  Pr(>t)   Lower    Upper
-## parent_0  97.6840 0.00039 85.9388 109.4292
-## k_parent   0.0589 0.00261  0.0431   0.0805
-## sigma      3.4323 0.04356 -1.2377   8.1023
-## 
-## $IORE
-##                Estimate Pr(>t)     Lower  Upper
-## parent_0         95.523 0.0055 74.539157 116.51
-## k__iore_parent    0.333 0.1433  0.000717 154.57
-## N_parent          0.568 0.0677 -0.989464   2.13
-## sigma             1.953 0.0975 -5.893100   9.80
-## 
-## $DFOP
-##          Estimate Pr(>t) Lower Upper
-## parent_0  97.6840    NaN   NaN   NaN
-## k1         0.0589    NaN    NA    NA
-## k2         0.0589    NaN    NA    NA
-## g          0.6473    NaN    NA    NA
-## sigma      3.4323    NaN   NaN   NaN
-## 
-## 
-## DTx values:
-##      DT50 DT90 DT50_rep
-## SFO  11.8 39.1    11.80
-## IORE 12.9 31.4     9.46
-## DFOP 11.8 39.1    11.80
-## 
-## Representative half-life:
-## [1] 9.46
+print(p12b)
+
## Sums of squares:
+##      SFO     IORE     DFOP 
+## 58.90242 19.06353 58.90242 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 51.51756
+## 
+## Parameters:
+## $SFO
+##          Estimate  Pr(>t)   Lower    Upper
+## parent_0  97.6840 0.00039 85.9388 109.4292
+## k_parent   0.0589 0.00261  0.0431   0.0805
+## sigma      3.4323 0.04356 -1.2377   8.1023
+## 
+## $IORE
+##                Estimate Pr(>t)     Lower  Upper
+## parent_0         95.523 0.0055 74.539157 116.51
+## k__iore_parent    0.333 0.1433  0.000717 154.57
+## N_parent          0.568 0.0677 -0.989464   2.13
+## sigma             1.953 0.0975 -5.893100   9.80
+## 
+## $DFOP
+##          Estimate Pr(>t) Lower Upper
+## parent_0  97.6840    NaN   NaN   NaN
+## k1         0.0589    NaN    NA    NA
+## k2         0.0589    NaN    NA    NA
+## g          0.6473    NaN    NA    NA
+## sigma      3.4323    NaN   NaN   NaN
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  11.8 39.1    11.80
+## IORE 12.9 31.4     9.46
+## DFOP 11.8 39.1    11.80
+## 
+## Representative half-life:
+## [1] 9.46
-
-

-Example on page 13

+
+

Example on page 13 +

 p13 <- nafta(NAFTA_SOP_Attachment[["p13"]])
-
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
-
## The half-life obtained from the IORE model may be used
+
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
+
## The half-life obtained from the IORE model may be used
-plot(p13)
+plot(p13)

-print(p13)
-
## Sums of squares:
-##      SFO     IORE     DFOP 
-## 174.5971 142.3951 174.5971 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 172.131
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 92.73500 5.99e-17 89.61936 95.85065
-## k_parent  0.00258 2.42e-09  0.00223  0.00299
-## sigma     3.41172 7.07e-05  2.05455  4.76888
-## 
-## $IORE
-##                Estimate   Pr(>t)    Lower  Upper
-## parent_0        91.6016 6.34e-16 88.53086 94.672
-## k__iore_parent   0.0396 2.36e-01  0.00207  0.759
-## N_parent         0.3541 1.46e-01 -0.35153  1.060
-## sigma            3.0811 9.64e-05  1.84296  4.319
-## 
-## $DFOP
-##          Estimate Pr(>t)    Lower    Upper
-## parent_0 92.73500     NA 8.95e+01 95.92118
-## k1        0.00258     NA 4.14e-04  0.01611
-## k2        0.00258     NA 1.74e-03  0.00383
-## g         0.16452     NA 0.00e+00  1.00000
-## sigma     3.41172     NA 2.02e+00  4.79960
-## 
-## 
-## DTx values:
-##      DT50 DT90 DT50_rep
-## SFO   269  892      269
-## IORE  261  560      169
-## DFOP  269  892      269
-## 
-## Representative half-life:
-## [1] 168.51
+print(p13)
+
## Sums of squares:
+##      SFO     IORE     DFOP 
+## 174.5971 142.3951 174.5971 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 172.131
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 92.73500 5.99e-17 89.61936 95.85065
+## k_parent  0.00258 2.42e-09  0.00223  0.00299
+## sigma     3.41172 7.07e-05  2.05455  4.76888
+## 
+## $IORE
+##                Estimate   Pr(>t)    Lower  Upper
+## parent_0        91.6016 6.34e-16 88.53086 94.672
+## k__iore_parent   0.0396 2.36e-01  0.00207  0.759
+## N_parent         0.3541 1.46e-01 -0.35153  1.060
+## sigma            3.0811 9.64e-05  1.84296  4.319
+## 
+## $DFOP
+##          Estimate Pr(>t)    Lower    Upper
+## parent_0 92.73500     NA 8.95e+01 95.92118
+## k1        0.00258     NA 4.14e-04  0.01611
+## k2        0.00258     NA 1.74e-03  0.00383
+## g         0.16452     NA 0.00e+00  1.00000
+## sigma     3.41172     NA 2.02e+00  4.79960
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO   269  892      269
+## IORE  261  560      169
+## DFOP  269  892      269
+## 
+## Representative half-life:
+## [1] 168.51
-
-

-DT50 not observed in the study and DFOP problems in PestDF

+
+

DT50 not observed in the study and DFOP problems in PestDF +

 p14 <- nafta(NAFTA_SOP_Attachment[["p14"]])
-
## Warning in sqrt(diag(covar)): NaNs produced
-
## Warning in sqrt(1/diag(V)): NaNs produced
-
## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
-## doubtful
-
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
-
## The half-life obtained from the IORE model may be used
+
## Warning in sqrt(diag(covar)): NaNs produced
+
## Warning in sqrt(1/diag(V)): NaNs produced
+
## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful
+
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
+
## The half-life obtained from the IORE model may be used
-plot(p14)
+plot(p14)

-print(p14)
-
## Sums of squares:
-##      SFO     IORE     DFOP 
-## 48.43249 28.67746 27.26248 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 32.83337
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 99.47124 2.06e-30 98.42254 1.01e+02
-## k_parent  0.00279 3.75e-15  0.00256 3.04e-03
-## sigma     1.55616 3.81e-06  1.03704 2.08e+00
-## 
-## $IORE
-##                Estimate Pr(>t) Lower Upper
-## parent_0       1.00e+02     NA   NaN   NaN
-## k__iore_parent 9.44e-08     NA   NaN   NaN
-## N_parent       3.31e+00     NA   NaN   NaN
-## sigma          1.20e+00     NA 0.796   1.6
-## 
-## $DFOP
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 1.00e+02 2.96e-28 99.40280 101.2768
-## k1       9.53e-03 1.20e-01  0.00638   0.0143
-## k2       6.08e-12 5.00e-01  0.00000      Inf
-## g        3.98e-01 2.19e-01  0.30481   0.4998
-## sigma    1.17e+00 7.68e-06  0.77406   1.5610
-## 
-## 
-## DTx values:
-##          DT50     DT90 DT50_rep
-## SFO  2.48e+02 8.25e+02 2.48e+02
-## IORE 4.34e+02 2.22e+04 6.70e+03
-## DFOP 3.05e+10 2.95e+11 1.14e+11
-## 
-## Representative half-life:
-## [1] 6697.44
+print(p14)
+
## Sums of squares:
+##      SFO     IORE     DFOP 
+## 48.43249 28.67746 27.26248 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 32.83337
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 99.47124 2.06e-30 98.42254 1.01e+02
+## k_parent  0.00279 3.75e-15  0.00256 3.04e-03
+## sigma     1.55616 3.81e-06  1.03704 2.08e+00
+## 
+## $IORE
+##                Estimate Pr(>t) Lower Upper
+## parent_0       1.00e+02     NA   NaN   NaN
+## k__iore_parent 9.44e-08     NA   NaN   NaN
+## N_parent       3.31e+00     NA   NaN   NaN
+## sigma          1.20e+00     NA 0.796   1.6
+## 
+## $DFOP
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 1.00e+02 2.96e-28 99.40280 101.2768
+## k1       9.53e-03 1.20e-01  0.00638   0.0143
+## k2       6.08e-12 5.00e-01  0.00000      Inf
+## g        3.98e-01 2.19e-01  0.30481   0.4998
+## sigma    1.17e+00 7.68e-06  0.77406   1.5610
+## 
+## 
+## DTx values:
+##          DT50     DT90 DT50_rep
+## SFO  2.48e+02 8.25e+02 2.48e+02
+## IORE 4.34e+02 2.22e+04 6.70e+03
+## DFOP 3.05e+10 2.95e+11 1.14e+11
+## 
+## Representative half-life:
+## [1] 6697.44

The slower rate constant reported by PestDF is negative, which is not physically realistic, and not possible in mkin. The other fits give the same results in mkin and PestDF.

-
-

-N is less than 1 and DFOP fraction parameter is below zero

+
+

N is less than 1 and DFOP fraction parameter is below zero +

 p15a <- nafta(NAFTA_SOP_Attachment[["p15a"]])
-
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
-
## The half-life obtained from the IORE model may be used
+
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
+
## The half-life obtained from the IORE model may be used
-plot(p15a)
+plot(p15a)

-print(p15a)
-
## Sums of squares:
-##      SFO     IORE     DFOP 
-## 245.5248 135.0132 245.5248 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 165.9335
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)    Lower   Upper
-## parent_0 97.96751 2.00e-15 94.32049 101.615
-## k_parent  0.00952 4.93e-09  0.00824   0.011
-## sigma     4.18778 1.28e-04  2.44588   5.930
-## 
-## $IORE
-##                Estimate   Pr(>t)  Lower  Upper
-## parent_0         95.874 2.94e-15 92.937 98.811
-## k__iore_parent    0.629 2.11e-01  0.044  8.982
-## N_parent          0.000 5.00e-01 -0.642  0.642
-## sigma             3.105 1.78e-04  1.795  4.416
-## 
-## $DFOP
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 97.96751 2.85e-13 94.21913 101.7159
-## k1        0.00952 6.28e-02  0.00250   0.0363
-## k2        0.00952 1.27e-04  0.00646   0.0140
-## g         0.21241 5.00e-01  0.00000   1.0000
-## sigma     4.18778 2.50e-04  2.39747   5.9781
-## 
-## 
-## DTx values:
-##      DT50 DT90 DT50_rep
-## SFO  72.8  242     72.8
-## IORE 76.3  137     41.3
-## DFOP 72.8  242     72.8
-## 
-## Representative half-life:
-## [1] 41.33
+print(p15a)
+
## Sums of squares:
+##      SFO     IORE     DFOP 
+## 245.5248 135.0132 245.5248 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 165.9335
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)    Lower   Upper
+## parent_0 97.96751 2.00e-15 94.32049 101.615
+## k_parent  0.00952 4.93e-09  0.00824   0.011
+## sigma     4.18778 1.28e-04  2.44588   5.930
+## 
+## $IORE
+##                Estimate   Pr(>t)  Lower  Upper
+## parent_0         95.874 2.94e-15 92.937 98.811
+## k__iore_parent    0.629 2.11e-01  0.044  8.982
+## N_parent          0.000 5.00e-01 -0.642  0.642
+## sigma             3.105 1.78e-04  1.795  4.416
+## 
+## $DFOP
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 97.96751 2.85e-13 94.21913 101.7159
+## k1        0.00952 6.28e-02  0.00250   0.0363
+## k2        0.00952 1.27e-04  0.00646   0.0140
+## g         0.21241 5.00e-01  0.00000   1.0000
+## sigma     4.18778 2.50e-04  2.39747   5.9781
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  72.8  242     72.8
+## IORE 76.3  137     41.3
+## DFOP 72.8  242     72.8
+## 
+## Representative half-life:
+## [1] 41.33
 p15b <- nafta(NAFTA_SOP_Attachment[["p15b"]])
-
## Warning in sqrt(diag(covar)): NaNs produced
-
## Warning in sqrt(1/diag(V)): NaNs produced
-
## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
-## doubtful
-
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
-
## The half-life obtained from the IORE model may be used
+
## Warning in sqrt(diag(covar)): NaNs produced
+
## Warning in sqrt(1/diag(V)): NaNs produced
+
## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful
+
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
+
## The half-life obtained from the IORE model may be used
-plot(p15b)
+plot(p15b) 

-print(p15b)
-
## Sums of squares:
-##       SFO      IORE      DFOP 
-## 106.91629  68.55574 106.91629 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 84.25618
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 1.01e+02 3.06e-17 98.31594 1.03e+02
-## k_parent 4.86e-03 2.48e-10  0.00435 5.42e-03
-## sigma    2.76e+00 1.28e-04  1.61402 3.91e+00
-## 
-## $IORE
-##                Estimate   Pr(>t)    Lower  Upper
-## parent_0          99.83 1.81e-16 97.51349 102.14
-## k__iore_parent     0.38 3.22e-01  0.00352  41.05
-## N_parent           0.00 5.00e-01 -1.07696   1.08
-## sigma              2.21 2.57e-04  1.23245   3.19
-## 
-## $DFOP
-##          Estimate Pr(>t)    Lower    Upper
-## parent_0 1.01e+02     NA 9.82e+01 1.04e+02
-## k1       4.86e-03     NA 8.63e-04 2.73e-02
-## k2       4.86e-03     NA 3.21e-03 7.35e-03
-## g        1.88e-01     NA       NA       NA
-## sigma    2.76e+00     NA 1.58e+00 3.94e+00
-## 
-## 
-## DTx values:
-##      DT50 DT90 DT50_rep
-## SFO   143  474    143.0
-## IORE  131  236     71.2
-## DFOP  143  474    143.0
-## 
-## Representative half-life:
-## [1] 71.18
+print(p15b) +
## Sums of squares:
+##       SFO      IORE      DFOP 
+## 106.91629  68.55574 106.91629 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 84.25618
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 1.01e+02 3.06e-17 98.31594 1.03e+02
+## k_parent 4.86e-03 2.48e-10  0.00435 5.42e-03
+## sigma    2.76e+00 1.28e-04  1.61402 3.91e+00
+## 
+## $IORE
+##                Estimate   Pr(>t)    Lower  Upper
+## parent_0          99.83 1.81e-16 97.51349 102.14
+## k__iore_parent     0.38 3.22e-01  0.00352  41.05
+## N_parent           0.00 5.00e-01 -1.07696   1.08
+## sigma              2.21 2.57e-04  1.23245   3.19
+## 
+## $DFOP
+##          Estimate Pr(>t)    Lower    Upper
+## parent_0 1.01e+02     NA 9.82e+01 1.04e+02
+## k1       4.86e-03     NA 8.63e-04 2.73e-02
+## k2       4.86e-03     NA 3.21e-03 7.35e-03
+## g        1.88e-01     NA       NA       NA
+## sigma    2.76e+00     NA 1.58e+00 3.94e+00
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO   143  474    143.0
+## IORE  131  236     71.2
+## DFOP  143  474    143.0
+## 
+## Representative half-life:
+## [1] 71.18

In mkin, only the IORE fit is affected (deemed unrealistic), as the fraction parameter of the DFOP model is restricted to the interval between 0 and 1 in mkin. The SFO fits give the same results for both mkin and PestDF.

-
-

-The DFOP fraction parameter is greater than 1

+
+

The DFOP fraction parameter is greater than 1 +

 p16 <- nafta(NAFTA_SOP_Attachment[["p16"]])
-
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
-
## The representative half-life of the IORE model is longer than the one corresponding
-
## to the terminal degradation rate found with the DFOP model.
-
## The representative half-life obtained from the DFOP model may be used
+
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
+
## The representative half-life of the IORE model is longer than the one corresponding
+
## to the terminal degradation rate found with the DFOP model.
+
## The representative half-life obtained from the DFOP model may be used
-plot(p16)
+plot(p16)

-print(p16)
-
## Sums of squares:
-##      SFO     IORE     DFOP 
-## 3831.804 2062.008 1550.980 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 2247.348
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)  Lower Upper
-## parent_0   71.953 2.33e-13 60.509 83.40
-## k_parent    0.159 4.86e-05  0.102  0.25
-## sigma      11.302 1.25e-08  8.308 14.30
-## 
-## $IORE
-##                Estimate   Pr(>t)    Lower    Upper
-## parent_0       8.74e+01 2.48e-16 7.72e+01 97.52972
-## k__iore_parent 4.55e-04 2.16e-01 3.48e-05  0.00595
-## N_parent       2.70e+00 1.21e-08 1.99e+00  3.40046
-## sigma          8.29e+00 1.61e-08 6.09e+00 10.49062
-## 
-## $DFOP
-##          Estimate   Pr(>t)   Lower  Upper
-## parent_0  88.5333 7.40e-18 79.9836 97.083
-## k1        18.8461 5.00e-01  0.0000    Inf
-## k2         0.0776 1.41e-05  0.0518  0.116
-## g          0.4733 1.41e-09  0.3674  0.582
-## sigma      7.1902 2.11e-08  5.2785  9.102
-## 
-## 
-## DTx values:
-##      DT50 DT90 DT50_rep
-## SFO  4.35 14.4     4.35
-## IORE 1.48 32.1     9.67
-## DFOP 0.67 21.4     8.93
-## 
-## Representative half-life:
-## [1] 8.93
+print(p16)
+
## Sums of squares:
+##      SFO     IORE     DFOP 
+## 3831.804 2062.008 1550.980 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 2247.348
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)  Lower Upper
+## parent_0   71.953 2.33e-13 60.509 83.40
+## k_parent    0.159 4.86e-05  0.102  0.25
+## sigma      11.302 1.25e-08  8.308 14.30
+## 
+## $IORE
+##                Estimate   Pr(>t)    Lower    Upper
+## parent_0       8.74e+01 2.48e-16 7.72e+01 97.52972
+## k__iore_parent 4.55e-04 2.16e-01 3.48e-05  0.00595
+## N_parent       2.70e+00 1.21e-08 1.99e+00  3.40046
+## sigma          8.29e+00 1.61e-08 6.09e+00 10.49062
+## 
+## $DFOP
+##          Estimate   Pr(>t)   Lower  Upper
+## parent_0  88.5333 7.40e-18 79.9836 97.083
+## k1        18.8461 5.00e-01  0.0000    Inf
+## k2         0.0776 1.41e-05  0.0518  0.116
+## g          0.4733 1.41e-09  0.3674  0.582
+## sigma      7.1902 2.11e-08  5.2785  9.102
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  4.35 14.4     4.35
+## IORE 1.48 32.1     9.67
+## DFOP 0.67 21.4     8.93
+## 
+## Representative half-life:
+## [1] 8.93

In PestDF, the DFOP fit seems to have stuck in a local minimum, as mkin finds a solution with a much lower \(\chi^2\) error level. As the half-life from the slower rate constant of the DFOP model is larger than the IORE derived half-life, the NAFTA recommendation obtained with mkin is to use the DFOP representative half-life of 8.9 days.

-
-

-Conclusions

+
+

Conclusions +

The results obtained with mkin deviate from the results obtained with PestDF either in cases where one of the interpretive rules would apply, i.e. the IORE parameter N is less than one or the DFOP k values obtained with PestDF are equal to the SFO k values, or in cases where the DFOP model did not converge, which often lead to negative rate constants returned by PestDF.

Therefore, mkin appears to suitable for kinetic evaluations according to the NAFTA guidance.

-
-

-References

+
+

References +

US EPA. 2015. “Standard Operating Procedure for Using the NAFTA Guidance to Calculate Representative Half-Life Values and Characterizing Pesticide Degradation.”

@@ -1015,11 +1020,13 @@
-

Developed by Johannes Ranke.

+

+

Developed by Johannes Ranke.

-

Site built with pkgdown 1.6.1.

+

+

Site built with pkgdown 2.0.2.

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+

Benchmark timings for mkin

-

Johannes Ranke

+

Johannes Ranke

-

Last change 13 May 2020 (rebuilt 2021-03-31)

+

Last change 13 May 2020 (rebuilt 2022-03-02)

- Source: vignettes/web_only/benchmarks.rmd + Source: vignettes/web_only/benchmarks.rmd
@@ -110,17 +115,17 @@

Each system is characterized by its CPU type, the operating system type and the mkin version. Currently only values for one system are available. A compiler was available, so if no analytical solution was available, compiled ODE models are used.

-
-

-Test cases

+
+

Test cases +

Parent only:

 FOCUS_C <- FOCUS_2006_C
-FOCUS_D <- subset(FOCUS_2006_D, value != 0)
-parent_datasets <- list(FOCUS_C, FOCUS_D)
+FOCUS_D <- subset(FOCUS_2006_D, value != 0)
+parent_datasets <- list(FOCUS_C, FOCUS_D)
 
-t1 <- system.time(mmkin_bench(c("SFO", "FOMC", "DFOP", "HS"), parent_datasets))[["elapsed"]]
-t2 <- system.time(mmkin_bench(c("SFO", "FOMC", "DFOP", "HS"), parent_datasets,
+t1 <- system.time(mmkin_bench(c("SFO", "FOMC", "DFOP", "HS"), parent_datasets))[["elapsed"]]
+t2 <- system.time(mmkin_bench(c("SFO", "FOMC", "DFOP", "HS"), parent_datasets,
     error_model = "tc"))[["elapsed"]]

One metabolite:

@@ -133,10 +138,10 @@
 DFOP_SFO <- mkinmod(
   parent = mkinsub("FOMC", "m1"),
   m1 = mkinsub("SFO"))
-t3 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_D)))[["elapsed"]]
-t4 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_D),
+t3 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_D)))[["elapsed"]]
+t4 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_D),
     error_model = "tc"))[["elapsed"]]
-t5 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_D),
+t5 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_D),
     error_model = "obs"))[["elapsed"]]

Two metabolites, synthetic data:

@@ -145,7 +150,7 @@
                            M2 = mkinsub("SFO"),
                            use_of_ff = "max", quiet = TRUE)
 
-m_synth_DFOP_par <- mkinmod(parent = mkinsub("DFOP", c("M1", "M2")),
+m_synth_DFOP_par <- mkinmod(parent = mkinsub("DFOP", c("M1", "M2")),
                            M1 = mkinsub("SFO"),
                            M2 = mkinsub("SFO"),
                            use_of_ff = "max", quiet = TRUE)
@@ -154,31 +159,31 @@
 
 DFOP_par_c <- synthetic_data_for_UBA_2014[[12]]$data
 
-t6 <- system.time(mmkin_bench(list(m_synth_SFO_lin), list(SFO_lin_a)))[["elapsed"]]
-t7 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c)))[["elapsed"]]
+t6 <- system.time(mmkin_bench(list(m_synth_SFO_lin), list(SFO_lin_a)))[["elapsed"]]
+t7 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c)))[["elapsed"]]
 
-t8 <- system.time(mmkin_bench(list(m_synth_SFO_lin), list(SFO_lin_a),
+t8 <- system.time(mmkin_bench(list(m_synth_SFO_lin), list(SFO_lin_a),
     error_model = "tc"))[["elapsed"]]
-t9 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c),
+t9 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c),
     error_model = "tc"))[["elapsed"]]
 
-t10 <- system.time(mmkin_bench(list(m_synth_SFO_lin), list(SFO_lin_a),
+t10 <- system.time(mmkin_bench(list(m_synth_SFO_lin), list(SFO_lin_a),
     error_model = "obs"))[["elapsed"]]
-t11 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c),
+t11 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c),
     error_model = "obs"))[["elapsed"]]
-mkin_benchmarks[system_string, paste0("t", 1:11)] <-
-  c(t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11)
-save(mkin_benchmarks, file = "~/git/mkin/vignettes/web_only/mkin_benchmarks.rda")
+mkin_benchmarks[system_string, paste0("t", 1:11)] <- + c(t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11) +save(mkin_benchmarks, file = "~/git/mkin/vignettes/web_only/mkin_benchmarks.rda")
-
-

-Results

+
+

Results +

Currently, we only have benchmark information on one system, therefore only the mkin version is shown with the results below. Timings are in seconds, shorter is better. All results were obtained by serial, i.e. not using multiple computing cores.

Benchmarks for all available error models are shown.

-
-

-Parent only

+
+

Parent only +

Constant variance (t1) and two-component error model (t2) for four models fitted to two datasets, i.e. eight fits for each test.

@@ -237,12 +242,17 @@ + + + + +
1.867 3.450
1.1.01.9383.517
-
-

-One metabolite

+
+

One metabolite +

Constant variance (t3), two-component error model (t4), and variance by variable (t5) for three models fitted to one dataset, i.e. three fits for each test.

@@ -312,12 +322,18 @@ + + + + + +
6.364 2.820
1.1.01.4706.5082.894
-
-

-Two metabolites

+
+

Two metabolites +

Constant variance (t6 and t7), two-component error model (t8 and t9), and variance by variable (t10 and t11) for one model fitted to one dataset, i.e. one fit for each test.

@@ -420,6 +436,15 @@ + + + + + + + + +
1.936 2.826
1.1.00.8101.2641.5033.0961.9842.847
@@ -437,11 +462,13 @@
-

Developed by Johannes Ranke.

+

+

Developed by Johannes Ranke.

-

Site built with pkgdown 1.6.1.

+

+

Site built with pkgdown 2.0.2.

@@ -450,5 +477,7 @@ + + diff --git a/docs/articles/web_only/compiled_models.html b/docs/articles/web_only/compiled_models.html index ce8d8481..35ea6f27 100644 --- a/docs/articles/web_only/compiled_models.html +++ b/docs/articles/web_only/compiled_models.html @@ -19,6 +19,8 @@ + +
+

Performance benefit by using compiled model definitions in mkin

-

Johannes Ranke

+

Johannes Ranke

-

2021-02-15

+

2022-03-02

- Source: vignettes/web_only/compiled_models.rmd + Source: vignettes/web_only/compiled_models.rmd
-
-

-How to benefit from compiled models

+
+

How to benefit from compiled models +

When using an mkin version equal to or greater than 0.9-36 and a C compiler is available, you will see a message that the model is being compiled from autogenerated C code when defining a model using mkinmod. Starting from version 0.9.49.9, the mkinmod() function checks for presence of a compiler using

-pkgbuild::has_compiler()
-

In previous versions, it used Sys.which("gcc") for this check.

+pkgbuild::has_compiler()
+

In previous versions, it used Sys.which("gcc") for this check.

On Linux, you need to have the essential build tools like make and gcc or clang installed. On Debian based linux distributions, these will be pulled in by installing the build-essential package.

On MacOS, which I do not use personally, I have had reports that a compiler is available by default.

On Windows, you need to install Rtools and have the path to its bin directory in your PATH variable. You do not need to modify the PATH variable when installing Rtools. Instead, I would recommend to put the line

-Sys.setenv(PATH = paste("C:/Rtools/bin", Sys.getenv("PATH"), sep=";"))
+Sys.setenv(PATH = paste("C:/Rtools/bin", Sys.getenv("PATH"), sep=";"))

into your .Rprofile startup file. This is just a text file with some R code that is executed when your R session starts. It has to be named .Rprofile and has to be located in your home directory, which will generally be your Documents folder. You can check the location of the home directory used by R by issuing

-Sys.getenv("HOME")
+Sys.getenv("HOME")
-
-

-Comparison with other solution methods

+
+

Comparison with other solution methods +

First, we build a simple degradation model for a parent compound with one metabolite, and we remove zero values from the dataset.

-library("mkin", quietly = TRUE)
+library("mkin", quietly = TRUE)
 SFO_SFO <- mkinmod(
   parent = mkinsub("SFO", "m1"),
   m1 = mkinsub("SFO"))
-
## Temporary DLL for differentials generated and loaded
+
## Temporary DLL for differentials generated and loaded
-FOCUS_D <- subset(FOCUS_2006_D, value != 0)
+FOCUS_D <- subset(FOCUS_2006_D, value != 0)

We can compare the performance of the Eigenvalue based solution against the compiled version and the R implementation of the differential equations using the benchmark package. In the output of below code, the warnings about zero being removed from the FOCUS D dataset are suppressed. Since mkin version 0.9.49.11, an analytical solution is also implemented, which is included in the tests below.

-if (require(rbenchmark)) {
-  b.1 <- benchmark(
+if (require(rbenchmark)) {
+  b.1 <- benchmark(
     "deSolve, not compiled" = mkinfit(SFO_SFO, FOCUS_D,
        solution_type = "deSolve",
        use_compiled = FALSE, quiet = TRUE),
@@ -152,50 +157,50 @@
        solution_type = "analytical",
        use_compiled = FALSE, quiet = TRUE),
     replications = 1, order = "relative",
-    columns = c("test", "replications", "relative", "elapsed"))
-  print(b.1)
+    columns = c("test", "replications", "relative", "elapsed"))
+  print(b.1)
 } else {
-  print("R package rbenchmark is not available")
+  print("R package rbenchmark is not available")
 }
-
##                    test replications relative elapsed
-## 4            analytical            1    1.000   0.181
-## 3     deSolve, compiled            1    1.812   0.328
-## 2      Eigenvalue based            1    2.088   0.378
-## 1 deSolve, not compiled            1   45.923   8.312
+
##                    test replications relative elapsed
+## 4            analytical            1    1.000   0.216
+## 3     deSolve, compiled            1    1.708   0.369
+## 2      Eigenvalue based            1    1.866   0.403
+## 1 deSolve, not compiled            1   34.009   7.346

We see that using the compiled model is by more than a factor of 10 faster than using deSolve without compiled code.

-
-

-Model without analytical solution

+
+

Model without analytical solution +

This evaluation is also taken from the example section of mkinfit. No analytical solution is available for this system, and now Eigenvalue based solution is possible, so only deSolve using with or without compiled code is available.

-if (require(rbenchmark)) {
+if (require(rbenchmark)) {
   FOMC_SFO <- mkinmod(
     parent = mkinsub("FOMC", "m1"),
     m1 = mkinsub( "SFO"))
 
-  b.2 <- benchmark(
+  b.2 <- benchmark(
     "deSolve, not compiled" = mkinfit(FOMC_SFO, FOCUS_D,
                                       use_compiled = FALSE, quiet = TRUE),
     "deSolve, compiled" = mkinfit(FOMC_SFO, FOCUS_D, quiet = TRUE),
     replications = 1, order = "relative",
-    columns = c("test", "replications", "relative", "elapsed"))
-  print(b.2)
-  factor_FOMC_SFO <- round(b.2["1", "relative"])
+    columns = c("test", "replications", "relative", "elapsed"))
+  print(b.2)
+  factor_FOMC_SFO <- round(b.2["1", "relative"])
 } else {
   factor_FOMC_SFO <- NA
-  print("R package benchmark is not available")
+  print("R package benchmark is not available")
 }
-
## Temporary DLL for differentials generated and loaded
-
##                    test replications relative elapsed
-## 2     deSolve, compiled            1    1.000   0.486
-## 1 deSolve, not compiled            1   31.597  15.356
-

Here we get a performance benefit of a factor of 32 using the version of the differential equation model compiled from C code!

-

This vignette was built with mkin 1.0.3 on

-
## R version 4.0.3 (2020-10-10)
-## Platform: x86_64-pc-linux-gnu (64-bit)
-## Running under: Debian GNU/Linux bullseye/sid
-
## CPU model: AMD Ryzen 7 1700 Eight-Core Processor
+
## Temporary DLL for differentials generated and loaded
+
##                    test replications relative elapsed
+## 2     deSolve, compiled            1    1.000   0.533
+## 1 deSolve, not compiled            1   25.146  13.403
+

Here we get a performance benefit of a factor of 25 using the version of the differential equation model compiled from C code!

+

This vignette was built with mkin 1.1.0 on

+
## R version 4.1.2 (2021-11-01)
+## Platform: x86_64-pc-linux-gnu (64-bit)
+## Running under: Debian GNU/Linux 11 (bullseye)
+
## CPU model: AMD Ryzen 7 1700 Eight-Core Processor
@@ -210,11 +215,13 @@
-

Developed by Johannes Ranke.

+

+

Developed by Johannes Ranke.

-

Site built with pkgdown 1.6.1.

+

+

Site built with pkgdown 2.0.2.

@@ -223,5 +230,7 @@ + + diff --git a/docs/articles/web_only/dimethenamid_2018.html b/docs/articles/web_only/dimethenamid_2018.html new file mode 100644 index 00000000..40e8a913 --- /dev/null +++ b/docs/articles/web_only/dimethenamid_2018.html @@ -0,0 +1,518 @@ + + + + + + + +Example evaluations of the dimethenamid data from 2018 • mkin + + + + + + + + + + + + +
+
+ + + + +
+
+
+

Example evaluations of the dimethenamid data from 2018

+

Johannes Ranke

+ +

Last change 10 February 2022, built on 02 Mär 2022

+ + Source: vignettes/web_only/dimethenamid_2018.rmd + + +
+ + + +

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

+
+

Introduction +

+

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

+

This vignette is an attempt to satisfy this need.

+
+
+

Data +

+

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

+

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

+

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

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

+

However, note that in the case of using this error model, the fits to the Flaach and BBA 2.3 datasets appear to be ill-defined, indicated by the fact that they did not converge:

+
+print(f_parent_mkin_tc["DFOP", ])
+
<mmkin> object
+Status of individual fits:
+
+      dataset
+model  Calke Borstel Flaach BBA 2.2 BBA 2.3 Elliot
+  DFOP OK    OK      C      OK      C       OK    
+
+OK: No warnings
+C: Optimisation did not converge:
+iteration limit reached without convergence (10)
+
+
+

Nonlinear mixed-effects models +

+

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 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", ])
+# 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.

+
+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  5 796.60 811.82 -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)
+

+
+
+

saemix +

+

The saemix package provided the first Open Source implementation of the Stochastic Approximation to the Expectation Maximisation (SAEM) algorithm. SAEM fits of degradation models can be conveniently performed using an interface to the saemix package available in current development versions of the mkin package.

+

The corresponding SAEM fits of the four combinations of degradation and error models are fitted below. As there is no convergence criterion implemented in the saemix package, the convergence plots need to be manually checked for every fit. As we will compare the SAEM implementation of saemix to the results obtained using the nlmixr package later, we define control settings that work well for all the parent data fits shown in this vignette.

+
+library(saemix)
+saemix_control <- saemixControl(nbiter.saemix = c(800, 300), nb.chains = 15,
+    print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
+saemix_control_moreiter <- saemixControl(nbiter.saemix = c(1600, 300), nb.chains = 15,
+    print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
+saemix_control_10k <- saemixControl(nbiter.saemix = c(10000, 300), nb.chains = 15,
+    print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
+

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

+
+f_parent_saemix_sfo_const <- mkin::saem(f_parent_mkin_const["SFO", ], quiet = TRUE,
+  control = saemix_control, transformations = "saemix")
+plot(f_parent_saemix_sfo_const$so, plot.type = "convergence")
+

+

Obviously the default number of iterations is sufficient to reach convergence. This can also be said for the SFO fit using the two-component error model.

+
+f_parent_saemix_sfo_tc <- mkin::saem(f_parent_mkin_tc["SFO", ], quiet = TRUE,
+  control = saemix_control, transformations = "saemix")
+plot(f_parent_saemix_sfo_tc$so, plot.type = "convergence")
+

+

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")
+

+

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")
+f_parent_saemix_dfop_tc_moreiter <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
+  control = saemix_control_moreiter, transformations = "saemix")
+plot(f_parent_saemix_dfop_tc$so, plot.type = "convergence")
+

+

Doubling the number of iterations in the first phase of the algorithm leads to a slightly lower likelihood, and therefore to slightly higher AIC and BIC values. With even more iterations, the algorithm stops with an error message. This is related to the variance of k2 approximating zero. This has been submitted as a bug to the saemix package, as the algorithm does not converge in this case.

+

An alternative way to fit DFOP in combination with the two-component error model is to use the model formulation with transformed parameters as used per default in mkin. When using this option, convergence is slower, but eventually the algorithm stops as well with the same error message.

+

The four combinations (SFO/const, SFO/tc, DFOP/const and DFOP/tc) and the version with increased iterations can be compared using the model comparison function of the saemix package:

+
+AIC_parent_saemix <- saemix::compare.saemix(
+  f_parent_saemix_sfo_const$so,
+  f_parent_saemix_sfo_tc$so,
+  f_parent_saemix_dfop_const$so,
+  f_parent_saemix_dfop_tc$so,
+  f_parent_saemix_dfop_tc_moreiter$so)
+
Likelihoods calculated by importance sampling
+
+rownames(AIC_parent_saemix) <- c(
+  "SFO const", "SFO tc", "DFOP const", "DFOP tc", "DFOP tc more iterations")
+print(AIC_parent_saemix)
+
                           AIC    BIC
+SFO const               796.38 795.34
+SFO tc                  798.38 797.13
+DFOP const              705.75 703.88
+DFOP tc                 665.65 663.57
+DFOP tc more iterations 665.88 663.80
+

In order to check the influence of the likelihood calculation algorithms implemented in saemix, the likelihood from Gaussian quadrature is added to the best fit, and the AIC values obtained from the three methods are compared.

+
+f_parent_saemix_dfop_tc$so <-
+  saemix::llgq.saemix(f_parent_saemix_dfop_tc$so)
+AIC_parent_saemix_methods <- c(
+  is = AIC(f_parent_saemix_dfop_tc$so, method = "is"),
+  gq = AIC(f_parent_saemix_dfop_tc$so, method = "gq"),
+  lin = AIC(f_parent_saemix_dfop_tc$so, method = "lin")
+)
+print(AIC_parent_saemix_methods)
+
    is     gq    lin 
+665.65 665.68 665.11
+

The AIC values based on importance sampling and Gaussian quadrature are very similar. Using linearisation is known to be less accurate, but still gives a similar value. In order to illustrate that the comparison of the three method depends on the degree of convergence obtained in the fit, the same comparison is shown below for the fit using the defaults for the number of iterations and the number of MCMC chains.

+
+f_parent_saemix_dfop_tc_defaults <- mkin::saem(f_parent_mkin_tc["DFOP", ])
+f_parent_saemix_dfop_tc_defaults$so <-
+  saemix::llgq.saemix(f_parent_saemix_dfop_tc_defaults$so)
+AIC_parent_saemix_methods_defaults <- c(
+  is = AIC(f_parent_saemix_dfop_tc_defaults$so, method = "is"),
+  gq = AIC(f_parent_saemix_dfop_tc_defaults$so, method = "gq"),
+  lin = AIC(f_parent_saemix_dfop_tc_defaults$so, method = "lin")
+)
+print(AIC_parent_saemix_methods_defaults)
+
    is     gq    lin 
+668.27 718.36 666.49
+
+
+

nlmixr +

+

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.

+
+library(nlmixr)
+f_parent_nlmixr_focei_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "focei")
+f_parent_nlmixr_focei_sfo_tc <- nlmixr(f_parent_mkin_tc["SFO", ], est = "focei")
+f_parent_nlmixr_focei_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "focei")
+f_parent_nlmixr_focei_dfop_tc<- nlmixr(f_parent_mkin_tc["DFOP", ], est = "focei")
+

For the SFO model with constant variance, the AIC values are the same, for the DFOP model, there are significant differences between the AIC values. These may be caused by different solutions that are found, but also by the fact that the AIC values for the nlmixr fits are calculated based on Gaussian quadrature, not on linearisation.

+
+aic_nlmixr_focei <- sapply(
+  list(f_parent_nlmixr_focei_sfo_const$nm, f_parent_nlmixr_focei_sfo_tc$nm,
+    f_parent_nlmixr_focei_dfop_const$nm, f_parent_nlmixr_focei_dfop_tc$nm),
+  AIC)
+aic_nlme <- sapply(
+  list(f_parent_nlme_sfo_const, NA, f_parent_nlme_sfo_tc, f_parent_nlme_dfop_tc),
+  function(x) if (is.na(x[1])) NA else AIC(x))
+aic_nlme_nlmixr_focei <- data.frame(
+  "Degradation model" = c("SFO", "SFO", "DFOP", "DFOP"),
+  "Error model" = rep(c("constant variance", "two-component"), 2),
+  "AIC (nlme)" = aic_nlme,
+  "AIC (nlmixr with FOCEI)" = aic_nlmixr_focei,
+  check.names = FALSE
+)
+print(aic_nlme_nlmixr_focei)
+
  Degradation model       Error model AIC (nlme) AIC (nlmixr with FOCEI)
+1               SFO constant variance     796.60                  796.60
+2               SFO     two-component         NA                  798.64
+3              DFOP constant variance     798.60                  745.87
+4              DFOP     two-component     671.91                  740.42
+

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

+
+nlmixr_saem_control_800 <- saemControl(logLik = TRUE,
+  nBurn = 800, nEm = 300, nmc = 15)
+nlmixr_saem_control_moreiter <- saemControl(logLik = TRUE,
+  nBurn = 1600, nEm = 300, nmc = 15)
+nlmixr_saem_control_10k <- saemControl(logLik = TRUE,
+  nBurn = 10000, nEm = 1000, nmc = 15)
+

Then we fit SFO with constant variance

+
+f_parent_nlmixr_saem_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "saem",
+  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_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 above for this model combination. Also note that the variance of k2 approximates zero, which was already observed in the saemix fits of the DFOP model.

+
+f_parent_nlmixr_saem_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "saem",
+  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, but the variance of k2 again approximates zero.

+
+f_parent_nlmixr_saem_dfop_tc <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
+  control = nlmixr_saem_control_800)
+traceplot(f_parent_nlmixr_saem_dfop_tc$nm)
+

+

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_moreiter <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
+  control = nlmixr_saem_control_moreiter)
+traceplot(f_parent_nlmixr_saem_dfop_tc_moreiter$nm)
+

+

Here the fit looks very similar, but we will see below that it shows a higher AIC than the fit with 800 iterations in the burn in phase. Next we choose 10 000 iterations for the burn in phase and 1000 iterations for the second phase for comparison with saemix.

+
+f_parent_nlmixr_saem_dfop_tc_10k <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
+  control = nlmixr_saem_control_10k)
+traceplot(f_parent_nlmixr_saem_dfop_tc_10k$nm)
+

+

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,
+  f_parent_nlmixr_saem_dfop_tc_moreiter$nm,
+  f_parent_nlmixr_saem_dfop_tc_10k$nm)
+
                                         df     AIC
+f_parent_nlmixr_saem_sfo_const$nm         5  798.71
+f_parent_nlmixr_saem_sfo_tc$nm            6  808.64
+f_parent_nlmixr_saem_dfop_const$nm        9 1995.96
+f_parent_nlmixr_saem_dfop_tc$nm          10  664.96
+f_parent_nlmixr_saem_dfop_tc_moreiter$nm 10 4464.93
+f_parent_nlmixr_saem_dfop_tc_10k$nm      10     Inf
+

We can see that again, the DFOP/tc model shows the best goodness of fit. However, increasing the number of burn-in iterations from 800 to 1600 results in a higher AIC. If we further increase the number of iterations to 10 000 (burn-in) and 1000 (second phase), the AIC cannot be calculated for the nlmixr/saem fit, confirming that this fit does not converge properly with the SAEM algorithm.

+
+
+

Comparison +

+

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"),
+  "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$so, f_parent_saemix_dfop_tc$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 modelError modelnlmenlmixr_foceisaemixnlmixr_saem
SFOconst796.60796.60796.38798.71
SFOtc798.60798.64798.38808.64
DFOPconstNA745.87705.751995.96
DFOPtc671.91740.42665.65664.96
+
+
+
+
+

References +

+ +
+
+

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

+
+
+

Ranke, Johannes, Janina Wöltjen, Jana Schmidt, and Emmanuelle Comets. 2021. “Taking Kinetic Evaluations of Degradation Data to the Next Level with Nonlinear Mixed-Effects Models.” Environments 8 (8). https://doi.org/10.3390/environments8080071.

+
+
+

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.

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

+

Developed by Johannes Ranke.

+
+ +
+

+

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