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"))

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

## Successfully compiled differential equation model from auto-generated C code.

m.Z.2a <- mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE)

+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

+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
@@ -148,16 +156,20 @@
 ## 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")

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

## Successfully compiled differential equation model from auto-generated C code.

m.Z.2a.ff <- mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE)

+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

+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
@@ -167,15 +179,19 @@
 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")
++Z.3 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
+               Z1 = mkinsub("SFO"), use_of_ff = "max")
 ## Successfully compiled differential equation model from auto-generated C code.
-m.Z.3 <- mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE)
++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)$bpar
++summary(m.Z.3, data = FALSE)$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
@@ -187,51 +203,59 @@
 
 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")
++Z.5 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
+               Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+               Z2 = mkinsub("SFO"), use_of_ff = "max")
 ## Successfully compiled differential equation model from auto-generated C code.
-m.Z.5 <- mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE)
++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")
++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")
 ## Successfully compiled differential equation model from auto-generated C code.
-m.Z.FOCUS <- mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin,
-                     parms.ini = m.Z.5$bparms.ode,
-                     quiet = TRUE)
++m.Z.FOCUS <- mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin,
+                     parms.ini = m.Z.5$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)$bpar
-##             Estimate se_notrans t value     Pr(>t)     Lower     Upper
-## Z0_0       96.840695   1.994285 48.5591 4.0254e-42 92.828744 100.85265
-## k_Z0        2.215467   0.118463 18.7018 1.0417e-23  1.989524   2.46707
-## k_Z1        0.478325   0.028259 16.9265 6.2441e-22  0.424725   0.53869
-## k_Z2        0.451638   0.042139 10.7177 1.6309e-14  0.374346   0.54489
-## k_Z3        0.058692   0.015245  3.8498 1.7807e-04  0.034806   0.09897
-## f_Z2_to_Z3  0.471484   0.058348  8.0805 9.6599e-11  0.357736   0.58827
-## sigma       3.984431   0.383402 10.3923 4.5576e-14  3.213126   4.75574
-endpoints(m.Z.FOCUS)
++summary(m.Z.FOCUS, data = FALSE)$bpar
+##             Estimate se_notrans t value     Pr(>t)     Lower      Upper
+## Z0_0       96.838721   1.994275 48.5584 4.0283e-42 92.826878 100.850563
+## k_Z0        2.215400   0.118459 18.7019 1.0414e-23  1.989462   2.466998
+## k_Z1        0.478301   0.028257 16.9267 6.2411e-22  0.424705   0.538662
+## k_Z2        0.451623   0.042138 10.7176 1.6313e-14  0.374336   0.544867
+## k_Z3        0.058694   0.015246  3.8499 1.7804e-04  0.034809   0.098967
+## f_Z2_to_Z3  0.471510   0.058352  8.0804 9.6640e-11  0.357775   0.588283
+## sigma       3.984431   0.383402 10.3923 4.5575e-14  3.213126   4.755736
++endpoints(m.Z.FOCUS)
 ## $ff
 ##   Z2_Z3 Z2_sink 
-## 0.47148 0.52852 
+## 0.47151 0.52849 
 ## 
 ## $distimes
 ##        DT50    DT90
-## Z0  0.31287  1.0393
-## Z1  1.44911  4.8138
-## Z2  1.53474  5.0983
-## Z3 11.80989 39.2316
+## Z0  0.31288  1.0394
+## Z1  1.44919  4.8141
+## Z2  1.53479  5.0985
+## Z3 11.80955 39.2305
 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.

Example on page 5, upper panel

p5a <- nafta(NAFTA_SOP_Attachment[["p5a"]])

+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)

+print(p5a)

## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 465.21753  56.27506  32.06401 
@@ -134,23 +140,23 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)  Lower   Upper
-## parent_0       95.8401 4.67e-21 92.245 99.4357
-## k_parent_sink   0.0102 3.92e-12  0.009  0.0117
-## sigma           4.8230 3.81e-06  3.214  6.4318
+##          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_sink 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
+##                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       2.86e-12 5.00e-01  0.0000      Inf
+## k2       2.17e-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
 ## 
@@ -159,7 +165,7 @@
 ##      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 4.42e+11 2.42e+11
+## DFOP 55.5 5.83e+11 3.20e+11
 ## 
 ## Representative half-life:
 ## [1] 321.51

@@ -167,12 +173,15 @@

Example on page 5, lower panel

p5b <- nafta(NAFTA_SOP_Attachment[["p5b"]])

+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)

+print(p5b)

## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 94.81123 10.10936  7.55871 
@@ -182,23 +191,23 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)    Lower    Upper
-## parent_0        96.497 2.32e-24 94.85271 98.14155
-## k_parent_sink    0.008 3.42e-14  0.00737  0.00869
-## sigma            2.295 1.22e-05  1.47976  3.11036
+##          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_sink 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
+##                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       1.16e-11 5.00e-01  0.0000     Inf
+## k2       1.04e-11 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
 ## 
@@ -207,7 +216,7 @@
 ##      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 9.80e+10 5.98e+10
+## DFOP 83.6 1.09e+11 6.67e+10
 ## 
 ## Representative half-life:
 ## [1] 215.87

@@ -215,12 +224,15 @@

Example on page 6

p6 <- nafta(NAFTA_SOP_Attachment[["p6"]])

+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)

+print(p6)

## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 188.45361  51.00699  42.46931 
@@ -230,23 +242,23 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)   Lower   Upper
-## parent_0       94.7759 7.29e-24 92.3478 97.2039
-## k_parent_sink   0.0179 8.02e-16  0.0166  0.0194
-## sigma           3.0696 3.81e-06  2.0456  4.0936
+##          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_sink  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
+##                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       4.90e-11 5.00e-01  0.0000     Inf
+## k2       3.88e-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
 ## 
@@ -255,7 +267,7 @@
 ##      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 6.66e+09 1.41e+10
+## DFOP 34.1 8.42e+09 1.79e+10
 ## 
 ## Representative half-life:
 ## [1] 53.17

@@ -263,12 +275,15 @@

Example on page 7

p7 <- nafta(NAFTA_SOP_Attachment[["p7"]])

+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)

+print(p7)

## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 3661.661 3195.030 3174.145 
@@ -278,23 +293,23 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)    Lower    Upper
-## parent_0      96.41796 4.80e-53 93.32245 99.51347
-## k_parent_sink  0.00735 7.64e-21  0.00641  0.00843
-## sigma          7.94557 1.83e-15  6.46713  9.42401
+##          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_sink 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
+##                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       1.97e-10 5.00e-01  0.0000      Inf
+## k2       2.30e-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
 ## 
@@ -303,7 +318,7 @@
 ##      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 6.97e+09 3.52e+09
+## DFOP 96.4 5.95e+09 3.01e+09
 ## 
 ## Representative half-life:
 ## [1] 454.55

@@ -316,12 +331,15 @@

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_sink = 1e-3))

+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)

+print(p8)

## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 1996.9408  444.9237  547.5616 
@@ -331,17 +349,17 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)    Lower    Upper
-## parent_0      88.16549 6.53e-29 83.37344 92.95754
-## k_parent_sink  0.00803 1.67e-13  0.00674  0.00957
-## sigma          7.44786 4.17e-10  5.66209  9.23363
+##          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_sink 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
+##                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
@@ -368,12 +386,15 @@
 
 
 Example on page 9, upper panel
-p9a <- nafta(NAFTA_SOP_Attachment[["p9a"]])
++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)
++print(p9a)
 ## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 839.35238  88.57064   9.93363 
@@ -383,23 +404,23 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)   Lower   Upper
-## parent_0       88.1933 3.06e-12 79.9447 96.4419
-## k_parent_sink   0.0409 2.07e-07  0.0324  0.0516
-## sigma           7.2429 3.92e-05  4.4768 10.0090
+##          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_sink 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
+##                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       6.02e-13 5.00e-01  0.000    Inf
+## k2       6.69e-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
 ## 
@@ -408,7 +429,7 @@
 ##      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 2.07e+12 1.15e+12
+## DFOP 10.5 1.86e+12 1.04e+12
 ## 
 ## Representative half-life:
 ## [1] 101.43
@@ -417,17 +438,15 @@
 
 
 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
++p9b <- nafta(NAFTA_SOP_Attachment[["p9b"]])
 ## 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)
++print(p9b)
 ## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 35.64867 23.22334 35.64867 
@@ -437,24 +456,24 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)  Lower   Upper
-## parent_0       94.7123 2.15e-19 93.178 96.2464
-## k_parent_sink   0.0389 4.47e-14  0.037  0.0408
-## sigma           1.5957 1.28e-04  0.932  2.2595
+##          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_sink    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
+##                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 1.43e-06  0.0312  0.0485
 ## k2         0.0389 6.67e-03  0.0186  0.0812
-## g          0.7742      NaN      NA      NA
+## g          0.7742 5.00e-01  0.0000  1.0000
 ## sigma      1.5957 2.50e-04  0.9135  2.2779
 ## 
 ## 
@@ -471,12 +490,15 @@
 
 
 Example on page 10
-p10 <- nafta(NAFTA_SOP_Attachment[["p10"]])
++p10 <- nafta(NAFTA_SOP_Attachment[["p10"]])
 ## 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)
++print(p10)
 ## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 899.4089 336.4348 899.4089 
@@ -486,25 +508,25 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)   Lower    Upper
-## parent_0      101.7315 6.42e-11 91.9259 111.5371
-## k_parent_sink   0.0495 1.70e-07  0.0404   0.0607
-## sigma           8.0152 1.28e-04  4.6813  11.3491
+##          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_sink     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
+##                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 6.42e-04  0.0301   0.0814
-## k2         0.0495 1.66e-02  0.0200   0.1225
-## g          0.6634 5.00e-01  0.0000   1.0000
-## sigma      8.0152 2.50e-04  4.5886  11.4418
+##          Estimate   Pr(>t)   Lower   Upper
+## parent_0 101.7315 1.41e-09 91.6534 111.810
+## k1         0.0495 6.48e-04  0.0303   0.081
+## k2         0.0495 1.67e-02  0.0201   0.122
+## g          0.6634 5.00e-01  0.0000   1.000
+## sigma      8.0152 2.50e-04  4.5886  11.442
 ## 
 ## 
 ## DTx values:
@@ -524,12 +546,15 @@
 
 
 Example on page 11
-p11 <- nafta(NAFTA_SOP_Attachment[["p11"]])
++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)
++print(p11)
 ## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 579.6805 204.7932 144.7783 
@@ -539,17 +564,17 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)    Lower    Upper
-## parent_0      96.15820 4.83e-13 90.24934 1.02e+02
-## k_parent_sink  0.00321 4.71e-05  0.00222 4.64e-03
-## sigma          6.43473 1.28e-04  3.75822 9.11e+00
+##          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_sink 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
+##                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
@@ -567,7 +592,7 @@
 ## DFOP 4.21e+11 2.64e+12 9.56e+11
 ## 
 ## Representative half-life:
-## [1] 41148169
+## [1] 41148171
 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.
 
 

@@ -578,14 +603,17 @@
 
 
 Example on page 12, upper panel
-p12a <- nafta(NAFTA_SOP_Attachment[["p12a"]])
++p12a <- nafta(NAFTA_SOP_Attachment[["p12a"]])
 ## Warning in summary.mkinfit(x): Could not calculate correlation; no covariance
 ## matrix
 ## 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)
++print(p12a)
 ## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 695.4440 220.0685 695.4440 
@@ -595,23 +623,23 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)  Lower   Upper
-## parent_0       100.521 8.75e-12 92.461 108.581
-## k_parent_sink    0.124 3.61e-08  0.104   0.148
-## sigma            7.048 1.28e-04  4.116   9.980
+##          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_sink    2.436     NA    NA    NA
-## N_parent               0.263     NA    NA    NA
-## sigma                  3.965     NA    NA    NA
+##                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 5.74e-06  0.0958   0.161
-## k2          0.124 6.61e-02  0.0319   0.484
+## k1          0.124 5.75e-06  0.0958   0.161
+## k2          0.124 6.72e-02  0.0319   0.484
 ## g           0.877 5.00e-01  0.0000   1.000
 ## sigma       7.048 2.50e-04  4.0349  10.061
 ## 
@@ -628,7 +656,8 @@
 
 
 Example on page 12, lower panel
-p12b <- nafta(NAFTA_SOP_Attachment[["p12b"]])
++p12b <- nafta(NAFTA_SOP_Attachment[["p12b"]])
 ## Warning in sqrt(diag(covar)): NaNs produced
 ## Warning in qt(alpha/2, rdf): NaNs produced
 ## Warning in qt(1 - alpha/2, rdf): NaNs produced
@@ -639,9 +668,11 @@
 ## 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(p12b)
++plot(p12b)
 
-print(p12b)
++print(p12b)
 ## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 58.90242 19.06353 58.90242 
@@ -651,17 +682,17 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate  Pr(>t)   Lower    Upper
-## parent_0       97.6840 0.00039 85.9388 109.4292
-## k_parent_sink   0.0589 0.00261  0.0431   0.0805
-## sigma           3.4323 0.04356 -1.2377   8.1023
+##          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_sink    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
+##                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
@@ -684,16 +715,15 @@
 
 
 Example on page 13
-p13 <- nafta(NAFTA_SOP_Attachment[["p13"]])
-## 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
++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)
++print(p13)
 ## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 174.5971 142.3951 174.5971 
@@ -703,24 +733,24 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)    Lower    Upper
-## parent_0      92.73500 5.99e-17 89.61936 95.85065
-## k_parent_sink  0.00258 2.42e-09  0.00223  0.00299
-## sigma          3.41172 7.07e-05  2.05455  4.76888
+##          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_sink   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
+##                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 9.25e-15 8.95e+01 9.59e+01
-## k1        0.00258 4.28e-01 1.70e-08 3.92e+02
+## k1        0.00258 4.28e-01 1.45e-08 4.61e+02
 ## k2        0.00258 3.69e-08 2.20e-03 3.03e-03
-## g         0.00442 5.00e-01       NA       NA
+## g         0.00442 5.00e-01 0.00e+00 1.00e+00
 ## sigma     3.41172 1.35e-04 2.02e+00 4.80e+00
 ## 
 ## 
@@ -737,16 +767,19 @@
 
 
 DT50 not observed in the study and DFOP problems in PestDF
-p14 <- nafta(NAFTA_SOP_Attachment[["p14"]])
++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)
++print(p14)
 ## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 48.43249 28.67746 27.26248 
@@ -756,23 +789,23 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)    Lower    Upper
-## parent_0      99.47124 2.06e-30 98.42254 1.01e+02
-## k_parent_sink  0.00279 3.75e-15  0.00256 3.04e-03
-## sigma          1.55616 3.81e-06  1.03704 2.08e+00
+##          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_sink 9.44e-08     NA   NaN   NaN
-## N_parent            3.31e+00     NA   NaN   NaN
-## sigma               1.20e+00     NA 0.796   1.6
+##                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       7.29e-12 5.00e-01  0.00000      Inf
+## k2       7.70e-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
 ## 
@@ -781,7 +814,7 @@
 ##          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 2.54e+10 2.46e+11 9.51e+10
+## DFOP 2.41e+10 2.33e+11 9.00e+10
 ## 
 ## Representative half-life:
 ## [1] 6697.44
@@ -790,17 +823,19 @@
 
 
 N is less than 1 and DFOP fraction parameter is below zero
-p15a <- nafta(NAFTA_SOP_Attachment[["p15a"]])
++p15a <- nafta(NAFTA_SOP_Attachment[["p15a"]])
 ## 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(p15a)
++plot(p15a)
 
-print(p15a)
++print(p15a)
 ## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 245.5248 135.0132 245.5248 
@@ -810,25 +845,25 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)    Lower   Upper
-## parent_0      97.96751 2.00e-15 94.32049 101.615
-## k_parent_sink  0.00952 4.93e-09  0.00824   0.011
-## sigma          4.18778 1.28e-04  2.44588   5.930
+##          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_sink    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
+##                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
 ## 
 ## $DFOP
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 97.96752 2.85e-13 94.21914 101.7159
-## k1        0.00952 6.80e-02  0.00277   0.0327
-## k2        0.00952 3.82e-06  0.00902   0.0100
-## g         0.17247      NaN       NA       NA
-## sigma     4.18778 2.50e-04  2.39747   5.9781
+##          Estimate Pr(>t)    Lower    Upper
+## parent_0 97.96752     NA 94.21914 101.7159
+## k1        0.00952     NA  0.00241   0.0377
+## k2        0.00952     NA  0.00747   0.0121
+## g         0.17247     NA       NA       NA
+## sigma     4.18778     NA  2.39747   5.9781
 ## 
 ## 
 ## DTx values:
@@ -839,16 +874,19 @@
 ## 
 ## Representative half-life:
 ## [1] 41.33
-p15b <- nafta(NAFTA_SOP_Attachment[["p15b"]])
++p15b <- nafta(NAFTA_SOP_Attachment[["p15b"]])
 ## Warning in sqrt(diag(covar)): NaNs produced
 ## Warning in sqrt(1/diag(V)): NaNs produced
 ## Warning in cov2cor(ans$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)
++print(p15b)
 ## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 106.91629  68.55574 106.91629 
@@ -858,25 +896,25 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)    Lower    Upper
-## parent_0      1.01e+02 3.06e-17 98.31594 1.03e+02
-## k_parent_sink 4.86e-03 2.48e-10  0.00435 5.42e-03
-## sigma         2.76e+00 1.28e-04  1.61402 3.91e+00
+##          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_sink     0.38 3.22e-01  0.00352  41.05
-## N_parent                0.00 5.00e-01 -1.07695   1.08
-## sigma                   2.21 2.57e-04  1.23245   3.19
+##                Estimate   Pr(>t)    Lower  Upper
+## parent_0          99.83 1.81e-16 97.51348 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 6.75e-04 3.49e-02
-## k2       4.86e-03     NA 3.37e-03 6.99e-03
+## parent_0 1.01e+02     NA 98.24464 1.04e+02
+## k1       4.86e-03     NA  0.00068 3.47e-02
+## k2       4.86e-03     NA  0.00338 6.99e-03
 ## g        1.50e-01     NA       NA       NA
-## sigma    2.76e+00     NA 1.58e+00 3.94e+00
+## sigma    2.76e+00     NA  1.58208 3.94e+00
 ## 
 ## 
 ## DTx values:
@@ -892,14 +930,17 @@
 
 
 The DFOP fraction parameter is greater than 1
-p16 <- nafta(NAFTA_SOP_Attachment[["p16"]])
++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)
++print(p16)
 ## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 3831.804 2062.008 1550.980 
@@ -909,22 +950,22 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)  Lower Upper
-## parent_0        71.953 2.33e-13 60.509 83.40
-## k_parent_sink    0.159 4.86e-05  0.102  0.25
-## sigma           11.302 1.25e-08  8.308 14.30
+##          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_sink 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
+##                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        18.5561 5.00e-01  0.0000    Inf
+## k1        18.5560 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
@@ -972,7 +1013,7 @@
 

 
 
-  Site built with pkgdown 1.5.1.
+  Site built with pkgdown 1.6.1.
 
 
       
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index 0698baf6..28a3b68a 100644
--- a/docs/articles/web_only/benchmarks.html
+++ b/docs/articles/web_only/benchmarks.html
@@ -5,13 +5,13 @@
 
 
 
-Benchmark timings for mkin on various systems • mkin
+Benchmark timings for mkin • mkin
 
 
 
 
 
-
+

Example evaluation of FOCUS dataset Z

Johannes Ranke

2020-05-27

2020-10-15

The data

Parent and one metabolite

Metabolites Z2 and Z3

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

Johannes Ranke

2020-05-27

2020-10-15

Example on page 5, upper panel

Example on page 5, lower panel

Example on page 6

Example on page 7

Example on page 8

Example on page 9, upper panel

Example on page 9, lower panel

Example on page 10

Example on page 11

Example on page 12, upper panel

Example on page 12, lower panel

Example on page 13

DT50 not observed in the study and DFOP problems in PestDF

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

The DFOP fraction parameter is greater than 1