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

- - - - -

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 -

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 -

-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)

-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 -

-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)

-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 -

-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)

-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 -

-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)

-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 -

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

-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

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

-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

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 -

-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)

-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 -

-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)

-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 -

-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)

-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 -

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 -

-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)

-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 -

-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)

-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 -

-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)

-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 -

-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)

-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 -

-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)

-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

-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

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 -

-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)

-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 -

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 -

-US EPA. 2015. “Standard Operating Procedure for Using the NAFTA -Guidance to Calculate Representative Half-Life Values and Characterizing -Pesticide Degradation.” https://www.epa.gov/pesticide-science-and-assessing-pesticide-risks/standard-operating-procedure-using-nafta-guidance. -

- - - -

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

Johannes -Ranke

26 February 2019 (rebuilt -2023-04-16)