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+
+ + + + +
+
+
+

Example evaluation of FOCUS Example Dataset D

+

Johannes Ranke

+ +

2020-05-27

+ + Source: vignettes/FOCUS_D.rmd + + +
+ + + +

This is just a very simple vignette showing how to fit a degradation model for a parent compound with one transformation product using mkin. After loading the library we look at the data. We have observed concentrations in the column named value at the times specified in column time for the two observed variables named parent and m1.

+
library(mkin, quietly = TRUE)
+print(FOCUS_2006_D)
+
##      name time  value
+## 1  parent    0  99.46
+## 2  parent    0 102.04
+## 3  parent    1  93.50
+## 4  parent    1  92.50
+## 5  parent    3  63.23
+## 6  parent    3  68.99
+## 7  parent    7  52.32
+## 8  parent    7  55.13
+## 9  parent   14  27.27
+## 10 parent   14  26.64
+## 11 parent   21  11.50
+## 12 parent   21  11.64
+## 13 parent   35   2.85
+## 14 parent   35   2.91
+## 15 parent   50   0.69
+## 16 parent   50   0.63
+## 17 parent   75   0.05
+## 18 parent   75   0.06
+## 19 parent  100     NA
+## 20 parent  100     NA
+## 21 parent  120     NA
+## 22 parent  120     NA
+## 23     m1    0   0.00
+## 24     m1    0   0.00
+## 25     m1    1   4.84
+## 26     m1    1   5.64
+## 27     m1    3  12.91
+## 28     m1    3  12.96
+## 29     m1    7  22.97
+## 30     m1    7  24.47
+## 31     m1   14  41.69
+## 32     m1   14  33.21
+## 33     m1   21  44.37
+## 34     m1   21  46.44
+## 35     m1   35  41.22
+## 36     m1   35  37.95
+## 37     m1   50  41.19
+## 38     m1   50  40.01
+## 39     m1   75  40.09
+## 40     m1   75  33.85
+## 41     m1  100  31.04
+## 42     m1  100  33.13
+## 43     m1  120  25.15
+## 44     m1  120  33.31
+

Next we specify the degradation model: The parent compound degrades with simple first-order kinetics (SFO) to one metabolite named m1, which also degrades with SFO kinetics.

+

The call to mkinmod returns a degradation model. The differential equations represented in R code can be found in the character vector $diffs of the mkinmod object. If a C compiler (gcc) is installed and functional, the differential equation model will be compiled from auto-generated C code.

+
SFO_SFO <- mkinmod(parent = mkinsub("SFO", "m1"), m1 = mkinsub("SFO"))
+
## Successfully compiled differential equation model from auto-generated C code.
+
print(SFO_SFO$diffs)
+
##                                                    parent 
+##                          "d_parent = - k_parent * parent" 
+##                                                        m1 
+## "d_m1 = + f_parent_to_m1 * k_parent * parent - k_m1 * m1"
+

We do the fitting without progress report (quiet = TRUE).

+
fit <- mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE)
+
## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE): Observations with value
+## of zero were removed from the data
+

A plot of the fit including a residual plot for both observed variables is obtained using the plot_sep method for mkinfit objects, which shows separate graphs for all compounds and their residuals.

+
plot_sep(fit, lpos = c("topright", "bottomright"))
+

+

Confidence intervals for the parameter estimates are obtained using the mkinparplot function.

+ +

+

A comprehensive report of the results is obtained using the summary method for mkinfit objects.

+
summary(fit)
+
## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.0 
+## Date of fit:     Wed May 27 06:02:21 2020 
+## Date of summary: Wed May 27 06:02:21 2020 
+## 
+## Equations:
+## d_parent/dt = - k_parent * parent
+## d_m1/dt = + f_parent_to_m1 * k_parent * parent - k_m1 * m1
+## 
+## Model predictions using solution type analytical 
+## 
+## Fitted using 421 model solutions performed in 0.177 s
+## 
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
+## 
+## Starting values for parameters to be optimised:
+##                   value   type
+## parent_0       100.7500  state
+## k_parent         0.1000 deparm
+## k_m1             0.1001 deparm
+## f_parent_to_m1   0.5000 deparm
+## 
+## Starting values for the transformed parameters actually optimised:
+##                     value lower upper
+## parent_0       100.750000  -Inf   Inf
+## log_k_parent    -2.302585  -Inf   Inf
+## log_k_m1        -2.301586  -Inf   Inf
+## f_parent_ilr_1   0.000000  -Inf   Inf
+## 
+## Fixed parameter values:
+##      value  type
+## m1_0     0 state
+## 
+## Results:
+## 
+##        AIC      BIC    logLik
+##   204.4486 212.6365 -97.22429
+## 
+## Optimised, transformed parameters with symmetric confidence intervals:
+##                Estimate Std. Error    Lower    Upper
+## parent_0       99.60000    1.57000 96.40000 102.8000
+## log_k_parent   -2.31600    0.04087 -2.39900  -2.2330
+## log_k_m1       -5.24800    0.13320 -5.51800  -4.9770
+## f_parent_ilr_1  0.04096    0.06312 -0.08746   0.1694
+## sigma           3.12600    0.35850  2.39600   3.8550
+## 
+## Parameter correlation:
+##                  parent_0 log_k_parent   log_k_m1 f_parent_ilr_1      sigma
+## parent_0        1.000e+00    5.174e-01 -1.688e-01     -5.471e-01 -3.190e-07
+## log_k_parent    5.174e-01    1.000e+00 -3.263e-01     -5.426e-01  3.168e-07
+## log_k_m1       -1.688e-01   -3.263e-01  1.000e+00      7.478e-01 -1.406e-07
+## f_parent_ilr_1 -5.471e-01   -5.426e-01  7.478e-01      1.000e+00 -1.587e-10
+## sigma          -3.190e-07    3.168e-07 -1.406e-07     -1.587e-10  1.000e+00
+## 
+## Backtransformed parameters:
+## Confidence intervals for internally transformed parameters are asymmetric.
+## t-test (unrealistically) based on the assumption of normal distribution
+## for estimators of untransformed parameters.
+##                 Estimate t value    Pr(>t)     Lower     Upper
+## parent_0       99.600000  63.430 2.298e-36 96.400000 1.028e+02
+## k_parent        0.098700  24.470 4.955e-23  0.090820 1.073e-01
+## k_m1            0.005261   7.510 6.165e-09  0.004012 6.898e-03
+## f_parent_to_m1  0.514500  23.070 3.104e-22  0.469100 5.596e-01
+## sigma           3.126000   8.718 2.235e-10  2.396000 3.855e+00
+## 
+## FOCUS Chi2 error levels in percent:
+##          err.min n.optim df
+## All data   6.398       4 15
+## parent     6.459       2  7
+## m1         4.690       2  8
+## 
+## Resulting formation fractions:
+##                 ff
+## parent_m1   0.5145
+## parent_sink 0.4855
+## 
+## Estimated disappearance times:
+##           DT50   DT90
+## parent   7.023  23.33
+## m1     131.761 437.70
+## 
+## Data:
+##  time variable observed predicted   residual
+##     0   parent    99.46  99.59848 -1.385e-01
+##     0   parent   102.04  99.59848  2.442e+00
+##     1   parent    93.50  90.23787  3.262e+00
+##     1   parent    92.50  90.23787  2.262e+00
+##     3   parent    63.23  74.07319 -1.084e+01
+##     3   parent    68.99  74.07319 -5.083e+00
+##     7   parent    52.32  49.91206  2.408e+00
+##     7   parent    55.13  49.91206  5.218e+00
+##    14   parent    27.27  25.01257  2.257e+00
+##    14   parent    26.64  25.01257  1.627e+00
+##    21   parent    11.50  12.53462 -1.035e+00
+##    21   parent    11.64  12.53462 -8.946e-01
+##    35   parent     2.85   3.14787 -2.979e-01
+##    35   parent     2.91   3.14787 -2.379e-01
+##    50   parent     0.69   0.71624 -2.624e-02
+##    50   parent     0.63   0.71624 -8.624e-02
+##    75   parent     0.05   0.06074 -1.074e-02
+##    75   parent     0.06   0.06074 -7.381e-04
+##     1       m1     4.84   4.80296  3.704e-02
+##     1       m1     5.64   4.80296  8.370e-01
+##     3       m1    12.91  13.02400 -1.140e-01
+##     3       m1    12.96  13.02400 -6.400e-02
+##     7       m1    22.97  25.04476 -2.075e+00
+##     7       m1    24.47  25.04476 -5.748e-01
+##    14       m1    41.69  36.69002  5.000e+00
+##    14       m1    33.21  36.69002 -3.480e+00
+##    21       m1    44.37  41.65310  2.717e+00
+##    21       m1    46.44  41.65310  4.787e+00
+##    35       m1    41.22  43.31312 -2.093e+00
+##    35       m1    37.95  43.31312 -5.363e+00
+##    50       m1    41.19  41.21831 -2.831e-02
+##    50       m1    40.01  41.21831 -1.208e+00
+##    75       m1    40.09  36.44703  3.643e+00
+##    75       m1    33.85  36.44703 -2.597e+00
+##   100       m1    31.04  31.98163 -9.416e-01
+##   100       m1    33.13  31.98163  1.148e+00
+##   120       m1    25.15  28.78984 -3.640e+00
+##   120       m1    33.31  28.78984  4.520e+00
+
+ + + +
+ + + +
+

Developed by Johannes Ranke.

+
+ +
+

Site built with pkgdown 1.5.1.

+
+ +
+
+ + + + + + diff --git a/docs/dev/articles/FOCUS_D_files/figure-html/plot-1.png b/docs/dev/articles/FOCUS_D_files/figure-html/plot-1.png new file mode 100644 index 00000000..306244b3 Binary files /dev/null and b/docs/dev/articles/FOCUS_D_files/figure-html/plot-1.png differ diff --git a/docs/dev/articles/FOCUS_D_files/figure-html/plot_2-1.png b/docs/dev/articles/FOCUS_D_files/figure-html/plot_2-1.png new file mode 100644 index 00000000..158e3c50 Binary files /dev/null and b/docs/dev/articles/FOCUS_D_files/figure-html/plot_2-1.png differ diff --git a/docs/dev/articles/FOCUS_L.html b/docs/dev/articles/FOCUS_L.html new file mode 100644 index 00000000..91043d0f --- /dev/null +++ b/docs/dev/articles/FOCUS_L.html @@ -0,0 +1,797 @@ + + + + + + + +Example evaluation of FOCUS Laboratory Data L1 to L3 • mkin + + + + + + + + + + + +
+
+ + + + +
+
+
+

Example evaluation of FOCUS Laboratory Data L1 to L3

+

Johannes Ranke

+ +

2020-05-27

+ + Source: vignettes/FOCUS_L.rmd + + +
+ + + +
+

+Laboratory Data L1

+

The following code defines example dataset L1 from the FOCUS kinetics report, p. 284:

+
library("mkin", quietly = TRUE)
+FOCUS_2006_L1 = data.frame(
+  t = rep(c(0, 1, 2, 3, 5, 7, 14, 21, 30), each = 2),
+  parent = c(88.3, 91.4, 85.6, 84.5, 78.9, 77.6,
+             72.0, 71.9, 50.3, 59.4, 47.0, 45.1,
+             27.7, 27.3, 10.0, 10.4, 2.9, 4.0))
+FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1)
+

Here we use the assumptions of simple first order (SFO), the case of declining rate constant over time (FOMC) and the case of two different phases of the kinetics (DFOP). For a more detailed discussion of the models, please see the FOCUS kinetics report.

+

Since mkin version 0.9-32 (July 2014), we can use shorthand notation like "SFO" for parent only degradation models. The following two lines fit the model and produce the summary report of the model fit. This covers the numerical analysis given in the FOCUS report.

+
m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet = TRUE)
+summary(m.L1.SFO)
+
## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.0 
+## Date of fit:     Wed May 27 06:02:23 2020 
+## Date of summary: Wed May 27 06:02:23 2020 
+## 
+## Equations:
+## d_parent/dt = - k_parent_sink * parent
+## 
+## Model predictions using solution type analytical 
+## 
+## Fitted using 133 model solutions performed in 0.03 s
+## 
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
+## 
+## Starting values for parameters to be optimised:
+##               value   type
+## parent_0      89.85  state
+## k_parent_sink  0.10 deparm
+## 
+## Starting values for the transformed parameters actually optimised:
+##                       value lower upper
+## parent_0          89.850000  -Inf   Inf
+## log_k_parent_sink -2.302585  -Inf   Inf
+## 
+## Fixed parameter values:
+## None
+## 
+## Results:
+## 
+##        AIC     BIC    logLik
+##   93.88778 96.5589 -43.94389
+## 
+## Optimised, transformed parameters with symmetric confidence intervals:
+##                   Estimate Std. Error  Lower  Upper
+## parent_0            92.470    1.28200 89.740 95.200
+## log_k_parent_sink   -2.347    0.03763 -2.428 -2.267
+## sigma                2.780    0.46330  1.792  3.767
+## 
+## Parameter correlation:
+##                     parent_0 log_k_parent_sink      sigma
+## parent_0           1.000e+00         6.186e-01 -1.712e-09
+## log_k_parent_sink  6.186e-01         1.000e+00 -3.237e-09
+## sigma             -1.712e-09        -3.237e-09  1.000e+00
+## 
+## Backtransformed parameters:
+## Confidence intervals for internally transformed parameters are asymmetric.
+## t-test (unrealistically) based on the assumption of normal distribution
+## for estimators of untransformed parameters.
+##               Estimate t value    Pr(>t)    Lower   Upper
+## parent_0      92.47000   72.13 8.824e-21 89.74000 95.2000
+## k_parent_sink  0.09561   26.57 2.487e-14  0.08824  0.1036
+## sigma          2.78000    6.00 1.216e-05  1.79200  3.7670
+## 
+## FOCUS Chi2 error levels in percent:
+##          err.min n.optim df
+## All data   3.424       2  7
+## parent     3.424       2  7
+## 
+## Estimated disappearance times:
+##         DT50  DT90
+## parent 7.249 24.08
+## 
+## Data:
+##  time variable observed predicted residual
+##     0   parent     88.3    92.471  -4.1710
+##     0   parent     91.4    92.471  -1.0710
+##     1   parent     85.6    84.039   1.5610
+##     1   parent     84.5    84.039   0.4610
+##     2   parent     78.9    76.376   2.5241
+##     2   parent     77.6    76.376   1.2241
+##     3   parent     72.0    69.412   2.5884
+##     3   parent     71.9    69.412   2.4884
+##     5   parent     50.3    57.330  -7.0301
+##     5   parent     59.4    57.330   2.0699
+##     7   parent     47.0    47.352  -0.3515
+##     7   parent     45.1    47.352  -2.2515
+##    14   parent     27.7    24.247   3.4528
+##    14   parent     27.3    24.247   3.0528
+##    21   parent     10.0    12.416  -2.4163
+##    21   parent     10.4    12.416  -2.0163
+##    30   parent      2.9     5.251  -2.3513
+##    30   parent      4.0     5.251  -1.2513
+

A plot of the fit is obtained with the plot function for mkinfit objects.

+
plot(m.L1.SFO, show_errmin = TRUE, main = "FOCUS L1 - SFO")
+

+

The residual plot can be easily obtained by

+
mkinresplot(m.L1.SFO, ylab = "Observed", xlab = "Time")
+

+

For comparison, the FOMC model is fitted as well, and the \(\chi^2\) error level is checked.

+
m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE)
+
## Warning in mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet = TRUE): Optimisation did not converge:
+## false convergence (8)
+
plot(m.L1.FOMC, show_errmin = TRUE, main = "FOCUS L1 - FOMC")
+

+
summary(m.L1.FOMC, data = FALSE)
+
## 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
+
## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.0 
+## Date of fit:     Wed May 27 06:02:24 2020 
+## Date of summary: Wed May 27 06:02:24 2020 
+## 
+## 
+## Warning: Optimisation did not converge:
+## false convergence (8) 
+## 
+## 
+## Equations:
+## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
+## 
+## Model predictions using solution type analytical 
+## 
+## Fitted using 899 model solutions performed in 0.204 s
+## 
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
+## 
+## Starting values for parameters to be optimised:
+##          value   type
+## parent_0 89.85  state
+## alpha     1.00 deparm
+## beta     10.00 deparm
+## 
+## Starting values for the transformed parameters actually optimised:
+##               value lower upper
+## parent_0  89.850000  -Inf   Inf
+## log_alpha  0.000000  -Inf   Inf
+## log_beta   2.302585  -Inf   Inf
+## 
+## Fixed parameter values:
+## None
+## 
+## Results:
+## 
+##        AIC      BIC    logLik
+##   95.88835 99.44984 -43.94418
+## 
+## Optimised, transformed parameters with symmetric confidence intervals:
+##           Estimate Std. Error  Lower  Upper
+## parent_0     92.47     1.2800 89.730 95.220
+## log_alpha    10.58        NaN    NaN    NaN
+## log_beta     12.93        NaN    NaN    NaN
+## sigma         2.78     0.4507  1.813  3.747
+## 
+## Parameter correlation:
+##           parent_0 log_alpha log_beta   sigma
+## parent_0   1.00000       NaN      NaN 0.01452
+## log_alpha      NaN         1      NaN     NaN
+## log_beta       NaN       NaN        1     NaN
+## sigma      0.01452       NaN      NaN 1.00000
+## 
+## Backtransformed parameters:
+## Confidence intervals for internally transformed parameters are asymmetric.
+## t-test (unrealistically) based on the assumption of normal distribution
+## for estimators of untransformed parameters.
+##           Estimate  t value    Pr(>t)  Lower  Upper
+## parent_0     92.47 72.13000 1.052e-19 89.730 95.220
+## alpha     39440.00  0.02397 4.906e-01     NA     NA
+## beta     412500.00  0.02397 4.906e-01     NA     NA
+## sigma         2.78  6.00000 1.628e-05  1.813  3.747
+## 
+## FOCUS Chi2 error levels in percent:
+##          err.min n.optim df
+## All data   3.619       3  6
+## parent     3.619       3  6
+## 
+## Estimated disappearance times:
+##         DT50  DT90 DT50back
+## parent 7.249 24.08    7.249
+

We get a warning that the default optimisation algorithm Port did not converge, which is an indication that the model is overparameterised, i.e. contains too many parameters that are ill-defined as a consequence.

+

And in fact, due to the higher number of parameters, and the lower number of degrees of freedom of the fit, the \(\chi^2\) error level is actually higher for the FOMC model (3.6%) than for the SFO model (3.4%). Additionally, the parameters log_alpha and log_beta internally fitted in the model have excessive confidence intervals, that span more than 25 orders of magnitude (!) when backtransformed to the scale of alpha and beta. Also, the t-test for significant difference from zero does not indicate such a significant difference, with p-values greater than 0.1, and finally, the parameter correlation of log_alpha and log_beta is 1.000, clearly indicating that the model is overparameterised.

+

The \(\chi^2\) error levels reported in Appendix 3 and Appendix 7 to the FOCUS kinetics report are rounded to integer percentages and partly deviate by one percentage point from the results calculated by mkin. The reason for this is not known. However, mkin gives the same \(\chi^2\) error levels as the kinfit package and the calculation routines of the kinfit package have been extensively compared to the results obtained by the KinGUI software, as documented in the kinfit package vignette. KinGUI was the first widely used standard package in this field. Also, the calculation of \(\chi^2\) error levels was compared with KinGUII, CAKE and DegKin manager in a project sponsored by the German Umweltbundesamt (Ranke 2014).

+
+
+

+Laboratory Data L2

+

The following code defines example dataset L2 from the FOCUS kinetics report, p. 287:

+
FOCUS_2006_L2 = data.frame(
+  t = rep(c(0, 1, 3, 7, 14, 28), each = 2),
+  parent = c(96.1, 91.8, 41.4, 38.7,
+             19.3, 22.3, 4.6, 4.6,
+             2.6, 1.2, 0.3, 0.6))
+FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2)
+
+

+SFO fit for L2

+

Again, the SFO model is fitted and the result is plotted. The residual plot can be obtained simply by adding the argument show_residuals to the plot command.

+
m.L2.SFO <- mkinfit("SFO", FOCUS_2006_L2_mkin, quiet=TRUE)
+plot(m.L2.SFO, show_residuals = TRUE, show_errmin = TRUE,
+     main = "FOCUS L2 - SFO")
+

+

The \(\chi^2\) error level of 14% suggests that the model does not fit very well. This is also obvious from the plots of the fit, in which we have included the residual plot.

+

In the FOCUS kinetics report, it is stated that there is no apparent systematic error observed from the residual plot up to the measured DT90 (approximately at day 5), and there is an underestimation beyond that point.

+

We may add that it is difficult to judge the random nature of the residuals just from the three samplings at days 0, 1 and 3. Also, it is not clear a priori why a consistent underestimation after the approximate DT90 should be irrelevant. However, this can be rationalised by the fact that the FOCUS fate models generally only implement SFO kinetics.

+
+
+

+FOMC fit for L2

+

For comparison, the FOMC model is fitted as well, and the \(\chi^2\) error level is checked.

+
m.L2.FOMC <- mkinfit("FOMC", FOCUS_2006_L2_mkin, quiet = TRUE)
+plot(m.L2.FOMC, show_residuals = TRUE,
+     main = "FOCUS L2 - FOMC")
+

+
summary(m.L2.FOMC, data = FALSE)
+
## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.0 
+## Date of fit:     Wed May 27 06:02:24 2020 
+## Date of summary: Wed May 27 06:02:24 2020 
+## 
+## Equations:
+## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
+## 
+## Model predictions using solution type analytical 
+## 
+## Fitted using 239 model solutions performed in 0.047 s
+## 
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
+## 
+## Starting values for parameters to be optimised:
+##          value   type
+## parent_0 93.95  state
+## alpha     1.00 deparm
+## beta     10.00 deparm
+## 
+## Starting values for the transformed parameters actually optimised:
+##               value lower upper
+## parent_0  93.950000  -Inf   Inf
+## log_alpha  0.000000  -Inf   Inf
+## log_beta   2.302585  -Inf   Inf
+## 
+## Fixed parameter values:
+## None
+## 
+## Results:
+## 
+##        AIC      BIC    logLik
+##   61.78966 63.72928 -26.89483
+## 
+## Optimised, transformed parameters with symmetric confidence intervals:
+##           Estimate Std. Error    Lower   Upper
+## parent_0   93.7700     1.6130 90.05000 97.4900
+## log_alpha   0.3180     0.1559 -0.04149  0.6776
+## log_beta    0.2102     0.2493 -0.36460  0.7850
+## sigma       2.2760     0.4645  1.20500  3.3470
+## 
+## Parameter correlation:
+##             parent_0  log_alpha   log_beta      sigma
+## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.637e-09
+## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.617e-07
+## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.387e-07
+## sigma     -7.637e-09 -1.617e-07 -1.387e-07  1.000e+00
+## 
+## Backtransformed parameters:
+## Confidence intervals for internally transformed parameters are asymmetric.
+## t-test (unrealistically) based on the assumption of normal distribution
+## for estimators of untransformed parameters.
+##          Estimate t value    Pr(>t)   Lower  Upper
+## parent_0   93.770  58.120 4.267e-12 90.0500 97.490
+## alpha       1.374   6.414 1.030e-04  0.9594  1.969
+## beta        1.234   4.012 1.942e-03  0.6945  2.192
+## sigma       2.276   4.899 5.977e-04  1.2050  3.347
+## 
+## FOCUS Chi2 error levels in percent:
+##          err.min n.optim df
+## All data   6.205       3  3
+## parent     6.205       3  3
+## 
+## Estimated disappearance times:
+##          DT50  DT90 DT50back
+## parent 0.8092 5.356    1.612
+

The error level at which the \(\chi^2\) test passes is much lower in this case. Therefore, the FOMC model provides a better description of the data, as less experimental error has to be assumed in order to explain the data.

+
+
+

+DFOP fit for L2

+

Fitting the four parameter DFOP model further reduces the \(\chi^2\) error level.

+
m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin, quiet = TRUE)
+plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
+     main = "FOCUS L2 - DFOP")
+

+
summary(m.L2.DFOP, data = FALSE)
+
## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.0 
+## Date of fit:     Wed May 27 06:02:24 2020 
+## Date of summary: Wed May 27 06:02:24 2020 
+## 
+## Equations:
+## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+##            time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+##            * parent
+## 
+## Model predictions using solution type analytical 
+## 
+## Fitted using 572 model solutions performed in 0.131 s
+## 
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
+## 
+## Starting values for parameters to be optimised:
+##          value   type
+## parent_0 93.95  state
+## k1        0.10 deparm
+## k2        0.01 deparm
+## g         0.50 deparm
+## 
+## Starting values for the transformed parameters actually optimised:
+##              value lower upper
+## parent_0 93.950000  -Inf   Inf
+## log_k1   -2.302585  -Inf   Inf
+## log_k2   -4.605170  -Inf   Inf
+## g_ilr     0.000000  -Inf   Inf
+## 
+## Fixed parameter values:
+## None
+## 
+## Results:
+## 
+##        AIC      BIC    logLik
+##   52.36695 54.79148 -21.18347
+## 
+## Optimised, transformed parameters with symmetric confidence intervals:
+##          Estimate Std. Error      Lower     Upper
+## parent_0  93.9500  9.998e-01    91.5900   96.3100
+## log_k1     3.1370  2.376e+03 -5616.0000 5622.0000
+## log_k2    -1.0880  6.285e-02    -1.2370   -0.9394
+## g_ilr     -0.2821  7.033e-02    -0.4484   -0.1158
+## sigma      1.4140  2.886e-01     0.7314    2.0960
+## 
+## Parameter correlation:
+##            parent_0     log_k1     log_k2      g_ilr      sigma
+## parent_0  1.000e+00  5.155e-07  2.371e-09  2.665e-01 -6.849e-09
+## log_k1    5.155e-07  1.000e+00  8.434e-05 -1.659e-04 -7.791e-06
+## log_k2    2.371e-09  8.434e-05  1.000e+00 -7.903e-01 -1.262e-08
+## g_ilr     2.665e-01 -1.659e-04 -7.903e-01  1.000e+00  3.241e-08
+## sigma    -6.849e-09 -7.791e-06 -1.262e-08  3.241e-08  1.000e+00
+## 
+## Backtransformed parameters:
+## Confidence intervals for internally transformed parameters are asymmetric.
+## t-test (unrealistically) based on the assumption of normal distribution
+## for estimators of untransformed parameters.
+##          Estimate   t value    Pr(>t)   Lower   Upper
+## parent_0  93.9500 9.397e+01 2.036e-12 91.5900 96.3100
+## k1        23.0400 4.303e-04 4.998e-01  0.0000     Inf
+## k2         0.3369 1.591e+01 4.697e-07  0.2904  0.3909
+## g          0.4016 1.680e+01 3.238e-07  0.3466  0.4591
+## sigma      1.4140 4.899e+00 8.776e-04  0.7314  2.0960
+## 
+## FOCUS Chi2 error levels in percent:
+##          err.min n.optim df
+## All data    2.53       4  2
+## parent      2.53       4  2
+## 
+## Estimated disappearance times:
+##          DT50  DT90 DT50_k1 DT50_k2
+## parent 0.5335 5.311 0.03009   2.058
+

Here, the DFOP model is clearly the best-fit model for dataset L2 based on the chi^2 error level criterion. However, the failure to calculate the covariance matrix indicates that the parameter estimates correlate excessively. Therefore, the FOMC model may be preferred for this dataset.

+
+
+
+

+Laboratory Data L3

+

The following code defines example dataset L3 from the FOCUS kinetics report, p. 290.

+
FOCUS_2006_L3 = data.frame(
+  t = c(0, 3, 7, 14, 30, 60, 91, 120),
+  parent = c(97.8, 60, 51, 43, 35, 22, 15, 12))
+FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3)
+
+

+Fit multiple models

+

As of mkin version 0.9-39 (June 2015), we can fit several models to one or more datasets in one call to the function mmkin. The datasets have to be passed in a list, in this case a named list holding only the L3 dataset prepared above.

+
# Only use one core here, not to offend the CRAN checks
+mm.L3 <- mmkin(c("SFO", "FOMC", "DFOP"), cores = 1,
+               list("FOCUS L3" = FOCUS_2006_L3_mkin), quiet = TRUE)
+plot(mm.L3)
+

+

The \(\chi^2\) error level of 21% as well as the plot suggest that the SFO model does not fit very well. The FOMC model performs better, with an error level at which the \(\chi^2\) test passes of 7%. Fitting the four parameter DFOP model further reduces the \(\chi^2\) error level considerably.

+
+
+

+Accessing mmkin objects

+

The objects returned by mmkin are arranged like a matrix, with models as a row index and datasets as a column index.

+

We can extract the summary and plot for e.g. the DFOP fit, using square brackets for indexing which will result in the use of the summary and plot functions working on mkinfit objects.

+
summary(mm.L3[["DFOP", 1]])
+
## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.0 
+## Date of fit:     Wed May 27 06:02:25 2020 
+## Date of summary: Wed May 27 06:02:25 2020 
+## 
+## Equations:
+## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+##            time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+##            * parent
+## 
+## Model predictions using solution type analytical 
+## 
+## Fitted using 373 model solutions performed in 0.08 s
+## 
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
+## 
+## Starting values for parameters to be optimised:
+##          value   type
+## parent_0 97.80  state
+## k1        0.10 deparm
+## k2        0.01 deparm
+## g         0.50 deparm
+## 
+## Starting values for the transformed parameters actually optimised:
+##              value lower upper
+## parent_0 97.800000  -Inf   Inf
+## log_k1   -2.302585  -Inf   Inf
+## log_k2   -4.605170  -Inf   Inf
+## g_ilr     0.000000  -Inf   Inf
+## 
+## Fixed parameter values:
+## None
+## 
+## Results:
+## 
+##        AIC      BIC    logLik
+##   32.97732 33.37453 -11.48866
+## 
+## Optimised, transformed parameters with symmetric confidence intervals:
+##          Estimate Std. Error   Lower      Upper
+## parent_0  97.7500    1.01900 94.5000 101.000000
+## log_k1    -0.6612    0.10050 -0.9812  -0.341300
+## log_k2    -4.2860    0.04322 -4.4230  -4.148000
+## g_ilr     -0.1229    0.03727 -0.2415  -0.004343
+## sigma      1.0170    0.25430  0.2079   1.827000
+## 
+## Parameter correlation:
+##            parent_0     log_k1     log_k2      g_ilr      sigma
+## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -6.872e-07
+## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  3.200e-07
+## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  7.673e-07
+## g_ilr     4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -8.731e-07
+## sigma    -6.872e-07  3.200e-07  7.673e-07 -8.731e-07  1.000e+00
+## 
+## Backtransformed parameters:
+## Confidence intervals for internally transformed parameters are asymmetric.
+## t-test (unrealistically) based on the assumption of normal distribution
+## for estimators of untransformed parameters.
+##          Estimate t value    Pr(>t)    Lower     Upper
+## parent_0 97.75000  95.960 1.248e-06 94.50000 101.00000
+## k1        0.51620   9.947 1.081e-03  0.37490   0.71090
+## k2        0.01376  23.140 8.840e-05  0.01199   0.01579
+## g         0.45660  34.920 2.581e-05  0.41540   0.49850
+## sigma     1.01700   4.000 1.400e-02  0.20790   1.82700
+## 
+## FOCUS Chi2 error levels in percent:
+##          err.min n.optim df
+## All data   2.225       4  4
+## parent     2.225       4  4
+## 
+## Estimated disappearance times:
+##         DT50 DT90 DT50_k1 DT50_k2
+## parent 7.464  123   1.343   50.37
+## 
+## Data:
+##  time variable observed predicted residual
+##     0   parent     97.8     97.75  0.05396
+##     3   parent     60.0     60.45 -0.44933
+##     7   parent     51.0     49.44  1.56338
+##    14   parent     43.0     43.84 -0.83632
+##    30   parent     35.0     35.15 -0.14707
+##    60   parent     22.0     23.26 -1.25919
+##    91   parent     15.0     15.18 -0.18181
+##   120   parent     12.0     10.19  1.81395
+
plot(mm.L3[["DFOP", 1]], show_errmin = TRUE)
+

+

Here, a look to the model plot, the confidence intervals of the parameters and the correlation matrix suggest that the parameter estimates are reliable, and the DFOP model can be used as the best-fit model based on the \(\chi^2\) error level criterion for laboratory data L3.

+

This is also an example where the standard t-test for the parameter g_ilr is misleading, as it tests for a significant difference from zero. In this case, zero appears to be the correct value for this parameter, and the confidence interval for the backtransformed parameter g is quite narrow.

+
+
+
+

+Laboratory Data L4

+

The following code defines example dataset L4 from the FOCUS kinetics report, p. 293:

+
FOCUS_2006_L4 = data.frame(
+  t = c(0, 3, 7, 14, 30, 60, 91, 120),
+  parent = c(96.6, 96.3, 94.3, 88.8, 74.9, 59.9, 53.5, 49.0))
+FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4)
+

Fits of the SFO and FOMC models, plots and summaries are produced below:

+
# Only use one core here, not to offend the CRAN checks
+mm.L4 <- mmkin(c("SFO", "FOMC"), cores = 1,
+               list("FOCUS L4" = FOCUS_2006_L4_mkin),
+               quiet = TRUE)
+plot(mm.L4)
+

+

The \(\chi^2\) error level of 3.3% as well as the plot suggest that the SFO model fits very well. The error level at which the \(\chi^2\) test passes is slightly lower for the FOMC model. However, the difference appears negligible.

+
summary(mm.L4[["SFO", 1]], data = FALSE)
+
## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.0 
+## Date of fit:     Wed May 27 06:02:25 2020 
+## Date of summary: Wed May 27 06:02:26 2020 
+## 
+## Equations:
+## d_parent/dt = - k_parent_sink * parent
+## 
+## Model predictions using solution type analytical 
+## 
+## Fitted using 142 model solutions performed in 0.029 s
+## 
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
+## 
+## Starting values for parameters to be optimised:
+##               value   type
+## parent_0       96.6  state
+## k_parent_sink   0.1 deparm
+## 
+## Starting values for the transformed parameters actually optimised:
+##                       value lower upper
+## parent_0          96.600000  -Inf   Inf
+## log_k_parent_sink -2.302585  -Inf   Inf
+## 
+## Fixed parameter values:
+## None
+## 
+## Results:
+## 
+##        AIC      BIC    logLik
+##   47.12133 47.35966 -20.56067
+## 
+## Optimised, transformed parameters with symmetric confidence intervals:
+##                   Estimate Std. Error  Lower   Upper
+## parent_0            96.440    1.69900 92.070 100.800
+## log_k_parent_sink   -5.030    0.07059 -5.211  -4.848
+## sigma                3.162    0.79050  1.130   5.194
+## 
+## Parameter correlation:
+##                    parent_0 log_k_parent_sink     sigma
+## parent_0          1.000e+00         5.938e-01 3.440e-07
+## log_k_parent_sink 5.938e-01         1.000e+00 5.885e-07
+## sigma             3.440e-07         5.885e-07 1.000e+00
+## 
+## Backtransformed parameters:
+## Confidence intervals for internally transformed parameters are asymmetric.
+## t-test (unrealistically) based on the assumption of normal distribution
+## for estimators of untransformed parameters.
+##                Estimate t value    Pr(>t)     Lower     Upper
+## parent_0      96.440000   56.77 1.604e-08 92.070000 1.008e+02
+## k_parent_sink  0.006541   14.17 1.578e-05  0.005455 7.842e-03
+## sigma          3.162000    4.00 5.162e-03  1.130000 5.194e+00
+## 
+## FOCUS Chi2 error levels in percent:
+##          err.min n.optim df
+## All data   3.287       2  6
+## parent     3.287       2  6
+## 
+## Estimated disappearance times:
+##        DT50 DT90
+## parent  106  352
+
summary(mm.L4[["FOMC", 1]], data = FALSE)
+
## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.0 
+## Date of fit:     Wed May 27 06:02:25 2020 
+## Date of summary: Wed May 27 06:02:26 2020 
+## 
+## Equations:
+## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
+## 
+## Model predictions using solution type analytical 
+## 
+## Fitted using 224 model solutions performed in 0.043 s
+## 
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
+## 
+## Starting values for parameters to be optimised:
+##          value   type
+## parent_0  96.6  state
+## alpha      1.0 deparm
+## beta      10.0 deparm
+## 
+## Starting values for the transformed parameters actually optimised:
+##               value lower upper
+## parent_0  96.600000  -Inf   Inf
+## log_alpha  0.000000  -Inf   Inf
+## log_beta   2.302585  -Inf   Inf
+## 
+## Fixed parameter values:
+## None
+## 
+## Results:
+## 
+##        AIC      BIC    logLik
+##   40.37255 40.69032 -16.18628
+## 
+## Optimised, transformed parameters with symmetric confidence intervals:
+##           Estimate Std. Error   Lower    Upper
+## parent_0   99.1400     1.2670 95.6300 102.7000
+## log_alpha  -0.3506     0.2616 -1.0770   0.3756
+## log_beta    4.1740     0.3938  3.0810   5.2670
+## sigma       1.8300     0.4575  0.5598   3.1000
+## 
+## Parameter correlation:
+##             parent_0  log_alpha   log_beta      sigma
+## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.563e-07
+## log_alpha -4.696e-01  1.000e+00  9.889e-01  4.066e-08
+## log_beta  -5.543e-01  9.889e-01  1.000e+00  6.818e-08
+## sigma     -2.563e-07  4.066e-08  6.818e-08  1.000e+00
+## 
+## Backtransformed parameters:
+## Confidence intervals for internally transformed parameters are asymmetric.
+## t-test (unrealistically) based on the assumption of normal distribution
+## for estimators of untransformed parameters.
+##          Estimate t value    Pr(>t)   Lower   Upper
+## parent_0  99.1400  78.250 7.993e-08 95.6300 102.700
+## alpha      0.7042   3.823 9.365e-03  0.3407   1.456
+## beta      64.9800   2.540 3.201e-02 21.7800 193.900
+## sigma      1.8300   4.000 8.065e-03  0.5598   3.100
+## 
+## FOCUS Chi2 error levels in percent:
+##          err.min n.optim df
+## All data   2.029       3  5
+## parent     2.029       3  5
+## 
+## Estimated disappearance times:
+##         DT50 DT90 DT50back
+## parent 108.9 1644    494.9
+
+
+

+References

+
+
+

Ranke, Johannes. 2014. “Prüfung und Validierung von Modellierungssoftware als Alternative zu ModelMaker 4.0.” Umweltbundesamt Projektnummer 27452.

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

Developed by Johannes Ranke.

+
+ +
+

Site built with pkgdown 1.5.1.

+
+ +
+
+ + + + + + diff --git a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-10-1.png b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-10-1.png new file mode 100644 index 00000000..88d03d24 Binary files /dev/null and b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-10-1.png differ diff --git a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png new file mode 100644 index 00000000..f23a4c97 Binary files /dev/null and b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png differ diff --git a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-13-1.png b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-13-1.png new file mode 100644 index 00000000..ed6a781d Binary files /dev/null and b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-13-1.png differ diff --git a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-15-1.png b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-15-1.png new file mode 100644 index 00000000..2e5071d9 Binary files /dev/null and b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-15-1.png differ diff --git a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-4-1.png b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-4-1.png new file mode 100644 index 00000000..04bee502 Binary files /dev/null and b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-4-1.png differ diff --git a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-5-1.png b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-5-1.png new file mode 100644 index 00000000..86af1cf9 Binary files /dev/null and b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-5-1.png differ diff --git a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png new file mode 100644 index 00000000..16235059 Binary files /dev/null and b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png differ diff --git a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-8-1.png b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-8-1.png new file mode 100644 index 00000000..8b39f0fc Binary files /dev/null and b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-8-1.png differ diff --git a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-9-1.png b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-9-1.png new file mode 100644 index 00000000..13019224 Binary files /dev/null and b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-9-1.png differ diff --git a/docs/dev/articles/index.html b/docs/dev/articles/index.html new file mode 100644 index 00000000..3d5dd360 --- /dev/null +++ b/docs/dev/articles/index.html @@ -0,0 +1,188 @@ + + + + + + + + +Articles • mkin + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + + +
+ +
+
+
+

Articles

+
+ +
+

All vignettes

+

+ +
+
Example evaluation of FOCUS Example Dataset D
+
+
Example evaluation of FOCUS Laboratory Data L1 to L3
+
+
Introduction to mkin
+
+
Calculation of time weighted average concentrations with mkin
+
+
Example evaluation of FOCUS dataset Z
+
+
Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance
+
+
Benchmark timings for mkin
+
+
Performance benefit by using compiled model definitions in mkin
+
+
+
+
+
+ + +
+
+

Developed by Johannes Ranke.

+
+ +
+

Site built with pkgdown 1.5.1.

+
+ +
+
+ + + + + + + + diff --git a/docs/dev/articles/mkin.html b/docs/dev/articles/mkin.html new file mode 100644 index 00000000..2dd6dcb8 --- /dev/null +++ b/docs/dev/articles/mkin.html @@ -0,0 +1,261 @@ + + + + + + + +Introduction to mkin • mkin + + + + + + + + + + + +
+
+ + + + +
+
+
+

Introduction to mkin

+

Johannes Ranke

+ +

2020-05-27

+ + Source: vignettes/mkin.rmd + + +
+ + + +

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

+
+

+Abstract

+

In the regulatory evaluation of chemical substances like plant protection products (pesticides), biocides and other chemicals, degradation data play an important role. For the evaluation of pesticide degradation experiments, detailed guidance has been developed, based on nonlinear optimisation. The R add-on package mkin implements fitting some of the models recommended in this guidance from within R and calculates some statistical measures for data series within one or more compartments, for parent and metabolites.

+
library("mkin", quietly = TRUE)
+# Define the kinetic model
+m_SFO_SFO_SFO <- mkinmod(parent = mkinsub("SFO", "M1"),
+                         M1 = mkinsub("SFO", "M2"),
+                         M2 = mkinsub("SFO"),
+                         use_of_ff = "max", quiet = TRUE)
+
+
+# Produce model predictions using some arbitrary parameters
+sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
+d_SFO_SFO_SFO <- mkinpredict(m_SFO_SFO_SFO,
+  c(k_parent = 0.03,
+    f_parent_to_M1 = 0.5, k_M1 = log(2)/100,
+    f_M1_to_M2 = 0.9, k_M2 = log(2)/50),
+  c(parent = 100, M1 = 0, M2 = 0),
+  sampling_times)
+
+# Generate a dataset by adding normally distributed errors with
+# standard deviation 3, for two replicates at each sampling time
+d_SFO_SFO_SFO_err <- add_err(d_SFO_SFO_SFO, reps = 2,
+                             sdfunc = function(x) 3,
+                             n = 1, seed = 123456789 )
+
+# Fit the model to the dataset
+f_SFO_SFO_SFO <- mkinfit(m_SFO_SFO_SFO, d_SFO_SFO_SFO_err[[1]], quiet = TRUE)
+
+# Plot the results separately for parent and metabolites
+plot_sep(f_SFO_SFO_SFO, lpos = c("topright", "bottomright", "bottomright"))
+

+
+
+

+Background

+

Many approaches are possible regarding the evaluation of chemical degradation data.

+

The mkin package (Ranke 2019) implements the approach recommended in the kinetics report provided by the FOrum for Co-ordination of pesticide fate models and their USe (FOCUS Work Group on Degradation Kinetics 2006, 2014) for simple decline data series, data series with transformation products, commonly termed metabolites, and for data series for more than one compartment. It is also possible to include back reactions, so equilibrium reactions and equilibrium partitioning can be specified, although this oftentimes leads to an overparameterisation of the model.

+

When the first mkin code was published in 2010, the most commonly used tools for fitting more complex kinetic degradation models to experimental data were KinGUI (Schäfer et al. 2007), a MATLAB based tool with a graphical user interface that was specifically tailored to the task and included some output as proposed by the FOCUS Kinetics Workgroup, and ModelMaker, a general purpose compartment based tool providing infrastructure for fitting dynamic simulation models based on differential equations to data.

+

The code was first uploaded to the BerliOS platform. When this was taken down, the version control history was imported into the R-Forge site (see e.g. the initial commit on 11 May 2010), where the code is still occasionally updated.

+

At that time, the R package FME (Flexible Modelling Environment) (Soetaert and Petzoldt 2010) was already available, and provided a good basis for developing a package specifically tailored to the task. The remaining challenge was to make it as easy as possible for the users (including the author of this vignette) to specify the system of differential equations and to include the output requested by the FOCUS guidance, such as the relative standard deviation that has to be assumed for the residuals, such that the \(\chi^2\) goodness-of-fit test as defined by the FOCUS kinetics workgroup would pass using an significance level \(\alpha\) of 0.05. This relative error, expressed as a percentage, is often termed \(\chi^2\) error level or similar.

+

Also, mkin introduced using analytical solutions for parent only kinetics for improved optimization speed. Later, Eigenvalue based solutions were introduced to mkin for the case of linear differential equations (i.e. where the FOMC or DFOP models were not used for the parent compound), greatly improving the optimization speed for these cases. This, however, has become somehow obsolete, as the use of compiled code described below gives even smaller execution times.

+

The possibility to specify back-reactions and a biphasic model (SFORB) for metabolites were present in mkin from the very beginning.

+
+

+Derived software tools

+

Soon after the publication of mkin, two derived tools were published, namely KinGUII (available from Bayer Crop Science) and CAKE (commissioned to Tessella by Syngenta), which added a graphical user interface (GUI), and added fitting by iteratively reweighted least squares (IRLS) and characterisation of likely parameter distributions by Markov Chain Monte Carlo (MCMC) sampling.

+

CAKE focuses on a smooth use experience, sacrificing some flexibility in the model definition, originally allowing only two primary metabolites in parallel. The current version 3.3 of CAKE release in March 2016 uses a basic scheme for up to six metabolites in a flexible arrangement, but does not support back-reactions (non-instantaneous equilibria) or biphasic kinetics for metabolites.

+

KinGUI offers an even more flexible widget for specifying complex kinetic models. Back-reactions (non-instantaneous equilibria) were supported early on, but until 2014, only simple first-order models could be specified for transformation products. Starting with KinGUII version 2.1, biphasic modelling of metabolites was also available in KinGUII.

+

A further graphical user interface (GUI) that has recently been brought to a decent degree of maturity is the browser based GUI named gmkin. Please see its documentation page and manual for further information.

+

A comparison of scope, usability and numerical results obtained with these tools has been recently been published by Ranke, Wöltjen, and Meinecke (2018).

+
+
+

+Recent developments

+

Currently (July 2019), the main features available in mkin which are not present in KinGUII or CAKE, are the speed increase by using compiled code when a compiler is present, parallel model fitting on multicore machines using the mmkin function, and the estimation of parameter confidence intervals based on transformed parameters.

+

In addition, the possibility to use two alternative error models to constant variance have been integrated. The variance by variable error model introduced by Gao et al. (2011) has been available via an iteratively reweighted least squares (IRLS) procedure since mkin version 0.9-22. With release 0.9.49.5, the IRLS algorithm has been replaced by direct or step-wise maximisation of the likelihood function, which makes it possible not only to fit the variance by variable error model but also a two-component error model inspired by error models developed in analytical chemistry.

+
+
+
+

+Internal parameter transformations

+

For rate constants, the log transformation is used, as proposed by Bates and Watts (1988, 77, 149). Approximate intervals are constructed for the transformed rate constants (compare Bates and Watts 1988, 135), i.e. for their logarithms. Confidence intervals for the rate constants are then obtained using the appropriate backtransformation using the exponential function.

+

In the first version of mkin allowing for specifying models using formation fractions, a home-made reparameterisation was used in order to ensure that the sum of formation fractions would not exceed unity.

+

This method is still used in the current version of KinGUII (v2.1 from April 2014), with a modification that allows for fixing the pathway to sink to zero. CAKE uses penalties in the objective function in order to enforce this constraint.

+

In 2012, an alternative reparameterisation of the formation fractions was proposed together with René Lehmann (Ranke and Lehmann 2012), based on isometric logratio transformation (ILR). The aim was to improve the validity of the linear approximation of the objective function during the parameter estimation procedure as well as in the subsequent calculation of parameter confidence intervals.

+
+

+Confidence intervals based on transformed parameters

+

In the first attempt at providing improved parameter confidence intervals introduced to mkin in 2013, confidence intervals obtained from FME on the transformed parameters were simply all backtransformed one by one to yield asymmetric confidence intervals for the backtransformed parameters.

+

However, while there is a 1:1 relation between the rate constants in the model and the transformed parameters fitted in the model, the parameters obtained by the isometric logratio transformation are calculated from the set of formation fractions that quantify the paths to each of the compounds formed from a specific parent compound, and no such 1:1 relation exists.

+

Therefore, parameter confidence intervals for formation fractions obtained with this method only appear valid for the case of a single transformation product, where only one formation fraction is to be estimated, directly corresponding to one component of the ilr transformed parameter.

+

The confidence intervals obtained by backtransformation for the cases where a 1:1 relation between transformed and original parameter exist are considered by the author of this vignette to be more accurate than those obtained using a re-estimation of the Hessian matrix after backtransformation, as implemented in the FME package.

+
+
+

+Parameter t-test based on untransformed parameters

+

The standard output of many nonlinear regression software packages includes the results from a test for significant difference from zero for all parameters. Such a test is also recommended to check the validity of rate constants in the FOCUS guidance (FOCUS Work Group on Degradation Kinetics 2014, 96ff).

+

It has been argued that the precondition for this test, i.e. normal distribution of the estimator for the parameters, is not fulfilled in the case of nonlinear regression (Ranke and Lehmann 2015). However, this test is commonly used by industry, consultants and national authorities in order to decide on the reliability of parameter estimates, based on the FOCUS guidance mentioned above. Therefore, the results of this one-sided t-test are included in the summary output from mkin.

+

As it is not reasonable to test for significant difference of the transformed parameters (e.g. \(log(k)\)) from zero, the t-test is calculated based on the model definition before parameter transformation, i.e. in a similar way as in packages that do not apply such an internal parameter transformation. A note is included in the mkin output, pointing to the fact that the t-test is based on the unjustified assumption of normal distribution of the parameter estimators.

+
+
+
+

+References

+ +
+
+

Bates, D., and D. Watts. 1988. Nonlinear Regression and Its Applications. Wiley-Interscience.

+
+
+

FOCUS Work Group on Degradation Kinetics. 2006. Guidance Document on Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration. Report of the Focus Work Group on Degradation Kinetics. http://esdac.jrc.ec.europa.eu/projects/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.

+
+
+

Gao, Z., J.W. Green, J. Vanderborght, and W. Schmitt. 2011. “Improving Uncertainty Analysis in Kinetic Evaluations Using Iteratively Reweighted Least Squares.” Journal. Environmental Science and Technology 45: 4429–37.

+
+
+

Ranke, J. 2019. ‘mkin‘: Kinetic Evaluation of Chemical Degradation Data. https://CRAN.R-project.org/package=mkin.

+
+
+

Ranke, J., and R. Lehmann. 2012. “Parameter Reliability in Kinetic Evaluation of Environmental Metabolism Data - Assessment and the Influence of Model Specification.” In SETAC World 20-24 May. Berlin.

+
+
+

———. 2015. “To T-Test or Not to T-Test, That Is the Question.” In XV Symposium on Pesticide Chemistry 2-4 September 2015. Piacenza. http://chem.uft.uni-bremen.de/ranke/posters/piacenza_2015.pdf.

+
+
+

Ranke, Johannes, Janina Wöltjen, and Stefan Meinecke. 2018. “Comparison of Software Tools for Kinetic Evaluation of Chemical Degradation Data.” Environmental Sciences Europe 30 (1): 17. https://doi.org/10.1186/s12302-018-0145-1.

+
+
+

Schäfer, D., B. Mikolasch, P. Rainbird, and B. Harvey. 2007. “KinGUI: A New Kinetic Software Tool for Evaluations According to FOCUS Degradation Kinetics.” In Proceedings of the Xiii Symposium Pesticide Chemistry, edited by Del Re A. A. M., Capri E., Fragoulis G., and Trevisan M., 916–23. Piacenza.

+
+
+

Soetaert, Karline, and Thomas Petzoldt. 2010. “Inverse Modelling, Sensitivity and Monte Carlo Analysis in R Using Package FME.” Journal of Statistical Software 33 (3): 1–28. http://www.jstatsoft.org/v33/i03/.

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

Developed by Johannes Ranke.

+
+ +
+

Site built with pkgdown 1.5.1.

+
+ +
+
+ + + + + + diff --git a/docs/dev/articles/mkin_files/figure-html/unnamed-chunk-2-1.png b/docs/dev/articles/mkin_files/figure-html/unnamed-chunk-2-1.png new file mode 100644 index 00000000..62ea16f2 Binary files /dev/null and b/docs/dev/articles/mkin_files/figure-html/unnamed-chunk-2-1.png differ diff --git a/docs/dev/articles/twa.html b/docs/dev/articles/twa.html new file mode 100644 index 00000000..d4754a1f --- /dev/null +++ b/docs/dev/articles/twa.html @@ -0,0 +1,175 @@ + + + + + + + +Calculation of time weighted average concentrations with mkin • mkin + + + + + + + + + + + +
+
+ + + + +
+
+
+

Calculation of time weighted average concentrations with mkin

+

Johannes Ranke

+ +

2020-05-27

+ + Source: vignettes/twa.rmd + + +
+ + + +

Since version 0.9.45.1 of the ‘mkin’ package, a function for calculating time weighted average concentrations for decline kinetics (i.e. only for the compound applied in the experiment) is included. Strictly speaking, they are maximum moving window time weighted average concentrations, i.e. the maximum time weighted average concentration that can be found when moving a time window of a specified width over the decline curve.

+

Time weighted average concentrations for the SFO, FOMC and the DFOP model are calculated using the formulas given in the FOCUS kinetics guidance (FOCUS Work Group on Degradation Kinetics 2014, 251):

+

SFO:

+

\[c_\textrm{twa} = c_0 \frac{\left( 1 - e^{- k t} \right)}{ k t} \]

+

FOMC:

+

\[c_\textrm{twa} = c_0 \frac{\beta}{t (1 - \alpha)} + \left( \left(\frac{t}{\beta} + 1 \right)^{1 - \alpha} - 1 \right) \]

+

DFOP:

+

\[c_\textrm{twa} = \frac{c_0}{t} \left( + \frac{g}{k_1} \left( 1 - e^{- k_1 t} \right) + + \frac{1-g}{k_2} \left( 1 - e^{- k_2 t} \right) \right) \]

+

HS for \(t > t_b\):

+

\[c_\textrm{twa} = \frac{c_0}{t} \left( + \frac{1}{k_1} \left( 1 - e^{- k_1 t_b} \right) + + \frac{e^{- k_1 t_b}}{k_2} \left( 1 - e^{- k_2 (t - t_b)} \right) \right) \]

+

Often, the ratio between the time weighted average concentration \(c_\textrm{twa}\) and the initial concentration \(c_0\)

+

\[f_\textrm{twa} = \frac{c_\textrm{twa}}{c_0}\]

+

is needed. This can be calculated from the fitted initial concentration \(c_0\) and the time weighted average concentration \(c_\textrm{twa}\), or directly from the model parameters using the following formulas:

+

SFO:

+

\[f_\textrm{twa} = \frac{\left( 1 - e^{- k t} \right)}{k t} \]

+

FOMC:

+

\[f_\textrm{twa} = \frac{\beta}{t (1 - \alpha)} + \left( \left(\frac{t}{\beta} + 1 \right)^{1 - \alpha} - 1 \right) \]

+

DFOP:

+

\[f_\textrm{twa} = \frac{1}{t} \left( + \frac{g}{k_1} \left( 1 - e^{- k_1 t} \right) + + \frac{1-g}{k_2} \left( 1 - e^{- k_2 t} \right) \right) \]

+

HS for \(t > t_b\):

+

\[f_\textrm{twa} = \frac{1}{t} \left( + \frac{1}{k_1} \left( 1 - e^{- k_1 t_b} \right) + + \frac{e^{- k_1 t_b}}{k_2} \left( 1 - e^{- k_2 (t - t_b)} \right) \right) \]

+

Note that a method for calculating maximum moving window time weighted average concentrations for a model fitted by ‘mkinfit’ or from parent decline model parameters is included in the max_twa_parent() function. If the same is needed for metabolites, the function pfm::max_twa() from the ‘pfm’ package can be used.

+
+
+

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.

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

Developed by Johannes Ranke.

+
+ +
+

Site built with pkgdown 1.5.1.

+
+ +
+
+ + + + + + diff --git a/docs/dev/articles/web_only/FOCUS_Z.html b/docs/dev/articles/web_only/FOCUS_Z.html new file mode 100644 index 00000000..7fca4e49 --- /dev/null +++ b/docs/dev/articles/web_only/FOCUS_Z.html @@ -0,0 +1,364 @@ + + + + + + + +Example evaluation of FOCUS dataset Z • mkin + + + + + + + + + + + +
+
+ + + + +
+
+
+

Example evaluation of FOCUS dataset Z

+

Johannes Ranke

+ +

2020-05-27

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

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)
+
+
+

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

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

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

+
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

+

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

+

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")
+
## 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$bparms.ode,
+                     quiet = TRUE)
+
## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, :
+## Observations with value of zero were removed from the data
+
## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, : Optimisation did not converge:
+## false convergence (8)
+
plot_sep(m.Z.FOCUS)
+

+
summary(m.Z.FOCUS, data = FALSE)$bpar
+
##             Estimate se_notrans t value     Pr(>t)     Lower     Upper
+## Z0_0       96.840695   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)
+
## $ff
+##   Z2_Z3 Z2_sink 
+## 0.47148 0.52852 
+## 
+## $distimes
+##        DT50    DT90
+## Z0  0.31287  1.0393
+## Z1  1.44911  4.8138
+## Z2  1.53474  5.0983
+## Z3 11.80989 39.2316
+

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

+

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

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

+

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

+

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

+

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
+
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)
+

+

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 
+## 2.4471337 0.0075125 0.0800071 0.0000000 
+## 
+## $distimes
+##      DT50   DT90 DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2
+## Z0 0.3043 1.1848    0.28325     92.266         NA         NA
+## Z1 1.5148 5.0320         NA         NA         NA         NA
+## Z2 1.6414 5.4526         NA         NA         NA         NA
+## Z3     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

+ +
+
+

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.

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

Developed by Johannes Ranke.

+
+ +
+

Site built with pkgdown 1.5.1.

+
+ +
+
+ + + + + + diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png new file mode 100644 index 00000000..23d051ce Binary files /dev/null and b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png differ diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png new file mode 100644 index 00000000..96738dd0 Binary files /dev/null and b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png differ diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png new file mode 100644 index 00000000..4f3c2554 Binary files /dev/null and b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png differ diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png new file mode 100644 index 00000000..b8c3ed26 Binary files /dev/null and b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png differ diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png new file mode 100644 index 00000000..132a7317 Binary files /dev/null and b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png differ diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png new file mode 100644 index 00000000..23d051ce Binary files /dev/null and b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png differ diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png new file mode 100644 index 00000000..6e9f4efa Binary files /dev/null and b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png differ diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png new file mode 100644 index 00000000..146acea9 Binary files /dev/null and b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png differ diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png new file mode 100644 index 00000000..b25bf26a Binary files /dev/null and b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png differ diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png new file mode 100644 index 00000000..7db8b07d Binary files /dev/null and b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png differ diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png new file mode 100644 index 00000000..dd5d89cd Binary files /dev/null and b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png differ diff --git a/docs/dev/articles/web_only/NAFTA_examples.html b/docs/dev/articles/web_only/NAFTA_examples.html new file mode 100644 index 00000000..29f4cd8b --- /dev/null +++ b/docs/dev/articles/web_only/NAFTA_examples.html @@ -0,0 +1,989 @@ + + + + + + + +Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance • mkin + + + + + + + + + + + +
+
+ + + + +
+
+
+

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

+

Johannes Ranke

+ +

2020-05-27

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

+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_sink   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
+## 
+## $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
+## 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 4.42e+11 2.42e+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_sink    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
+## 
+## $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
+## 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 9.80e+10 5.98e+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_sink   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
+## 
+## $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
+## 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 6.66e+09 1.41e+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_sink  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
+## 
+## $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
+## 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 6.97e+09 3.52e+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_sink = 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_sink  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
+## 
+## $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_sink   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
+## 
+## $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
+## 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 2.07e+12 1.15e+12
+## 
+## 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_sink   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
+## 
+## $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
+## 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"]])
+
## 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_sink   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
+## 
+## $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
+## 
+## 
+## 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_sink  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
+## 
+## $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       7.25e-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 4.21e+11 2.64e+12 9.56e+11
+## 
+## Representative half-life:
+## [1] 41148169
+

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
+
## 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_sink    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
+## 
+## $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
+## g           0.877 5.00e-01  0.0000   1.000
+## 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 sqrt(diag(covar)): NaNs produced
+
## 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
+
## 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(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_sink   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
+## 
+## $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          0.6902    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"]])
+
## 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(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_sink  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
+## 
+## $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
+## k2        0.00258 3.69e-08 2.20e-03 3.03e-03
+## g         0.00442 5.00e-01       NA       NA
+## sigma     3.41172 1.35e-04 2.02e+00 4.80e+00
+## 
+## 
+## 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_sink  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
+## 
+## $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
+## 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 2.54e+10 2.46e+11 9.51e+10
+## 
+## 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"]])
+
## 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)
+

+
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_sink  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
+## 
+## $DFOP
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 97.96752 2.85e-13 94.21914 101.7159
+## k1        0.00952 6.80e-02  0.00277   0.0327
+## k2        0.00952 3.82e-06  0.00902   0.0100
+## g         0.17247      NaN       NA       NA
+## sigma     4.18778 2.50e-04  2.39747   5.9781
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  72.8  242     72.8
+## IORE 76.3  137     41.3
+## DFOP 72.8  242     72.8
+## 
+## Representative half-life:
+## [1] 41.33
+
p15b <- nafta(NAFTA_SOP_Attachment[["p15b"]])
+
## Warning in sqrt(diag(covar)): NaNs produced
+
## Warning in sqrt(1/diag(V)): NaNs produced
+
## Warning in cov2cor(ans$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_sink 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
+## 
+## $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
+## g        1.50e-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_sink    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
+## 
+## $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
+## 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.”

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

Developed by Johannes Ranke.

+
+ +
+

Site built with pkgdown 1.5.1.

+
+ +
+
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--git a/docs/dev/articles/web_only/benchmarks.html b/docs/dev/articles/web_only/benchmarks.html new file mode 100644 index 00000000..b46b873c --- /dev/null +++ b/docs/dev/articles/web_only/benchmarks.html @@ -0,0 +1,391 @@ + + + + + + + +Benchmark timings for mkin • mkin + + + + + + + + + + + +
+
+ + + + +
+
+
+

Benchmark timings for mkin

+

Johannes Ranke

+ +

2020-05-27

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

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

+
+

+Test cases

+

Parent only:

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

One metabolite:

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

Two metabolites, synthetic data:

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

+Results

+

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

+

Benchmarks for all available error models are shown.

+
+

+Parent only

+

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

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
mkin versiont1 [s]t2 [s]
0.9.48.13.61011.019
0.9.49.18.18422.889
0.9.49.27.06412.558
0.9.49.37.29621.239
0.9.49.45.93620.545
0.9.50.21.7143.971
0.9.50.31.7523.728
+
+
+

+One metabolite

+

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

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
mkin versiont3 [s]t4 [s]t5 [s]
0.9.48.13.76414.3479.495
0.9.49.14.64913.7896.395
0.9.49.24.7868.4615.675
0.9.49.34.51013.8057.386
0.9.49.44.44615.3356.002
0.9.50.21.4026.1742.764
0.9.50.31.3896.5792.740
+
+
+

+Two metabolites

+

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

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
mkin versiont6 [s]t7 [s]t8 [s]t9 [s]t10 [s]t11 [s]
0.9.48.12.6234.5877.52516.6218.57631.267
0.9.49.12.5424.1284.6328.1713.6765.636
0.9.49.22.7234.4784.8627.6183.5795.574
0.9.49.32.6434.3747.02011.1245.3887.365
0.9.49.42.6354.2594.7377.7633.4275.626
0.9.50.20.7771.2361.3322.8722.0692.987
0.9.50.30.7601.2521.4574.2012.0072.979
+
+
+
+ + + +
+ + + +
+

Developed by Johannes Ranke.

+
+ +
+

Site built with pkgdown 1.5.1.

+
+ +
+
+ + + + + + diff --git a/docs/dev/articles/web_only/compiled_models.html b/docs/dev/articles/web_only/compiled_models.html new file mode 100644 index 00000000..7b5dc8ca --- /dev/null +++ b/docs/dev/articles/web_only/compiled_models.html @@ -0,0 +1,221 @@ + + + + + + + +Performance benefit by using compiled model definitions in mkin • mkin + + + + + + + + + + + +
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+

Performance benefit by using compiled model definitions in mkin

+

Johannes Ranke

+ +

2020-05-27

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

+How to benefit from compiled models

+

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

+
pkgbuild::has_compiler()
+

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

+

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

+

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

+

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

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

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

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

+Comparison with other solution methods

+

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

+
library("mkin", quietly = TRUE)
+SFO_SFO <- mkinmod(
+  parent = mkinsub("SFO", "m1"),
+  m1 = mkinsub("SFO"))
+
## Successfully compiled differential equation model from auto-generated C code.
+
FOCUS_D <- subset(FOCUS_2006_D, value != 0)
+

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

+
if (require(rbenchmark)) {
+  b.1 <- benchmark(
+    "deSolve, not compiled" = mkinfit(SFO_SFO, FOCUS_D,
+       solution_type = "deSolve",
+       use_compiled = FALSE, quiet = TRUE),
+    "Eigenvalue based" = mkinfit(SFO_SFO, FOCUS_D,
+       solution_type = "eigen", quiet = TRUE),
+    "deSolve, compiled" = mkinfit(SFO_SFO, FOCUS_D,
+       solution_type = "deSolve", quiet = TRUE),
+    "analytical" = mkinfit(SFO_SFO, FOCUS_D,
+       solution_type = "analytical",
+       use_compiled = FALSE, quiet = TRUE),
+    replications = 1, order = "relative",
+    columns = c("test", "replications", "relative", "elapsed"))
+  print(b.1)
+} else {
+  print("R package rbenchmark is not available")
+}
+
##                    test replications relative elapsed
+## 4            analytical            1    1.000   0.202
+## 3     deSolve, compiled            1    1.703   0.344
+## 2      Eigenvalue based            1    1.990   0.402
+## 1 deSolve, not compiled            1   40.173   8.115
+

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

+
+
+

+Model without analytical solution

+

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

+
if (require(rbenchmark)) {
+  FOMC_SFO <- mkinmod(
+    parent = mkinsub("FOMC", "m1"),
+    m1 = mkinsub( "SFO"))
+
+  b.2 <- benchmark(
+    "deSolve, not compiled" = mkinfit(FOMC_SFO, FOCUS_D,
+                                      use_compiled = FALSE, quiet = TRUE),
+    "deSolve, compiled" = mkinfit(FOMC_SFO, FOCUS_D, quiet = TRUE),
+    replications = 1, order = "relative",
+    columns = c("test", "replications", "relative", "elapsed"))
+  print(b.2)
+  factor_FOMC_SFO <- round(b.2["1", "relative"])
+} else {
+  factor_FOMC_SFO <- NA
+  print("R package benchmark is not available")
+}
+
## Successfully compiled differential equation model from auto-generated C code.
+
##                    test replications relative elapsed
+## 2     deSolve, compiled            1    1.000   0.469
+## 1 deSolve, not compiled            1   30.384  14.250
+

Here we get a performance benefit of a factor of 30 using the version of the differential equation model compiled from C code!

+

This vignette was built with mkin 0.9.50.3 on

+
## R version 4.0.0 (2020-04-24)
+## Platform: x86_64-pc-linux-gnu (64-bit)
+## Running under: Debian GNU/Linux 10 (buster)
+
## CPU model: AMD Ryzen 7 1700 Eight-Core Processor
+
+
+ + + +
+ + + + +
+ + + + + + -- cgit v1.2.1