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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)
-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,
-        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,
-         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,
-         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,
-         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,
-         25.2, 17.2, 4.8, 4.5, 2.8, 4.4))
-
-FOCUS_2006_Z_mkin <- mkin_wide_to_long(FOCUS_2006_Z)

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,
+        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,
+         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,
+         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,
+         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,
+         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

Z.2a <- mkinmod(Z0 = mkinsub("SFO", "Z1"),
+                Z1 = mkinsub("SFO"))

## 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

+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

-plot_sep(m.Z.2a)

+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

Z.2a.ff <- mkinmod(Z0 = mkinsub("SFO", "Z1"),
+                   Z1 = mkinsub("SFO"),
+                   use_of_ff = "max")

## 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

+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

-plot_sep(m.Z.2a.ff)

+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

Z.3 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
+               Z1 = mkinsub("SFO"), use_of_ff = "max")

## 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

+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

-plot_sep(m.Z.3)

+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

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

-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

+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

-plot_sep(m.Z.5)

+plot_sep(m.Z.5)

Finally, metabolite Z3 is added to the model. We use the optimised differential equation parameter values from the previous fit in order to accelerate the optimization.

-Z.FOCUS <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
-                   Z1 = mkinsub("SFO", "Z2", sink = FALSE),
-                   Z2 = mkinsub("SFO", "Z3"),
-                   Z3 = mkinsub("SFO"),
-                   use_of_ff = "max")

## Temporary DLL for differentials generated and loaded

Z.FOCUS <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
+                   Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                   Z2 = mkinsub("SFO", "Z3"),
+                   Z3 = mkinsub("SFO"),
+                   use_of_ff = "max")

## 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)

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)

-plot_sep(m.Z.FOCUS)

+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

+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

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.

-Z.mkin.1 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
-                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
-                    Z2 = mkinsub("SFO", "Z3"),
-                    Z3 = mkinsub("SFORB"))

## Temporary DLL for differentials generated and loaded

Z.mkin.1 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
+                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                    Z2 = mkinsub("SFO", "Z3"),
+                    Z3 = mkinsub("SFORB"))

## 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

+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

-plot_sep(m.Z.mkin.1)

+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

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

-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

+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

-plot_sep(m.Z.mkin.3)

+plot_sep(m.Z.mkin.3)

This results in a much better representation of the behaviour of the parent compound Z0.

Finally, Z3 is added as well. These models appear overparameterised (no covariance matrix returned) if the sink for Z1 is left in the models.

-Z.mkin.4 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
-                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
-                    Z2 = mkinsub("SFO", "Z3"),
-                    Z3 = mkinsub("SFO"))

## Temporary DLL for differentials generated and loaded

Z.mkin.4 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
+                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                    Z2 = mkinsub("SFO", "Z3"),
+                    Z3 = mkinsub("SFO"))

## 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

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

-plot_sep(m.Z.mkin.4)

+plot_sep(m.Z.mkin.4)

The error level of the fit, but especially of metabolite Z3, can be improved if the SFORB model is chosen for this metabolite, as this model is capable of representing the tailing of the metabolite decline phase.

-Z.mkin.5 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
-                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
-                    Z2 = mkinsub("SFO", "Z3"),
-                    Z3 = mkinsub("SFORB"))

## Temporary DLL for differentials generated and loaded

Z.mkin.5 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
+                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                    Z2 = mkinsub("SFO", "Z3"),
+                    Z3 = mkinsub("SFORB"))

## 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

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

-plot_sep(m.Z.mkin.5)

+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],
-                                     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

m.Z.mkin.5a <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin,
+                       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

-plot_sep(m.Z.mkin.5a)

+plot_sep(m.Z.mkin.5a)

As expected, the residual plots for Z0 and Z3 are more random than in the case of the all SFO model for which they were shown above. In conclusion, the model is proposed as the best-fit model for the dataset from Appendix 7 of the FOCUS report.

A graphical representation of the confidence intervals can finally be obtained.

-mkinparplot(m.Z.mkin.5a)

+mkinparplot(m.Z.mkin.5a)

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

+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      Z0_g     Z3_b1     Z3_b2      Z3_g 
+## 2.4471322 0.0075125 0.9519862 0.0800069 0.0000000 0.9347820 
+## 
+## $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.

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-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

+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

-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

+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

-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

+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

-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

+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

-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

+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

-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

+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

-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

+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

-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

+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

-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

+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

-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

+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

-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

+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

-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

+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

-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

+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

-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

+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

-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

+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

-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.”

@@ -1016,11 +1027,13 @@ @@ -1029,5 +1042,7 @@ + + diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p10-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p10-1.png index f5420ce8..75611a70 100644 Binary files a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p10-1.png and b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p10-1.png differ diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p11-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p11-1.png index 0ae4bd9f..55466e47 100644 Binary files a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p11-1.png and b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p11-1.png differ diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p12a-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p12a-1.png index 57a48119..d3143afa 100644 Binary files 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a/docs/dev/articles/web_only/benchmarks.html +++ b/docs/dev/articles/web_only/benchmarks.html @@ -34,7 +34,7 @@

@@ -112,7 +112,7 @@

Benchmark timings for mkin

Johannes Ranke

Last change 14 July 2022 (rebuilt 2022-11-15)

Last change 14 July 2022 (rebuilt 2022-11-24)

Source: vignettes/web_only/benchmarks.rmd

benchmarks.rmd

@@ -351,8 +351,16 @@ Ryzen 7 1700 4.2.2 1.2.0 -2.129 -3.784 +2.140 +3.774 + + +Linux +Ryzen 7 1700 +4.2.2 +1.2.2 +2.187 +3.851 @@ -530,9 +538,18 @@ Ryzen 7 1700 4.2.2 1.2.0 -1.559 -6.097 -2.841 +1.554 +6.193 +2.843 + + +Linux +Ryzen 7 1700 +4.2.2 +1.2.2 +1.585 +6.335 +3.003 @@ -764,12 +781,24 @@ Ryzen 7 1700 4.2.2 1.2.0 -0.911 -1.328 -1.519 -2.986 -1.957 -2.769 +0.913 +1.345 +1.539 +3.011 +1.987 +2.802 + + +Linux +Ryzen 7 1700 +4.2.2 +1.2.2 +0.935 +1.381 +1.551 +3.209 +1.976 +3.013 diff --git a/docs/dev/articles/web_only/compiled_models.html b/docs/dev/articles/web_only/compiled_models.html index ade86bc5..e9d80420 100644 --- a/docs/dev/articles/web_only/compiled_models.html +++ b/docs/dev/articles/web_only/compiled_models.html @@ -34,7 +34,7 @@

@@ -78,7 +78,10 @@ Example evaluation of NAFTA SOP Attachment examples

- Some benchmark timings + Benchmark timings for mkin +

+ Benchmark timings for saem.mmkin

@@ -109,7 +112,7 @@

Performance benefit by using compiled model definitions in mkin

Johannes Ranke

2022-11-01

2022-11-24

Source: vignettes/web_only/compiled_models.rmd

compiled_models.rmd

@@ -167,10 +170,10 @@ print("R package rbenchmark is not available") }

##                    test replications relative elapsed
-## 4            analytical            1    1.000   0.186
-## 3     deSolve, compiled            1    1.656   0.308
-## 2      Eigenvalue based            1    2.102   0.391
-## 1 deSolve, not compiled            1   38.968   7.248

+## 4 analytical 1 1.000 0.221 +## 3 deSolve, compiled 1 1.561 0.345 +## 2 Eigenvalue based 1 1.932 0.427 +## 1 deSolve, not compiled 1 33.629 7.432

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

@@ -197,10 +200,10 @@ }

## Temporary DLL for differentials generated and loaded

##                    test replications relative elapsed
-## 2     deSolve, compiled            1    1.000   0.452
-## 1 deSolve, not compiled            1   29.431  13.303

Here we get a performance benefit of a factor of 29 using the version of the differential equation model compiled from C code!

This vignette was built with mkin 1.2.0 on

+## 2 deSolve, compiled 1 1.000 0.482 +## 1 deSolve, not compiled 1 27.865 13.431 +

Here we get a performance benefit of a factor of 28 using the version of the differential equation model compiled from C code!

This vignette was built with mkin 1.2.2 on

## R version 4.2.2 (2022-10-31)
 ## Platform: x86_64-pc-linux-gnu (64-bit)
 ## Running under: Debian GNU/Linux 11 (bullseye)

diff --git a/docs/dev/articles/web_only/dimethenamid_2018.html b/docs/dev/articles/web_only/dimethenamid_2018.html index 60f1ab5a..ec7f54d8 100644 --- a/docs/dev/articles/web_only/dimethenamid_2018.html +++ b/docs/dev/articles/web_only/dimethenamid_2018.html @@ -34,7 +34,7 @@

@@ -63,11 +63,14 @@ Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models

- Example evaluation of FOCUS Example Dataset Z + Short demo of the multistart method

Performance benefit by using compiled model definitions in mkin

+ Example evaluation of FOCUS Example Dataset Z +

Calculation of time weighted average concentrations with mkin

@@ -75,7 +78,10 @@ Example evaluation of NAFTA SOP Attachment examples

- Some benchmark timings + Benchmark timings for mkin +

+ Benchmark timings for saem.mmkin

@@ -106,7 +112,7 @@

Example evaluations of the dimethenamid data from 2018

Johannes Ranke

Last change 1 July 2022, built on 16 Sep 2022

Last change 1 July 2022, built on 24 Nov 2022

Source: vignettes/web_only/dimethenamid_2018.rmd

dimethenamid_2018.rmd

@@ -366,7 +372,7 @@ DFOP tc more iterations 665.88 663.80 ) print(AIC_parent_saemix_methods_defaults)

    is     gq    lin 
-668.27 718.36 666.49

+669.77 669.36 670.95

@@ -437,7 +443,7 @@ DFOP tc more iterations 665.88 663.80

 sessionInfo()

R version 4.2.1 (2022-06-23)
+R version 4.2.2 (2022-10-31)
 Platform: x86_64-pc-linux-gnu (64-bit)
 Running under: Debian GNU/Linux 11 (bullseye)
 
@@ -457,24 +463,24 @@ attached base packages:
 [1] stats     graphics  grDevices utils     datasets  methods   base     
 
 other attached packages:
-[1] nlme_3.1-158 mkin_1.1.2   knitr_1.39  
+[1] saemix_3.2   npde_3.2     nlme_3.1-160 mkin_1.2.2   knitr_1.41  
 
 loaded via a namespace (and not attached):
- [1] deSolve_1.33       zoo_1.8-10         tidyselect_1.1.2   xfun_0.31         
- [5] bslib_0.4.0        purrr_0.3.4        lattice_0.20-45    colorspace_2.0-3  
- [9] vctrs_0.4.1        generics_0.1.3     htmltools_0.5.3    yaml_2.3.5        
-[13] utf8_1.2.2         rlang_1.0.4        pkgdown_2.0.6      saemix_3.1        
-[17] jquerylib_0.1.4    pillar_1.8.0       glue_1.6.2         DBI_1.1.3         
-[21] lifecycle_1.0.1    stringr_1.4.0      munsell_0.5.0      gtable_0.3.0      
-[25] ragg_1.2.2         memoise_2.0.1      evaluate_0.15      npde_3.2          
-[29] fastmap_1.1.0      lmtest_0.9-40      parallel_4.2.1     fansi_1.0.3       
-[33] highr_0.9          KernSmooth_2.23-20 scales_1.2.0       cachem_1.0.6      
-[37] desc_1.4.1         jsonlite_1.8.0     systemfonts_1.0.4  fs_1.5.2          
-[41] textshaping_0.3.6  gridExtra_2.3      ggplot2_3.3.6      digest_0.6.29     
-[45] stringi_1.7.8      dplyr_1.0.9        grid_4.2.1         rprojroot_2.0.3   
-[49] cli_3.3.0          tools_4.2.1        magrittr_2.0.3     sass_0.4.2        
-[53] tibble_3.1.8       pkgconfig_2.0.3    assertthat_0.2.1   rmarkdown_2.14.3  
-[57] mclust_5.4.10      R6_2.5.1           compiler_4.2.1    
+ [1] deSolve_1.34      zoo_1.8-11        tidyselect_1.2.0  xfun_0.35        
+ [5] bslib_0.4.1       purrr_0.3.5       lattice_0.20-45   colorspace_2.0-3 
+ [9] vctrs_0.5.1       generics_0.1.3    htmltools_0.5.3   yaml_2.3.6       
+[13] utf8_1.2.2        rlang_1.0.6       pkgdown_2.0.6     jquerylib_0.1.4  
+[17] pillar_1.8.1      glue_1.6.2        DBI_1.1.3         lifecycle_1.0.3  
+[21] stringr_1.4.1     munsell_0.5.0     gtable_0.3.1      ragg_1.2.4       
+[25] codetools_0.2-18  memoise_2.0.1     evaluate_0.18     fastmap_1.1.0    
+[29] lmtest_0.9-40     parallel_4.2.2    fansi_1.0.3       highr_0.9        
+[33] scales_1.2.1      cachem_1.0.6      desc_1.4.2        jsonlite_1.8.3   
+[37] systemfonts_1.0.4 fs_1.5.2          textshaping_0.3.6 gridExtra_2.3    
+[41] ggplot2_3.4.0     digest_0.6.30     stringi_1.7.8     dplyr_1.0.10     
+[45] grid_4.2.2        rprojroot_2.0.3   cli_3.4.1         tools_4.2.2      
+[49] magrittr_2.0.3    sass_0.4.3        tibble_3.1.8      pkgconfig_2.0.3  
+[53] assertthat_0.2.1  rmarkdown_2.18    R6_2.5.1          mclust_6.0.0     
+[57] compiler_4.2.2

References diff --git a/docs/dev/articles/web_only/multistart.html b/docs/dev/articles/web_only/multistart.html index 50a57d1b..fd05f340 100644 --- a/docs/dev/articles/web_only/multistart.html +++ b/docs/dev/articles/web_only/multistart.html @@ -34,7 +34,7 @@ mkin - 1.2.0 + 1.2.2

@@ -78,7 +78,10 @@ Example evaluation of NAFTA SOP Attachment examples

- Some benchmark timings + Benchmark timings for mkin +

+ Benchmark timings for saem.mmkin

@@ -109,7 +112,7 @@

Short demo of the multistart method

Johannes Ranke

Last change 26 September 2022 (rebuilt 2022-11-01)

Last change 26 September 2022 (rebuilt 2022-11-24)

Source: vignettes/web_only/multistart.rmd

multistart.rmd

@@ -163,8 +166,8 @@

## Data: 155 observations of 1 variable(s) grouped in 6 datasets
 ## 
 ##                            npar    AIC    BIC     Lik Chisq Df Pr(>Chisq)
-## best(f_saem_reduced_multi)    9 663.64 661.77 -322.82                    
-## f_saem_full                  10 668.27 666.19 -324.13     0  1          1

+## best(f_saem_reduced_multi) 9 663.69 661.82 -322.85 +## f_saem_full 10 669.77 667.69 -324.89 0 1 1

While AIC and BIC are lower for the reduced model, the likelihood ratio test does not indicate a significant difference between the fits.

diff --git a/docs/dev/articles/web_only/multistart_files/figure-html/unnamed-chunk-3-1.png b/docs/dev/articles/web_only/multistart_files/figure-html/unnamed-chunk-3-1.png index 79543765..13bdb94b 100644 Binary files a/docs/dev/articles/web_only/multistart_files/figure-html/unnamed-chunk-3-1.png and b/docs/dev/articles/web_only/multistart_files/figure-html/unnamed-chunk-3-1.png differ diff --git a/docs/dev/articles/web_only/multistart_files/figure-html/unnamed-chunk-4-1.png b/docs/dev/articles/web_only/multistart_files/figure-html/unnamed-chunk-4-1.png index 4466d437..56147ae2 100644 Binary files a/docs/dev/articles/web_only/multistart_files/figure-html/unnamed-chunk-4-1.png and b/docs/dev/articles/web_only/multistart_files/figure-html/unnamed-chunk-4-1.png differ diff --git a/docs/dev/articles/web_only/multistart_files/figure-html/unnamed-chunk-5-1.png b/docs/dev/articles/web_only/multistart_files/figure-html/unnamed-chunk-5-1.png index 3dd36f91..f0b89dba 100644 Binary files a/docs/dev/articles/web_only/multistart_files/figure-html/unnamed-chunk-5-1.png and b/docs/dev/articles/web_only/multistart_files/figure-html/unnamed-chunk-5-1.png differ diff --git a/docs/dev/articles/web_only/multistart_files/figure-html/unnamed-chunk-6-1.png b/docs/dev/articles/web_only/multistart_files/figure-html/unnamed-chunk-6-1.png index 3963e993..c57c247f 100644 Binary files a/docs/dev/articles/web_only/multistart_files/figure-html/unnamed-chunk-6-1.png and b/docs/dev/articles/web_only/multistart_files/figure-html/unnamed-chunk-6-1.png differ diff --git a/docs/dev/articles/web_only/saem_benchmarks.html b/docs/dev/articles/web_only/saem_benchmarks.html index afff038f..66f4b075 100644 --- a/docs/dev/articles/web_only/saem_benchmarks.html +++ b/docs/dev/articles/web_only/saem_benchmarks.html @@ -34,7 +34,7 @@ @@ -112,7 +112,7 @@

Benchmark timings for saem.mmkin

Johannes Ranke

Last change 14 November 2022 (rebuilt 2022-11-16)

Last change 14 November 2022 (rebuilt 2022-11-24)

Source: vignettes/web_only/saem_benchmarks.rmd

saem_benchmarks.rmd

@@ -304,16 +304,28 @@ t3 t4 - + + Ryzen 7 1700 Linux 1.2.0 3.2 -2.156 -4.647 -4.296 -4.951 - +2.140 +4.626 +4.328 +4.998 + + +Ryzen 7 1700 +Linux +1.2.2 +3.2 +2.427 +4.550 +4.217 +4.851 + +

Two-component error fits for SFO, DFOP, SFORB and HS.

@@ -327,16 +339,28 @@ - + + - - - - - + + + + + + + + + + + + + + + +

t7	t8
Ryzen 7 1700	Linux	1.2.0	3.2	5.645	7.415	7.848	7.967
5.678	7.441	8.000	7.980
Ryzen 7 1700	Linux	1.2.2	3.2	5.352	7.201	8.174	8.401

@@ -352,14 +376,24 @@ t9 t10 - + + Ryzen 7 1700 Linux 1.2.0 3.2 -24.182 -783.932 - +24.465 +800.266 + + +Ryzen 7 1700 +Linux +1.2.2 +3.2 +25.193 +798.580 + +

@@ -374,13 +408,22 @@ saemix t11 - + + Ryzen 7 1700 Linux 1.2.0 3.2 -1322.5 - +1289.198 + + +Ryzen 7 1700 +Linux +1.2.2 +3.2 +1312.445 + +

-- cgit v1.2.1 From 4200e566ad2600f56bc3987669aeab88582139eb Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Sat, 28 Jan 2023 18:37:52 +0100 Subject: Update saem benchmark with new CPU --- docs/dev/articles/web_only/saem_benchmarks.html | 143 ++++++++++++++++++++---- 1 file changed, 122 insertions(+), 21 deletions(-) (limited to 'docs/dev/articles/web_only') diff --git a/docs/dev/articles/web_only/saem_benchmarks.html b/docs/dev/articles/web_only/saem_benchmarks.html index 66f4b075..4fe648c6 100644 --- a/docs/dev/articles/web_only/saem_benchmarks.html +++ b/docs/dev/articles/web_only/saem_benchmarks.html @@ -41,7 +41,7 @@

@@ -106,13 +127,15 @@ -

Benchmark timings for saem.mmkin

Johannes Ranke

Johannes +Ranke

Last change 14 November 2022 (rebuilt 2022-11-24)

Last change 14 November 2022 +(rebuilt 2023-01-28)

Source: vignettes/web_only/saem_benchmarks.rmd

saem_benchmarks.rmd

@@ -121,15 +144,19 @@ -

Each system is characterized by operating system type, CPU type, mkin version, saemix version and R version. A compiler was available, so if no analytical solution was available, compiled ODE models are used.

Every fit is only performed once, so the accuracy of the benchmarks is limited.

Each system is characterized by operating system type, CPU type, mkin +version, saemix version and R version. A compiler was available, so if +no analytical solution was available, compiled ODE models are used.

Every fit is only performed once, so the accuracy of the benchmarks +is limited.

For the initial mmkin fits, we use all available cores.

 n_cores <- parallel::detectCores()

Test data

Please refer to the vignette dimethenamid_2018 for an explanation of the following preprocessing.

Please refer to the vignette dimethenamid_2018 for an +explanation of the following preprocessing.

 dmta_ds <- lapply(1:7, function(i) {
   ds_i <- dimethenamid_2018$ds[[i]]$data
@@ -232,19 +259,24 @@
 
 
 
-The above model comparison suggests to use the SFORB model with two-component error. For comparison, we keep the DFOP model with two-component error, as it competes with SFORB for biphasic curves.
+The above model comparison suggests to use the SFORB model with
+two-component error. For comparison, we keep the DFOP model with
+two-component error, as it competes with SFORB for biphasic curves.
  illparms(dfop_tc)
 ## [1] "sd(log_k2)"
  illparms(sforb_tc)
 ## [1] "sd(log_k_DMTA_bound_free)"
-For these two models, random effects for the transformed parameters k2 and k_DMTA_bound_free could not be quantified.
+For these two models, random effects for the transformed parameters
+k2 and k_DMTA_bound_free could not be
+quantified.


 
 One metabolite
 
-We remove parameters that were found to be ill-defined in the parent only fits.
+We remove parameters that were found to be ill-defined in the parent
+only fits.
  one_met_mods <- list(
   DFOP_SFO = mkinmod(
@@ -267,7 +299,11 @@
 
 Three metabolites
 
-For the case of three metabolites, we only keep the SFORB model in order to limit the time for compiling this vignette, and as fitting in parallel may disturb the benchmark. Again, we do not include random effects that were ill-defined in previous fits of subsets of the degradation model.
+For the case of three metabolites, we only keep the SFORB model in
+order to limit the time for compiling this vignette, and as fitting in
+parallel may disturb the benchmark. Again, we do not include random
+effects that were ill-defined in previous fits of subsets of the
+degradation model.
  illparms(sforb_sfo_tc)
 @@ -288,12 +324,24 @@
 
 Results
 
-Benchmarks for all available error models are shown. They are intended for improving mkin, not for comparing CPUs or operating systems. All trademarks belong to their respective owners.
+Benchmarks for all available error models are shown. They are
+intended for improving mkin, not for comparing CPUs or operating
+systems. All trademarks belong to their respective owners.
 
 Parent only
 
 Constant variance for SFO, DFOP, SFORB and HS.
-
+
++++++++++
@@ -325,10 +373,30 @@
 
+
+
+
+
+
+
+
+
+
+









 
 CPU
 OS 4.217
 4.851
 
Ryzen 9 7950X 16-Core Processor Linux 1.2.2 3.2 1.470 2.263 1.840 2.299
 
 
 Two-component error fits for SFO, DFOP, SFORB and HS.
-
+
++++++++++
@@ -360,6 +428,16 @@
 
+
+
+
+
+
+
+
+
+
+









 
 CPU
 OS 8.174
 8.401
 
Ryzen 9 7950X 16-Core Processor Linux 1.2.2 3.2 2.118 3.528 3.295 3.157
 
 
 
@@ -368,6 +446,14 @@
 
 Two-component error for DFOP-SFO and SFORB-SFO.
 
++++++++
@@ -393,6 +479,14 @@
 
+
+
+
+
+
+
+
+







 
 CPU
 OS 25.193
 798.580
 
Ryzen 9 7950X 16-Core Processor Linux 1.2.2 3.2 12.336 277.666
 
 
 
@@ -423,6 +517,13 @@
 3.2
 1312.445
 
+
+Ryzen 9 7950X 16-Core Processor
+Linux
+1.2.2
+3.2
+459.051
+
 
 
 
@@ -446,7 +547,7 @@
 
 
   
-Site built with pkgdown 2.0.6.
+Site built with pkgdown 2.0.7.
 
 
       
-- 
cgit v1.2.1

Benchmark timings for saem.mmkin

Johannes Ranke

Last change 14 November 2022 (rebuilt 2022-11-15)

Last change 14 November 2022 (rebuilt 2022-11-16)

Example evaluation of FOCUS dataset Z

Johannes Ranke

Johannes Ranke

Last change 16 January 2018 (rebuilt 2021-02-15)

Last change 16 January 2018 (rebuilt 2022-11-24)

-The data

The data +

-Parent and one metabolite

Parent and one metabolite +

-Metabolites Z2 and Z3

Metabolites Z2 and Z3 +

-Using the SFORB model

Using the SFORB model +

-References

References +

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

Johannes Ranke

Johannes Ranke

26 February 2019 (rebuilt 2021-02-15)

26 February 2019 (rebuilt 2022-11-24)

-Introduction

Introduction +

-Examples where DFOP did not converge with PestDF 0.8.4

Examples where DFOP did not converge with PestDF 0.8.4 +

-Example on page 5, upper panel

Example on page 5, upper panel +

-Example on page 5, lower panel

Example on page 5, lower panel +

-Example on page 6

Example on page 6 +

-Example on page 7

Example on page 7 +

-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 +

-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 +

-Example on page 9, lower panel

Example on page 9, lower panel +

-Example on page 10

Example on page 10 +

-The DT50 was not observed during the study

-Example on page 11

The DT50 was not observed during the study +

Example on page 11 +

-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 +

-Example on page 12, upper panel

Example on page 12, upper panel +

-Example on page 12, lower panel

Example on page 12, lower panel +

-Example on page 13

Example on page 13 +

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

DT50 not observed in the study and DFOP problems in 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 +

-The DFOP fraction parameter is greater than 1

The DFOP fraction parameter is greater than 1 +

-Conclusions

Conclusions +

-References

References +

Benchmark timings for mkin

Johannes Ranke

Last change 14 July 2022 (rebuilt 2022-11-15)

Last change 14 July 2022 (rebuilt 2022-11-24)

Performance benefit by using compiled model definitions in mkin

Johannes Ranke

2022-11-01

2022-11-24

Example evaluations of the dimethenamid data from 2018

Johannes Ranke