diff options
| author | Johannes Ranke <jranke@uni-bremen.de> | 2013-11-17 16:13:13 +0100 |
|---|---|---|
| committer | Johannes Ranke <jranke@uni-bremen.de> | 2013-11-17 16:13:13 +0100 |
| commit | ebc6f65e4c8b865fb9207ab11dc43cf4ac122c72 (patch) | |
| tree | 25329171e98a014beafdd1f8db25be21bbe7ce07 /vignettes | |
| parent | d8dbf2ad866fb9d34cd1100000b9c116219ecef6 (diff) | |
Change vignette format to knitr (see ChangeLog)
Diffstat (limited to 'vignettes')
32 files changed, 1512 insertions, 706 deletions
diff --git a/vignettes/FOCUS_L.Rmd b/vignettes/FOCUS_L.Rmd new file mode 100644 index 0000000..957b34a --- /dev/null +++ b/vignettes/FOCUS_L.Rmd @@ -0,0 +1,243 @@ +<!--
+%\VignetteEngine{knitr::knitr}
+%\VignetteIndexEntry{Example evaluation of FOCUS Laboratory Data L1 to L3}
+-->
+
+# Example evaluation of FOCUS Laboratory Data L1 to L3
+
+## Laboratory Data L1
+
+The following code defines example dataset L1 from the FOCUS kinetics
+report, p. 284
+
+```{r}
+library("mkin")
+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)
+```
+
+The next step is to set up the models used for the kinetic analysis. Note that
+the model definitions contain the names of the observed variables in the data.
+In this case, there is only one variable called `parent`.
+
+```{r}
+SFO <- mkinmod(parent = list(type = "SFO"))
+FOMC <- mkinmod(parent = list(type = "FOMC"))
+DFOP <- mkinmod(parent = list(type = "DFOP"))
+```
+
+The three models cover the first assumption 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.
+
+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.
+
+```{r}
+m.L1.SFO <- mkinfit(SFO, FOCUS_2006_L1_mkin, quiet=TRUE)
+summary(m.L1.SFO)
+```
+
+A plot of the fit is obtained with the plot function for mkinfit objects.
+
+```{r fig.width=7, fig.height = 5}
+plot(m.L1.SFO)
+```
+The residual plot can be easily obtained by
+
+```{r fig.width=7, fig.height = 5}
+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.
+
+```{r}
+m.L1.FOMC <- mkinfit(FOMC, FOCUS_2006_L1_mkin, quiet=TRUE)
+summary(m.L1.FOMC, data = FALSE)
+```
+
+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 covariance
+matrix can not be obtained, indicating overparameterisation of the model.
+As a consequence, no standard errors for transformed parameters nor
+confidence intervals for backtransformed parameters are available.
+
+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.
+
+Furthermore, 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 is a widely used standard package in this field.
+Therefore, the reason for the difference was not investigated further.
+
+## Laboratory Data L2
+
+The following code defines example dataset L2 from the FOCUS kinetics
+report, p. 287
+
+```{r}
+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)
+```
+
+Again, the SFO model is fitted and a summary is obtained.
+
+```{r}
+m.L2.SFO <- mkinfit(SFO, FOCUS_2006_L2_mkin, quiet=TRUE)
+summary(m.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 and the residuals.
+
+```{r fig.height = 8}
+par(mfrow = c(2, 1))
+plot(m.L2.SFO)
+mkinresplot(m.L2.SFO)
+```
+
+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.
+
+For comparison, the FOMC model is fitted as well, and the chi^2 error level
+is checked.
+
+```{r fig.height = 8}
+m.L2.FOMC <- mkinfit(FOMC, FOCUS_2006_L2_mkin, quiet = TRUE)
+par(mfrow = c(2, 1))
+plot(m.L2.FOMC)
+mkinresplot(m.L2.FOMC)
+summary(m.L2.FOMC, data = FALSE)
+```
+
+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.
+
+Fitting the four parameter DFOP model further reduces the chi^2 error level.
+
+```{r fig.height = 5}
+m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin, quiet = TRUE)
+plot(m.L2.DFOP)
+```
+
+Here, the default starting parameters for the DFOP model obviously do not lead
+to a reasonable solution. Therefore the fit is repeated with different starting
+parameters.
+
+```{r fig.height = 5}
+m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin,
+ parms.ini = c(k1 = 1, k2 = 0.01, g = 0.8),
+ quiet=TRUE)
+plot(m.L2.DFOP)
+summary(m.L2.DFOP, data = FALSE)
+```
+
+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.
+
+```{r}
+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)
+```
+
+SFO model, summary and plot:
+
+```{r fig.height = 5}
+m.L3.SFO <- mkinfit(SFO, FOCUS_2006_L3_mkin, quiet = TRUE)
+plot(m.L3.SFO)
+summary(m.L3.SFO)
+```
+
+The chi^2 error level of 21% as well as the plot suggest that the model
+does not fit very well.
+
+The FOMC model performs better:
+
+```{r fig.height = 5}
+m.L3.FOMC <- mkinfit(FOMC, FOCUS_2006_L3_mkin, quiet = TRUE)
+plot(m.L3.FOMC)
+summary(m.L3.FOMC, data = FALSE)
+```
+
+The error level at which the chi^2 test passes is 7% in this case.
+
+Fitting the four parameter DFOP model further reduces the chi^2 error level
+considerably:
+
+```{r fig.height = 5}
+m.L3.DFOP <- mkinfit(DFOP, FOCUS_2006_L3_mkin, quiet = TRUE)
+plot(m.L3.DFOP)
+summary(m.L3.DFOP, data = FALSE)
+```
+
+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.
+
+## Laboratory Data L4
+
+The following code defines example dataset L4 from the FOCUS kinetics
+report, p. 293
+
+```{r}
+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)
+```
+
+SFO model, summary and plot:
+
+```{r fig.height = 5}
+m.L4.SFO <- mkinfit(SFO, FOCUS_2006_L4_mkin, quiet = TRUE)
+plot(m.L4.SFO)
+summary(m.L4.SFO, data = FALSE)
+```
+
+The chi^2 error level of 3.3% as well as the plot suggest that the model
+fits very well.
+
+The FOMC model for comparison
+
+```{r fig.height = 5}
+m.L4.FOMC <- mkinfit(FOMC, FOCUS_2006_L4_mkin, quiet = TRUE)
+plot(m.L4.FOMC)
+summary(m.L4.FOMC, data = FALSE)
+```
+
+The error level at which the chi^2 test passes is slightly lower for the FOMC
+model. However, the difference appears negligible.
+
diff --git a/vignettes/FOCUS_L.md b/vignettes/FOCUS_L.md new file mode 100644 index 0000000..6c43889 --- /dev/null +++ b/vignettes/FOCUS_L.md @@ -0,0 +1,931 @@ +<!-- +%\VignetteEngine{knitr::knitr} +%\VignetteIndexEntry{Example evaluation of FOCUS Laboratory Data L1 to L3} +--> + +# Example evaluation of FOCUS Laboratory Data L1 to L3 + +## Laboratory Data L1 + +The following code defines example dataset L1 from the FOCUS kinetics +report, p. 284 + + +```r +library("mkin") +``` + +``` +## Loading required package: FME +## Loading required package: deSolve +## Loading required package: rootSolve +## Loading required package: minpack.lm +## Loading required package: MASS +## Loading required package: coda +## Loading required package: lattice +``` + +```r +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, 71.9, 50.3, 59.4, 47, + 45.1, 27.7, 27.3, 10, 10.4, 2.9, 4)) +FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1) +``` + + +The next step is to set up the models used for the kinetic analysis. Note that +the model definitions contain the names of the observed variables in the data. +In this case, there is only one variable called `parent`. + + +```r +SFO <- mkinmod(parent = list(type = "SFO")) +FOMC <- mkinmod(parent = list(type = "FOMC")) +DFOP <- mkinmod(parent = list(type = "DFOP")) +``` + + +The three models cover the first assumption 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. + +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. + + +```r +m.L1.SFO <- mkinfit(SFO, FOCUS_2006_L1_mkin, quiet = TRUE) +summary(m.L1.SFO) +``` + +``` +## mkin version: 0.9.25 +## R version: 3.0.2 +## Date of fit: Sun Nov 17 15:02:54 2013 +## Date of summary: Sun Nov 17 15:02:54 2013 +## +## Equations: +## [1] d_parent = - k_parent_sink * parent +## +## Method used for solution of differential equation system: +## analytical +## +## Weighting: none +## +## Starting values for optimised parameters: +## value type transformed +## parent_0 100.0 state 100.000 +## k_parent_sink 0.1 deparm -2.303 +## +## Fixed parameter values: +## None +## +## Optimised, transformed parameters: +## Estimate Std. Error Lower Upper +## parent_0 92.50 1.3700 89.60 95.40 +## k_parent_sink -2.35 0.0406 -2.43 -2.26 +## +## Backtransformed parameters: +## Estimate Lower Upper +## parent_0 92.5000 89.6000 95.400 +## k_parent_sink 0.0956 0.0877 0.104 +## +## Residual standard error: 2.95 on 16 degrees of freedom +## +## Chi2 error levels in percent: +## err.min n.optim df +## All data 3.42 2 7 +## parent 3.42 2 7 +## +## Estimated disappearance times: +## DT50 DT90 +## parent 7.25 24.1 +## +## Estimated formation fractions: +## ff +## parent_sink 1 +## +## Parameter correlation: +## parent_0 k_parent_sink +## parent_0 1.000 0.625 +## k_parent_sink 0.625 1.000 +## +## Data: +## time variable observed predicted residual +## 0 parent 88.3 92.47 -4.171 +## 0 parent 91.4 92.47 -1.071 +## 1 parent 85.6 84.04 1.561 +## 1 parent 84.5 84.04 0.461 +## 2 parent 78.9 76.38 2.524 +## 2 parent 77.6 76.38 1.224 +## 3 parent 72.0 69.41 2.588 +## 3 parent 71.9 69.41 2.488 +## 5 parent 50.3 57.33 -7.030 +## 5 parent 59.4 57.33 2.070 +## 7 parent 47.0 47.35 -0.352 +## 7 parent 45.1 47.35 -2.252 +## 14 parent 27.7 24.25 3.453 +## 14 parent 27.3 24.25 3.053 +## 21 parent 10.0 12.42 -2.416 +## 21 parent 10.4 12.42 -2.016 +## 30 parent 2.9 5.25 -2.351 +## 30 parent 4.0 5.25 -1.251 +``` + + +A plot of the fit is obtained with the plot function for mkinfit objects. + + +```r +plot(m.L1.SFO) +``` + + + +The residual plot can be easily obtained by + + +```r +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. + + +```r +m.L1.FOMC <- mkinfit(FOMC, FOCUS_2006_L1_mkin, quiet = TRUE) +summary(m.L1.FOMC, data = FALSE) +``` + +``` +## mkin version: 0.9.25 +## R version: 3.0.2 +## Date of fit: Sun Nov 17 15:02:55 2013 +## Date of summary: Sun Nov 17 15:02:55 2013 +## +## Equations: +## [1] d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent +## +## Method used for solution of differential equation system: +## analytical +## +## Weighting: none +## +## Starting values for optimised parameters: +## value type transformed +## parent_0 100 state 100.000 +## alpha 1 deparm 0.000 +## beta 10 deparm 2.303 +## +## Fixed parameter values: +## None +## +## Optimised, transformed parameters: +## Estimate Std. Error Lower Upper +## parent_0 92.5 NA NA NA +## alpha 25.6 NA NA NA +## beta 28.0 NA NA NA +## +## Backtransformed parameters: +## Estimate Lower Upper +## parent_0 9.25e+01 NA NA +## alpha 1.35e+11 NA NA +## beta 1.41e+12 NA NA +## +## Residual standard error: 3.05 on 15 degrees of freedom +## +## Chi2 error levels in percent: +## err.min n.optim df +## All data 3.62 3 6 +## parent 3.62 3 6 +## +## Estimated disappearance times: +## DT50 DT90 +## parent 7.25 24.1 +## +## Estimated formation fractions: +## ff +## parent_sink 1 +## +## Parameter correlation: +## Could not estimate covariance matrix; singular system: +``` + + +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 covariance +matrix can not be obtained, indicating overparameterisation of the model. +As a consequence, no standard errors for transformed parameters nor +confidence intervals for backtransformed parameters are available. + +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. + +Furthermore, 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 is a widely used standard package in this field. +Therefore, the reason for the difference was not investigated further. + +## Laboratory Data L2 + +The following code defines example dataset L2 from the FOCUS kinetics +report, p. 287 + + +```r +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) +``` + + +Again, the SFO model is fitted and a summary is obtained. + + +```r +m.L2.SFO <- mkinfit(SFO, FOCUS_2006_L2_mkin, quiet = TRUE) +summary(m.L2.SFO) +``` + +``` +## mkin version: 0.9.25 +## R version: 3.0.2 +## Date of fit: Sun Nov 17 15:02:55 2013 +## Date of summary: Sun Nov 17 15:02:55 2013 +## +## Equations: +## [1] d_parent = - k_parent_sink * parent +## +## Method used for solution of differential equation system: +## analytical +## +## Weighting: none +## +## Starting values for optimised parameters: +## value type transformed +## parent_0 100.0 state 100.000 +## k_parent_sink 0.1 deparm -2.303 +## +## Fixed parameter values: +## None +## +## Optimised, transformed parameters: +## Estimate Std. Error Lower Upper +## parent_0 91.500 3.810 83.000 99.900 +## k_parent_sink -0.411 0.107 -0.651 -0.172 +## +## Backtransformed parameters: +## Estimate Lower Upper +## parent_0 91.500 83.000 99.900 +## k_parent_sink 0.663 0.522 0.842 +## +## Residual standard error: 5.51 on 10 degrees of freedom +## +## Chi2 error levels in percent: +## err.min n.optim df +## All data 14.4 2 4 +## parent 14.4 2 4 +## +## Estimated disappearance times: +## DT50 DT90 +## parent 1.05 3.47 +## +## Estimated formation fractions: +## ff +## parent_sink 1 +## +## Parameter correlation: +## parent_0 k_parent_sink +## parent_0 1.00 0.43 +## k_parent_sink 0.43 1.00 +## +## Data: +## time variable observed predicted residual +## 0 parent 96.1 9.15e+01 4.634 +## 0 parent 91.8 9.15e+01 0.334 +## 1 parent 41.4 4.71e+01 -5.740 +## 1 parent 38.7 4.71e+01 -8.440 +## 3 parent 19.3 1.25e+01 6.779 +## 3 parent 22.3 1.25e+01 9.779 +## 7 parent 4.6 8.83e-01 3.717 +## 7 parent 4.6 8.83e-01 3.717 +## 14 parent 2.6 8.53e-03 2.591 +## 14 parent 1.2 8.53e-03 1.191 +## 28 parent 0.3 7.96e-07 0.300 +## 28 parent 0.6 7.96e-07 0.600 +``` + + +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 and the residuals. + + +```r +par(mfrow = c(2, 1)) +plot(m.L2.SFO) +mkinresplot(m.L2.SFO) +``` + + + + +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. + +For comparison, the FOMC model is fitted as well, and the chi^2 error level +is checked. + + +```r +m.L2.FOMC <- mkinfit(FOMC, FOCUS_2006_L2_mkin, quiet = TRUE) +par(mfrow = c(2, 1)) +plot(m.L2.FOMC) +mkinresplot(m.L2.FOMC) +``` + + + +```r +summary(m.L2.FOMC, data = FALSE) +``` + +``` +## mkin version: 0.9.25 +## R version: 3.0.2 +## Date of fit: Sun Nov 17 15:02:56 2013 +## Date of summary: Sun Nov 17 15:02:56 2013 +## +## Equations: +## [1] d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent +## +## Method used for solution of differential equation system: +## analytical +## +## Weighting: none +## +## Starting values for optimised parameters: +## value type transformed +## parent_0 100 state 100.000 +## alpha 1 deparm 0.000 +## beta 10 deparm 2.303 +## +## Fixed parameter values: +## None +## +## Optimised, transformed parameters: +## Estimate Std. Error Lower Upper +## parent_0 93.800 1.860 89.600 98.000 +## alpha 0.318 0.187 -0.104 0.740 +## beta 0.210 0.294 -0.456 0.876 +## +## Backtransformed parameters: +## Estimate Lower Upper +## parent_0 93.80 89.600 98.0 +## alpha 1.37 0.901 2.1 +## beta 1.23 0.634 2.4 +## +## Residual standard error: 2.63 on 9 degrees of freedom +## +## Chi2 error levels in percent: +## err.min n.optim df +## All data 6.2 3 3 +## parent 6.2 3 3 +## +## Estimated disappearance times: +## DT50 DT90 +## parent 0.809 5.36 +## +## Estimated formation fractions: +## ff +## parent_sink 1 +## +## Parameter correlation: +## parent_0 alpha beta +## parent_0 1.0000 -0.0955 -0.186 +## alpha -0.0955 1.0000 0.976 +## beta -0.1863 0.9757 1.000 +``` + + +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. + +Fitting the four parameter DFOP model further reduces the chi^2 error level. + + +```r +m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin, quiet = TRUE) +plot(m.L2.DFOP) +``` + + + + +Here, the default starting parameters for the DFOP model obviously do not lead +to a reasonable solution. Therefore the fit is repeated with different starting +parameters. + + +```r +m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin, parms.ini = c(k1 = 1, k2 = 0.01, + g = 0.8), quiet = TRUE) +plot(m.L2.DFOP) +``` + + + +```r +summary(m.L2.DFOP, data = FALSE) +``` + +``` +## mkin version: 0.9.25 +## R version: 3.0.2 +## Date of fit: Sun Nov 17 15:02:57 2013 +## Date of summary: Sun Nov 17 15:02:57 2013 +## +## Equations: +## [1] d_parent = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) * parent +## +## Method used for solution of differential equation system: +## analytical +## +## Weighting: none +## +## Starting values for optimised parameters: +## value type transformed +## parent_0 1e+02 state 100.0000 +## k1 1e+00 deparm 0.0000 +## k2 1e-02 deparm -4.6052 +## g 8e-01 deparm 0.9803 +## +## Fixed parameter values: +## None +## +## Optimised, transformed parameters: +## Estimate Std. Error Lower Upper +## parent_0 93.900 NA NA NA +## k1 4.960 NA NA NA +## k2 -1.090 NA NA NA +## g -0.282 NA NA NA +## +## Backtransformed parameters: +## Estimate Lower Upper +## parent_0 93.900 NA NA +## k1 142.000 NA NA +## k2 0.337 NA NA +## g 0.402 NA NA +## +## Residual standard error: 1.73 on 8 degrees of freedom +## +## 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 +## parent NA NA +## +## Estimated formation fractions: +## ff +## parent_sink 1 +## +## Parameter correlation: +## Could not estimate covariance matrix; singular system: +``` + + +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. + + +```r +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) +``` + + +SFO model, summary and plot: + + +```r +m.L3.SFO <- mkinfit(SFO, FOCUS_2006_L3_mkin, quiet = TRUE) +plot(m.L3.SFO) +``` + + + +```r +summary(m.L3.SFO) +``` + +``` +## mkin version: 0.9.25 +## R version: 3.0.2 +## Date of fit: Sun Nov 17 15:02:57 2013 +## Date of summary: Sun Nov 17 15:02:57 2013 +## +## Equations: +## [1] d_parent = - k_parent_sink * parent +## +## Method used for solution of differential equation system: +## analytical +## +## Weighting: none +## +## Starting values for optimised parameters: +## value type transformed +## parent_0 100.0 state 100.000 +## k_parent_sink 0.1 deparm -2.303 +## +## Fixed parameter values: +## None +## +## Optimised, transformed parameters: +## Estimate Std. Error Lower Upper +## parent_0 74.90 8.460 54.20 95.60 +## k_parent_sink -3.68 0.326 -4.48 -2.88 +## +## Backtransformed parameters: +## Estimate Lower Upper +## parent_0 74.9000 54.2000 95.6000 +## k_parent_sink 0.0253 0.0114 0.0561 +## +## Residual standard error: 12.9 on 6 degrees of freedom +## +## Chi2 error levels in percent: +## err.min n.optim df +## All data 21.2 2 6 +## parent 21.2 2 6 +## +## Estimated disappearance times: +## DT50 DT90 +## parent 27.4 91.1 +## +## Estimated formation fractions: +## ff +## parent_sink 1 +## +## Parameter correlation: +## parent_0 k_parent_sink +## parent_0 1.000 0.548 +## k_parent_sink 0.548 1.000 +## +## Data: +## time variable observed predicted residual +## 0 parent 97.8 74.87 22.9273 +## 3 parent 60.0 69.41 -9.4065 +## 7 parent 51.0 62.73 -11.7340 +## 14 parent 43.0 52.56 -9.5634 +## 30 parent 35.0 35.08 -0.0828 +## 60 parent 22.0 16.44 5.5614 +## 91 parent 15.0 7.51 7.4896 +## 120 parent 12.0 3.61 8.3908 +``` + + +The chi^2 error level of 21% as well as the plot suggest that the model +does not fit very well. + +The FOMC model performs better: + + +```r +m.L3.FOMC <- mkinfit(FOMC, FOCUS_2006_L3_mkin, quiet = TRUE) +plot(m.L3.FOMC) +``` + + + +```r +summary(m.L3.FOMC, data = FALSE) +``` + +``` +## mkin version: 0.9.25 +## R version: 3.0.2 +## Date of fit: Sun Nov 17 15:02:57 2013 +## Date of summary: Sun Nov 17 15:02:57 2013 +## +## Equations: +## [1] d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent +## +## Method used for solution of differential equation system: +## analytical +## +## Weighting: none +## +## Starting values for optimised parameters: +## value type transformed +## parent_0 100 state 100.000 +## alpha 1 deparm 0.000 +## beta 10 deparm 2.303 +## +## Fixed parameter values: +## None +## +## Optimised, transformed parameters: +## Estimate Std. Error Lower Upper +## parent_0 97.000 4.550 85.3 109.000 +## alpha -0.862 0.170 -1.3 -0.424 +## beta 0.619 0.474 -0.6 1.840 +## +## Backtransformed parameters: +## Estimate Lower Upper +## parent_0 97.000 85.300 109.000 +## alpha 0.422 0.273 0.655 +## beta 1.860 0.549 6.290 +## +## Residual standard error: 4.57 on 5 degrees of freedom +## +## Chi2 error levels in percent: +## err.min n.optim df +## All data 7.32 3 5 +## parent 7.32 3 5 +## +## Estimated disappearance times: +## DT50 DT90 +## parent 7.73 431 +## +## Estimated formation fractions: +## ff +## parent_sink 1 +## +## Parameter correlation: +## parent_0 alpha beta +## parent_0 1.000 -0.151 -0.427 +## alpha -0.151 1.000 0.911 +## beta -0.427 0.911 1.000 +``` + + +The error level at which the chi^2 test passes is 7% in this case. + +Fitting the four parameter DFOP model further reduces the chi^2 error level +considerably: + + +```r +m.L3.DFOP <- mkinfit(DFOP, FOCUS_2006_L3_mkin, quiet = TRUE) +plot(m.L3.DFOP) +``` + + + +```r +summary(m.L3.DFOP, data = FALSE) +``` + +``` +## mkin version: 0.9.25 +## R version: 3.0.2 +## Date of fit: Sun Nov 17 15:02:58 2013 +## Date of summary: Sun Nov 17 15:02:58 2013 +## +## Equations: +## [1] d_parent = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) * parent +## +## Method used for solution of differential equation system: +## analytical +## +## Weighting: none +## +## Starting values for optimised parameters: +## value type transformed +## parent_0 1e+02 state 100.000 +## k1 1e-01 deparm -2.303 +## k2 1e-02 deparm -4.605 +## g 5e-01 deparm 0.000 +## +## Fixed parameter values: +## None +## +## Optimised, transformed parameters: +## Estimate Std. Error Lower Upper +## parent_0 97.700 1.4400 93.800 102.0000 +## k1 -0.661 0.1330 -1.030 -0.2910 +## k2 -4.290 0.0590 -4.450 -4.1200 +## g -0.123 0.0512 -0.265 0.0193 +## +## Backtransformed parameters: +## Estimate Lower Upper +## parent_0 97.7000 93.8000 102.0000 +## k1 0.5160 0.3560 0.7480 +## k2 0.0138 0.0117 0.0162 +## g 0.4570 0.4070 0.5070 +## +## Residual standard error: 1.44 on 4 degrees of freedom +## +## Chi2 error levels in percent: +## err.min n.optim df +## All data 2.23 4 4 +## parent 2.23 4 4 +## +## Estimated disappearance times: +## DT50 DT90 +## parent 7.46 123 +## +## Estimated formation fractions: +## ff +## parent_sink 1 +## +## Parameter correlation: +## parent_0 k1 k2 g +## parent_0 1.0000 0.164 0.0131 0.425 +## k1 0.1640 1.000 0.4648 -0.553 +## k2 0.0131 0.465 1.0000 -0.663 +## g 0.4253 -0.553 -0.6631 1.000 +``` + + +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. + +## Laboratory Data L4 + +The following code defines example dataset L4 from the FOCUS kinetics +report, p. 293 + + +```r +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)) +FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4) +``` + + +SFO model, summary and plot: + + +```r +m.L4.SFO <- mkinfit(SFO, FOCUS_2006_L4_mkin, quiet = TRUE) +plot(m.L4.SFO) +``` + + + +```r +summary(m.L4.SFO, data = FALSE) +``` + +``` +## mkin version: 0.9.25 +## R version: 3.0.2 +## Date of fit: Sun Nov 17 15:02:58 2013 +## Date of summary: Sun Nov 17 15:02:58 2013 +## +## Equations: +## [1] d_parent = - k_parent_sink * parent +## +## Method used for solution of differential equation system: +## analytical +## +## Weighting: none +## +## Starting values for optimised parameters: +## value type transformed +## parent_0 100.0 state 100.000 +## k_parent_sink 0.1 deparm -2.303 +## +## Fixed parameter values: +## None +## +## Optimised, transformed parameters: +## Estimate Std. Error Lower Upper +## parent_0 96.40 1.95 91.70 101.00 +## k_parent_sink -5.03 0.08 -5.23 -4.83 +## +## Backtransformed parameters: +## Estimate Lower Upper +## parent_0 96.40000 91.70000 1.01e+02 +## k_parent_sink 0.00654 0.00538 7.95e-03 +## +## Residual standard error: 3.65 on 6 degrees of freedom +## +## Chi2 error levels in percent: +## err.min n.optim df +## All data 3.29 2 6 +## parent 3.29 2 6 +## +## Estimated disappearance times: +## DT50 DT90 +## parent 106 352 +## +## Estimated formation fractions: +## ff +## parent_sink 1 +## +## Parameter correlation: +## parent_0 k_parent_sink +## parent_0 1.000 0.587 +## k_parent_sink 0.587 1.000 +``` + + +The chi^2 error level of 3.3% as well as the plot suggest that the model +fits very well. + +The FOMC model for comparison + + +```r +m.L4.FOMC <- mkinfit(FOMC, FOCUS_2006_L4_mkin, quiet = TRUE) +plot(m.L4.FOMC) +``` + + + +```r +summary(m.L4.FOMC, data = FALSE) +``` + +``` +## mkin version: 0.9.25 +## R version: 3.0.2 +## Date of fit: Sun Nov 17 15:02:59 2013 +## Date of summary: Sun Nov 17 15:02:59 2013 +## +## Equations: +## [1] d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent +## +## Method used for solution of differential equation system: +## analytical +## +## Weighting: none +## +## Starting values for optimised parameters: +## value type transformed +## parent_0 100 state 100.000 +## alpha 1 deparm 0.000 +## beta 10 deparm 2.303 +## +## Fixed parameter values: +## None +## +## Optimised, transformed parameters: +## Estimate Std. Error Lower Upper +## parent_0 99.100 1.680 94.80 103.000 +## alpha -0.351 0.372 -1.31 0.607 +## beta 4.170 0.564 2.73 5.620 +## +## Backtransformed parameters: +## Estimate Lower Upper +## parent_0 99.100 94.80 103.00 +## alpha 0.704 0.27 1.83 +## beta 65.000 15.30 277.00 +## +## Residual standard error: 2.31 on 5 degrees of freedom +## +## Chi2 error levels in percent: +## err.min n.optim df +## All data 2.03 3 5 +## parent 2.03 3 5 +## +## Estimated disappearance times: +## DT50 DT90 +## parent 109 1644 +## +## Estimated formation fractions: +## ff +## parent_sink 1 +## +## Parameter correlation: +## parent_0 alpha beta +## parent_0 1.000 -0.536 -0.608 +## alpha -0.536 1.000 0.991 +## beta -0.608 0.991 1.000 +``` + + +The error level at which the chi^2 test passes is slightly lower for the FOMC +model. However, the difference appears negligible. + diff --git a/vignettes/FOCUS_Z.Rnw b/vignettes/FOCUS_Z.Rnw new file mode 100644 index 0000000..44cfa46 --- /dev/null +++ b/vignettes/FOCUS_Z.Rnw @@ -0,0 +1,261 @@ +%\VignetteIndexEntry{Examples evaluation of FOCUS dataset Z} +%\VignetteEngine{knitr::knitr} +\documentclass[12pt,a4paper]{article} +\usepackage{a4wide} +\input{header} +\hypersetup{ + pdftitle = {Example evaluation of FOCUS dataset Z}, + pdfsubject = {Manuscript}, + pdfauthor = {Johannes Ranke}, + colorlinks = {true}, + linkcolor = {blue}, + citecolor = {blue}, + urlcolor = {red}, + hyperindex = {true}, + linktocpage = {true}, +} + +\begin{document} + +<<include=FALSE>>= +require(knitr) +opts_chunk$set(engine='R', tidy=FALSE) +@ + +\title{Example evaluation of FOCUS dataset Z} +\author{\textbf{Johannes Ranke} \\[0.5cm] +%EndAName +Eurofins Regulatory AG\\ +Weidenweg 15, CH--4310 Rheinfelden, Switzerland\\[0.5cm] +and\\[0.5cm] +University of Bremen\\ +} +\maketitle + +\thispagestyle{empty} \setcounter{page}{0} + +\clearpage + +\tableofcontents + +\textbf{Key words}: Kinetics, FOCUS, nonlinear optimisation + +\section{The data} + +The following code defines the example dataset from Appendix 7 to the FOCUS kinetics +report \citep{FOCUSkinetics2011}, p.350. + +<<FOCUS_2006_Z_data, echo=TRUE, eval=TRUE>>= +require(mkin) +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) +@ + +\section{Parent compound 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). + +<<FOCUS_2006_Z_fits_1, echo=TRUE, fig.height=4>>= +Z.2a <- mkinmod(Z0 = list(type = "SFO", to = "Z1"), + Z1 = list(type = "SFO")) +m.Z.2a <- mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE) +plot(m.Z.2a) +summary(m.Z.2a, data = FALSE) +@ + +As obvious from the summary, the kinetic rate constant from parent compound Z to sink +is negligible. Accordingly, the exact magnitude of the fitted parameter +\texttt{log k\_Z\_sink} is ill-defined and the covariance matrix is not returned. +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: + +<<FOCUS_2006_Z_fits_2, echo=TRUE, fig.height=4>>= +Z.2a.ff <- mkinmod(Z0 = list(type = "SFO", to = "Z1"), + Z1 = list(type = "SFO"), + use_of_ff = "max") + +m.Z.2a.ff <- mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE) +plot(m.Z.2a.ff) +summary(m.Z.2a.ff, data = FALSE) +@ + +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. Again, +the covariance matrix is not returned as the model is overparameterised. + +The simplified model is obtained by setting the list component \texttt{sink} to +\texttt{FALSE}. This model definition is not supported when formation fractions +are used. + +<<FOCUS_2006_Z_fits_3, echo=TRUE, fig.height=4>>= +Z.3 <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE), + Z1 = list(type = "SFO")) +m.Z.3 <- mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE) +plot(m.Z.3) +summary(m.Z.3, data = FALSE) +@ + +\section{Including 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. + +<<FOCUS_2006_Z_fits_5, echo=TRUE, fig.height=4>>= +Z.5 <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE), + Z1 = list(type = "SFO", to = "Z2", sink = FALSE), + Z2 = list(type = "SFO")) +m.Z.5 <- mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE) +plot(m.Z.5) +summary(m.Z.5, data = FALSE) +@ + +Finally, metabolite Z3 is added to the model. The fit is accellerated +by using the starting parameters from the previous fit. + +<<FOCUS_2006_Z_fits_6, echo=TRUE, fig.height=4>>= +Z.FOCUS <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE), + Z1 = list(type = "SFO", to = "Z2", sink = FALSE), + Z2 = list(type = "SFO", to = "Z3"), + Z3 = list(type = "SFO")) +m.Z.FOCUS <- mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, + parms.ini = m.Z.5$bparms.ode, + quiet = TRUE) +plot(m.Z.FOCUS) +summary(m.Z.FOCUS, data = FALSE) +@ + +This is the fit corresponding to the final result chosen in Appendix 7 of the +FOCUS report. The residual plots can be obtained by + +<<FOCUS_2006_Z_residuals_6, echo=TRUE>>= +par(mfrow = c(2, 2)) +mkinresplot(m.Z.FOCUS, "Z0", lpos = "bottomright") +mkinresplot(m.Z.FOCUS, "Z1", lpos = "bottomright") +mkinresplot(m.Z.FOCUS, "Z2", lpos = "bottomright") +mkinresplot(m.Z.FOCUS, "Z3", lpos = "bottomright") +@ + +\section{Using the SFORB model for parent and metabolites} + +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. + +<<FOCUS_2006_Z_fits_7, echo=TRUE, fig.height=4>>= +Z.mkin.1 <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE), + Z1 = list(type = "SFO", to = "Z2", sink = FALSE), + Z2 = list(type = "SFO", to = "Z3"), + Z3 = list(type = "SFORB")) +m.Z.mkin.1 <- mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, + parms.ini = c(k_Z0_Z1 = 0.5, k_Z1_Z2 = 0.3), + quiet = TRUE) +plot(m.Z.mkin.1) +summary(m.Z.mkin.1, data = FALSE) +@ + +Therefore, a further stepwise model building is performed starting from the +stage of parent and one metabolite, starting from the assumption that the model +fit for the parent compound can be improved by using the SFORB model. + +<<FOCUS_2006_Z_fits_8, echo=TRUE, fig.height=4>>= +Z.mkin.2 <- mkinmod(Z0 = list(type = "SFORB", to = "Z1", sink = FALSE), + Z1 = list(type = "SFO")) +m.Z.mkin.2 <- mkinfit(Z.mkin.2, FOCUS_2006_Z_mkin, quiet = TRUE) +plot(m.Z.mkin.2) +summary(m.Z.mkin.2, data = FALSE) +@ + +When metabolite Z2 is added, the additional sink for Z1 is turned off again, +for the same reasons as in the original analysis. + +<<FOCUS_2006_Z_fits_9, echo=TRUE, fig.height=4>>= +Z.mkin.3 <- mkinmod(Z0 = list(type = "SFORB", to = "Z1", sink = FALSE), + Z1 = list(type = "SFO", to = "Z2"), + Z2 = list(type = "SFO")) +m.Z.mkin.3 <- mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE) +plot(m.Z.mkin.3) +summary(m.Z.mkin.3, data = FALSE) +@ + +This results in a much better representation of the behaviour of the parent +compound Z0. + +Finally, Z3 is added as well. This model appears overparameterised (no +covariance matrix returned) if the sink for Z1 is left in the model. + +<<FOCUS_2006_Z_fits_10, echo=TRUE, fig.height=4>>= +Z.mkin.4 <- mkinmod(Z0 = list(type = "SFORB", to = "Z1", sink = FALSE), + Z1 = list(type = "SFO", to = "Z2", sink = FALSE), + Z2 = list(type = "SFO", to = "Z3"), + Z3 = list(type = "SFO")) +m.Z.mkin.4 <- mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, + parms.ini = c(k_Z1_Z2 = 0.05), + quiet = TRUE) +plot(m.Z.mkin.4) +summary(m.Z.mkin.4, data = FALSE) +@ + +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. + +<<FOCUS_2006_Z_fits_11, echo=TRUE, fig.height=4>>= +Z.mkin.5 <- mkinmod(Z0 = list(type = "SFORB", to = "Z1", sink = FALSE), + Z1 = list(type = "SFO", to = "Z2", sink = FALSE), + Z2 = list(type = "SFO", to = "Z3"), + Z3 = list(type = "SFORB")) +m.Z.mkin.5 <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, + parms.ini = m.Z.mkin.4$bparms.ode[1:5], + quiet = TRUE) +plot(m.Z.mkin.5) +summary(m.Z.mkin.5, data = FALSE) +@ + +Looking at the confidence intervals of the SFORB model parameters of Z3, it is +clear that nothing can be said about the degradation rate of Z3 towards the end +of the experiment. However, this appears to be a feature of the data. + +<<FOCUS_2006_Z_residuals_11>>= +par(mfrow = c(2, 2)) +mkinresplot(m.Z.mkin.5, "Z0", lpos = "bottomright") +mkinresplot(m.Z.mkin.5, "Z1", lpos = "bottomright") +mkinresplot(m.Z.mkin.5, "Z2", lpos = "bottomright") +mkinresplot(m.Z.mkin.5, "Z3", lpos = "bottomright") +@ + +As expected, the residual plots are much more random than in the case of the +all SFO model for which they were shown above. In conclusion, the model +\texttt{Z.mkin.5} is proposed as the best-fit model for the dataset from +Appendix 7 of the FOCUS report. + +\bibliographystyle{plainnat} +\bibliography{references} + +\end{document} +% vim: set foldmethod=syntax: diff --git a/vignettes/FOCUS_Z.pdf b/vignettes/FOCUS_Z.pdf Binary files differnew file mode 100644 index 0000000..ca67191 --- /dev/null +++ b/vignettes/FOCUS_Z.pdf diff --git a/vignettes/examples.Rnw b/vignettes/examples.Rnw deleted file mode 100644 index f876d14..0000000 --- a/vignettes/examples.Rnw +++ /dev/null @@ -1,524 +0,0 @@ -% $Id: examples.Rnw 66 2010-09-03 08:50:26Z jranke $
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- pdfsubject = {Manuscript},
- pdfauthor = {Johannes Ranke},
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-\begin{document}
-\title{Examples for kinetic evaluations using mkin}
-\author{\textbf{Johannes Ranke} \\[0.5cm]
-%EndAName
-Eurofins Regulatory AG\\
-Weidenweg 15, CH--4310 Rheinfelden, Switzerland\\[0.5cm]
-and\\[0.5cm]
-University of Bremen\\
-}
-\maketitle
-
-%\begin{abstract}
-%\end{abstract}
-
-
-\thispagestyle{empty} \setcounter{page}{0}
-
-\clearpage
-
-\tableofcontents
-
-
-\textbf{Key words}: Kinetics, FOCUS, nonlinear optimisation
-
-\section{Kinetic evaluations for parent compounds}
-
-These examples are also evaluated in a parallel vignette of the
-\Rpackage{kinfit} package \citep{pkg:kinfit}. The datasets are from Appendix 3,
-of the FOCUS kinetics report \citep{FOCUS2006, FOCUSkinetics2011}.
-
-\subsection{Laboratory Data L1}
-
-The following code defines example dataset L1 from the FOCUS kinetics
-report, p. 284
-
-<<FOCUS_2006_L1_data, echo=TRUE, eval=TRUE>>=
-library("mkin")
-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)
-@
-
-The next step is to set up the models used for the kinetic analysis. Note that
-the model definitions contain the names of the observed variables in the data.
-In this case, there is only one variable called \texttt{parent}.
-
-<<Simple_models, echo=TRUE>>=
-SFO <- mkinmod(parent = list(type = "SFO"))
-FOMC <- mkinmod(parent = list(type = "FOMC"))
-DFOP <- mkinmod(parent = list(type = "DFOP"))
-@
-
-The three models cover the first assumption 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.
-
-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.
-
-<<L1_SFO, echo=TRUE>>=
-m.L1.SFO <- mkinfit(SFO, FOCUS_2006_L1_mkin, quiet=TRUE)
-summary(m.L1.SFO)
-@
-
-A plot of the fit is obtained with the plot function for mkinfit objects.
-
-<<L1_SFO_plot, fig=TRUE, echo=TRUE, height=4>>=
-plot(m.L1.SFO)
-@
-
-The residual plot can be easily obtained by
-
-<<L1_SFO_residuals, fig=TRUE, echo=TRUE, height=4>>=
-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.
-
-<<L1_FOMC, echo=TRUE>>=
-m.L1.FOMC <- mkinfit(FOMC, FOCUS_2006_L1_mkin, quiet=TRUE)
-summary(m.L1.FOMC)
-@
-
-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 covariance matrix can not be obtained,
-indicating overparameterisation of the model.
-
-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 \texttt{mkin}. The reason for this is not known. However,
-\texttt{mkin} gives the same $\chi^2$ error levels as the \Rpackage{kinfit} package.
-Furthermore, 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 is a widely used standard package in this field.
-Therefore, the reason for the difference was not investigated further.
-
-\subsection{Laboratory Data L2}
-
-The following code defines example dataset L2 from the FOCUS kinetics
-report, p. 287
-
-<<FOCUS_2006_L2_data, echo=TRUE, eval=TRUE>>=
-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)
-@
-
-Again, the SFO model is fitted and a summary is obtained.
-
-<<L2_SFO, echo=TRUE>>=
-m.L2.SFO <- mkinfit(SFO, FOCUS_2006_L2_mkin, quiet=TRUE)
-summary(m.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 and the residuals.
-
-<<L2_SFO_plot, fig=TRUE, echo=TRUE, height=8>>=
-par(mfrow = c(2, 1))
-plot(m.L2.SFO)
-mkinresplot(m.L2.SFO)
-@
-
-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 \textit{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.
-
-For comparison, the FOMC model is fitted as well, and the $\chi^2$ error level
-is checked.
-
-<<L2_FOMC, echo=TRUE, fig=TRUE, height=8>>=
-m.L2.FOMC <- mkinfit(FOMC, FOCUS_2006_L2_mkin, quiet = TRUE)
-par(mfrow = c(2, 1))
-plot(m.L2.FOMC)
-mkinresplot(m.L2.FOMC)
-summary(m.L2.FOMC, data = FALSE)
-@
-
-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.
-
-Fitting the four parameter DFOP model further reduces the $\chi^2$ error level.
-
-<<L2_DFOP, echo=TRUE, fig=TRUE, height=4>>=
-m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin, quiet = TRUE)
-plot(m.L2.DFOP)
-@
-
-Here, the default starting parameters for the DFOP model obviously do not lead
-to a reasonable solution. Therefore the fit is repeated with different starting
-parameters.
-
-<<L2_DFOP_2, echo=TRUE, fig=TRUE, height=4>>=
-m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin,
- parms.ini = c(k1 = 1, k2 = 0.01, g = 0.8),
- quiet=TRUE)
-plot(m.L2.DFOP)
-summary(m.L2.DFOP, data = FALSE)
-@
-
-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.
-
-\subsection{Laboratory Data L3}
-
-The following code defines example dataset L3 from the FOCUS kinetics report,
-p. 290.
-
-<<FOCUS_2006_L3_data, echo=TRUE, eval=TRUE>>=
-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)
-@
-
-SFO model, summary and plot:
-
-<<L3_SFO, echo=TRUE, fig=TRUE, height=4>>=
-m.L3.SFO <- mkinfit(SFO, FOCUS_2006_L3_mkin, quiet = TRUE)
-plot(m.L3.SFO)
-summary(m.L3.SFO)
-@
-
-The $\chi^2$ error level of 22\% as well as the plot suggest that the model
-does not fit very well.
-
-The FOMC model performs better:
-
-<<L3_FOMC, echo=TRUE, fig=TRUE, height=4>>=
-m.L3.FOMC <- mkinfit(FOMC, FOCUS_2006_L3_mkin, quiet = TRUE)
-plot(m.L3.FOMC)
-summary(m.L3.FOMC, data = FALSE)
-@
-
-The error level at which the $\chi^2$ test passes is 7\% in this case.
-
-Fitting the four parameter DFOP model further reduces the $\chi^2$ error level
-considerably:
-
-<<L3_DFOP, echo=TRUE, fig=TRUE, height=4>>=
-m.L3.DFOP <- mkinfit(DFOP, FOCUS_2006_L3_mkin, quiet = TRUE)
-plot(m.L3.DFOP)
-summary(m.L3.DFOP, data = FALSE)
-@
-
-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.
-
-\subsection{Laboratory Data L4}
-
-The following code defines example dataset L4 from the FOCUS kinetics
-report, p. 293
-
-<<FOCUS_2006_L4_data, echo=TRUE, eval=TRUE>>=
-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)
-@
-
-SFO model, summary and plot:
-
-<<L4_SFO, echo=TRUE, fig=TRUE, height=4>>=
-m.L4.SFO <- mkinfit(SFO, FOCUS_2006_L4_mkin, quiet = TRUE)
-plot(m.L4.SFO)
-summary(m.L4.SFO, data = FALSE)
-@
-
-The $\chi^2$ error level of 3.3\% as well as the plot suggest that the model
-fits very well.
-
-The FOMC model for comparison
-
-<<L4_FOMC, echo=TRUE, fig=TRUE, height=4>>=
-m.L4.FOMC <- mkinfit(FOMC, FOCUS_2006_L4_mkin, quiet = TRUE)
-plot(m.L4.FOMC)
-summary(m.L4.FOMC, data = FALSE)
-@
-
-The error level at which the $\chi^2$ test passes is slightly lower for the FOMC
-model. However, the difference appears negligible.
-
-\section{Kinetic evaluations for parent and metabolites}
-
-\subsection{Laboratory Data for example compound Z}
-
-The following code defines the example dataset from Appendix 7 to the FOCUS kinetics
-report, p.350
-
-<<FOCUS_2006_Z_data, echo=TRUE, eval=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)
-@
-
-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).
-
-<<FOCUS_2006_Z_fits_1, echo=TRUE, fig=TRUE, height=4>>=
-Z.2a <- mkinmod(Z0 = list(type = "SFO", to = "Z1"),
- Z1 = list(type = "SFO"))
-m.Z.2a <- mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE)
-plot(m.Z.2a)
-summary(m.Z.2a, data = FALSE)
-@
-
-As obvious from the summary, the kinetic rate constant from parent compound Z to sink
-is negligible. Accordingly, the exact magnitude of the fitted parameter
-\texttt{log k\_Z\_sink} is ill-defined and the covariance matrix is not returned.
-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:
-
-<<FOCUS_2006_Z_fits_2, echo=TRUE, fig=TRUE, height=4>>=
-Z.2a.ff <- mkinmod(Z0 = list(type = "SFO", to = "Z1"),
- Z1 = list(type = "SFO"), use_of_ff = "max")
-
-m.Z.2a.ff <- mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE)
-plot(m.Z.2a.ff)
-summary(m.Z.2a.ff, data = FALSE)
-@
-
-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. Again,
-the covariance matrix is not returned as the model is overparameterised.
-
-The simplified model is obtained by setting the list component \texttt{sink} to
-\texttt{FALSE}. This model definition is not supported when formation fractions
-are used.
-
-<<FOCUS_2006_Z_fits_3, echo=TRUE, fig=TRUE, height=4>>=
-Z.3 <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE),
- Z1 = list(type = "SFO"))
-m.Z.3 <- mkinfit(Z.3, FOCUS_2006_Z_mkin, parms.ini = c(k_Z0_Z1 = 0.5),
- quiet = TRUE)
-#m.Z.3 <- mkinfit(Z.3, FOCUS_2006_Z_mkin, solution_type = "deSolve")
-plot(m.Z.3)
-summary(m.Z.3, data = FALSE)
-@
-
-The first attempt to fit the model failed, as the default solution type chosen
-by mkinfit is based on eigenvalues, and the system defined by the starting
-parameters is identified as being singular to the solver. This is caused by the
-fact that the rate constants for both state variables are the same using the
-default starting paramters. Setting a different starting value for one of the
-parameters overcomes this. Alternatively, the \Rpackage{deSolve} based model
-solution can be chosen, at the cost of a bit more computing time.
-
-<<FOCUS_2006_Z_fits_4, echo=TRUE, fig=TRUE, height=4>>=
-Z.4a <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE),
- Z1 = list(type = "SFO", to = "Z2"),
- Z2 = list(type = "SFO"))
-m.Z.4a <- mkinfit(Z.4a, FOCUS_2006_Z_mkin, parms.ini = c(k_Z0_Z1 = 0.5),
- quiet = TRUE)
-plot(m.Z.4a)
-summary(m.Z.4a, data = FALSE)
-@
-
-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. Again, in order to avoid a singular system when using default starting
-parameters, the starting parameter for the pathway without sink term has to be adapted.
-
-<<FOCUS_2006_Z_fits_5, echo=TRUE, fig=TRUE, height=4>>=
-Z.5 <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE),
- Z1 = list(type = "SFO", to = "Z2", sink = FALSE),
- Z2 = list(type = "SFO"))
-m.Z.5 <- mkinfit(Z.5, FOCUS_2006_Z_mkin,
- parms.ini = c(k_Z0_Z1 = 0.5, k_Z1_Z2 = 0.2), quiet = TRUE)
-plot(m.Z.5)
-summary(m.Z.5, data = FALSE)
-@
-
-Finally, metabolite Z3 is added to the model.
-
-<<FOCUS_2006_Z_fits_6, echo=TRUE, fig=TRUE, height=4>>=
-Z.FOCUS <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE),
- Z1 = list(type = "SFO", to = "Z2", sink = FALSE),
- Z2 = list(type = "SFO", to = "Z3"),
- Z3 = list(type = "SFO"))
-m.Z.FOCUS <- mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin,
- parms.ini = c(k_Z0_Z1 = 0.5, k_Z1_Z2 = 0.2, k_Z2_Z3 = 0.3),
- quiet = TRUE)
-plot(m.Z.FOCUS)
-summary(m.Z.FOCUS, data = FALSE)
-@
-
-This is the fit corresponding to the final result chosen in Appendix 7 of the
-FOCUS report. The residual plots can be obtained by
-
-<<FOCUS_2006_Z_residuals_6, echo=TRUE, fig=TRUE>>=
-par(mfrow = c(2, 2))
-mkinresplot(m.Z.FOCUS, "Z0", lpos = "bottomright")
-mkinresplot(m.Z.FOCUS, "Z1", lpos = "bottomright")
-mkinresplot(m.Z.FOCUS, "Z2", lpos = "bottomright")
-mkinresplot(m.Z.FOCUS, "Z3", lpos = "bottomright")
-@
-
-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.
-
-<<FOCUS_2006_Z_fits_7, echo=TRUE, fig=TRUE, height=4>>=
-Z.mkin.1 <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE),
- Z1 = list(type = "SFO", to = "Z2", sink = FALSE),
- Z2 = list(type = "SFO", to = "Z3"),
- Z3 = list(type = "SFORB"))
-m.Z.mkin.1 <- mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin,
- parms.ini = c(k_Z0_Z1 = 0.5, k_Z1_Z2 = 0.3),
- quiet = TRUE)
-plot(m.Z.mkin.1)
-summary(m.Z.mkin.1, data = FALSE)
-@
-
-Therefore, a further stepwise model building is performed starting from the
-stage of parent and one metabolite, starting from the assumption that the model
-fit for the parent compound can be improved by using the SFORB model.
-
-<<FOCUS_2006_Z_fits_8, echo=TRUE, fig=TRUE, height=4>>=
-Z.mkin.2 <- mkinmod(Z0 = list(type = "SFORB", to = "Z1", sink = FALSE),
- Z1 = list(type = "SFO"))
-m.Z.mkin.2 <- mkinfit(Z.mkin.2, FOCUS_2006_Z_mkin, quiet = TRUE)
-plot(m.Z.mkin.2)
-summary(m.Z.mkin.2, data = FALSE)
-@
-
-When metabolite Z2 is added, the additional sink for Z1 is turned off again,
-for the same reasons as in the original analysis.
-
-<<FOCUS_2006_Z_fits_9, echo=TRUE, fig=TRUE, height=4>>=
-Z.mkin.3 <- mkinmod(Z0 = list(type = "SFORB", to = "Z1", sink = FALSE),
- Z1 = list(type = "SFO", to = "Z2"),
- Z2 = list(type = "SFO"))
-m.Z.mkin.3 <- mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE)
-plot(m.Z.mkin.3)
-summary(m.Z.mkin.3, data = FALSE)
-@
-
-This results in a much better representation of the behaviour of the parent
-compound Z0.
-
-Finally, Z3 is added as well. This model appears overparameterised (no
-covariance matrix returned) if the sink for Z1 is left in the model.
-
-<<FOCUS_2006_Z_fits_10, echo=TRUE, fig=TRUE, height=4>>=
-Z.mkin.4 <- mkinmod(Z0 = list(type = "SFORB", to = "Z1", sink = FALSE),
- Z1 = list(type = "SFO", to = "Z2", sink = FALSE),
- Z2 = list(type = "SFO", to = "Z3"),
- Z3 = list(type = "SFO"))
-m.Z.mkin.4 <- mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin,
- parms.ini = c(k_Z1_Z2 = 0.05), quiet = TRUE)
-plot(m.Z.mkin.4)
-summary(m.Z.mkin.4, data = FALSE)
-@
-
-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.
-
-Using the SFORB additionally for Z1 or Z2 did not further improve the result.
-
-<<FOCUS_2006_Z_fits_11, echo=TRUE, fig=TRUE, height=4>>=
-Z.mkin.5 <- mkinmod(Z0 = list(type = "SFORB", to = "Z1", sink = FALSE),
- Z1 = list(type = "SFO", to = "Z2", sink = FALSE),
- Z2 = list(type = "SFO", to = "Z3"),
- Z3 = list(type = "SFORB"))
-m.Z.mkin.5 <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin,
- parms.ini = c(k_Z1_Z2 = 0.2), quiet = TRUE)
-plot(m.Z.mkin.5)
-summary(m.Z.mkin.5, data = FALSE)
-@
-
-Looking at the confidence intervals of the SFORB model parameters of Z3, it is
-clear that nothing can be said about the degradation rate of Z3 towards the end
-of the experiment. However, this appears to be a feature of the data.
-
-<<FOCUS_2006_Z_residuals_11, fig=TRUE>>=
-par(mfrow = c(2, 2))
-mkinresplot(m.Z.mkin.5, "Z0", lpos = "bottomright")
-mkinresplot(m.Z.mkin.5, "Z1", lpos = "bottomright")
-mkinresplot(m.Z.mkin.5, "Z2", lpos = "bottomright")
-mkinresplot(m.Z.mkin.5, "Z3", lpos = "bottomright")
-@
-
-As expected, the residual plots are much more random than in the case of the
-all SFO model for which they were shown above. In conclusion, the model
-\texttt{Z.mkin.5} is proposed as the best-fit model for the dataset from
-Appendix 7 of the FOCUS report.
-
-\bibliographystyle{plainnat}
-\bibliography{references}
-
-
-\end{document}
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b/vignettes/figure/unnamed-chunk-9.png diff --git a/vignettes/header.tex b/vignettes/header.tex index 707997c..476415e 100644 --- a/vignettes/header.tex +++ b/vignettes/header.tex @@ -21,11 +21,3 @@ \RequirePackage{graphicx,ae,fancyvrb}
\IfFileExists{upquote.sty}{\RequirePackage{upquote}}{}
\usepackage{relsize}
-
-\DefineVerbatimEnvironment{Sinput}{Verbatim}{baselinestretch=1.05}
-\DefineVerbatimEnvironment{Soutput}{Verbatim}{fontfamily=courier,
- baselinestretch=1.05,
- fontshape=it,
- fontsize=\relsize{-1}}
-\DefineVerbatimEnvironment{Scode}{Verbatim}{}
-\newenvironment{Schunk}{}{}
diff --git a/vignettes/mkin.Rnw b/vignettes/mkin.Rnw index 5c71e8b..398b541 100644 --- a/vignettes/mkin.Rnw +++ b/vignettes/mkin.Rnw @@ -1,168 +1,74 @@ -% $Id: mkin.Rnw 66 2010-09-03 08:50:26Z jranke $
-%%\VignetteIndexEntry{Routines for fitting kinetic models with one or more state variables to chemical degradation data}
-%%VignetteDepends{FME}
-%%\usepackage{Sweave}
-\documentclass[12pt,a4paper]{article}
-\usepackage{a4wide}
-%%\usepackage[lists,heads]{endfloat}
-\input{header}
-\hypersetup{
- pdftitle = {mkin - Routines for fitting kinetic models with one or more state variables to chemical degradation data},
- pdfsubject = {Manuscript},
- pdfauthor = {Johannes Ranke},
- colorlinks = {true},
- linkcolor = {blue},
- citecolor = {blue},
- urlcolor = {red},
- hyperindex = {true},
- linktocpage = {true},
-}
-\SweaveOpts{engine=R, eps=FALSE, keep.source = TRUE}
-<<setup, echo = FALSE, results = hide>>=
-options(prompt = "R> ")
-options(SweaveHooks = list(
- cex = function() par(cex.lab = 1.3, cex.axis = 1.3)))
-@
-\begin{document}
-\title{mkin -\\
-Routines for fitting kinetic models with one or more state variables to chemical degradation data}
-\author{\textbf{Johannes Ranke} \\[0.5cm]
-%EndAName
-Eurofins Regulatory AG\\
-Weidenweg 15, CH--4310 Rheinfelden, Switzerland\\[0.5cm]
-and\\[0.5cm]
-University of Bremen\\
-}
-\maketitle
-
-\begin{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 \RR{} add-on package \Rpackage{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.
-\end{abstract}
-
-
-\thispagestyle{empty} \setcounter{page}{0}
-
-\clearpage
-
-\tableofcontents
-
-\textbf{Key words}: Kinetics, FOCUS, nonlinear optimisation
-
-\section{Introduction}
-\label{intro}
-
-Many approaches are possible regarding the evaluation of chemical degradation
-data. The \Rpackage{kinfit} package \citep{pkg:kinfit} in \RR{}
-\citep{rcore2013} implements the approach recommended in the kinetics report
-provided by the FOrum for Co-ordination of pesticide fate models and their
-USe \citep{FOCUS2006, FOCUSkinetics2011} for simple data series for one parent
-compound in one compartment.
-
-The \Rpackage{mkin} package \citep{pkg:mkin} extends this approach to data series
-with metabolites and more than one compartment and includes the possibility
-for back reactions.
-
-\section{Example}
-\label{exam}
-
-In the following, requirements for data formatting are explained. Then the
-procedure for fitting the four kinetic models recommended by the FOCUS group
-to an example dataset for parent only given in the FOCUS kinetics report is
-illustrated. The explanations are kept rather verbose in order to lower the
-barrier for \RR{} newcomers.
-
-\subsection{Data format}
-
-The following listing shows example dataset C from the FOCUS kinetics
-report as distributed with the \Rpackage{mkin} package
-
-<<FOCUS_2006_C_data, echo=TRUE, eval=TRUE>>=
-library("mkin")
-FOCUS_2006_C
-@
-
-Note that the data needs to be in the format of a data frame containing a
-variable \Robject{name} specifying the observed variable, indicating the
-compound name and, if applicable, the compartment, a variable \Robject{time}
-containing sampling times, and a numeric variable \Robject{value} specifying
-the observed value of the variable. If a further variable \Robject{error}
-is present, this will be used to give different weights to the data points
-(the higher the error, the lower the weight, see the help page of the
-\Robject{modCost} function of the \Rpackage{FME} package \citep{soetaert10}).
-Replicate measurements are not recorded in extra columns but simply appended,
-leading to multiple occurrences of the sampling times \Robject{time}.
-
-Small to medium size dataset can be conveniently entered directly as \RR{} code
-as shown in the following listing
-
-<<data_format, echo=TRUE>>=
-example_data <- data.frame(
- name = rep("parent", 9),
- time = c(0, 1, 3, 7, 14, 28, 63, 91, 119),
- value = c(85.1, 57.9, 29.9, 14.6, 9.7, 6.6, 4, 3.9, 0.6)
-)
-@
-
-\subsection{Model definition}
-
-The next task is to define the model to be fitted to the data. In order to
-facilitate this task, a convenience function \Robject{mkinmod} is available.
-
-<<model_definition, echo=TRUE>>=
-SFO <- mkinmod(parent = list(type = "SFO"))
-SFORB <- mkinmod(parent = list(type = "SFORB"))
-SFO_SFO <- mkinmod(
- parent = list(type = "SFO", to = "m1", sink = TRUE),
- m1 = list(type = "SFO"))
-SFORB_SFO <- mkinmod(
- parent = list(type = "SFORB", to = "m1", sink = TRUE),
- m1 = list(type = "SFO"))
-@
-
-The model definitions given above define sets of linear first-order ordinary
-differential equations. In these cases, a coefficient matrix is also returned.
-
-Other models that include time on the right-hand side of the differential
-equation are the first-order multi-compartment (FOMC) model and the
-Hockey-Stick (HS) model. At present, these models can only be used only for the
-parent compound.
-
-\subsection{Fitting the model}
-
-Then the model parameters should be fitted to the data. The function
-\Robject{mkinfit} internally creates a cost function using \Robject{modCost}
-from the \Rpackage{FME} package and then produces a fit using \Robject{modFit}
-from the same package. In cases of linear first-order differential
-equations, the solution used for calculating the cost function is based
-on the fundamental system of the coefficient matrix, as proposed by
-\citet{bates88}.
-
-<<model_fitting, echo=TRUE>>=
-SFO.fit <- mkinfit(SFO, FOCUS_2006_C)
-summary(SFO.fit)
-SFORB.fit <- mkinfit(SFORB, FOCUS_2006_C)
-summary(SFORB.fit)
-SFO_SFO.fit <- mkinfit(SFO_SFO, FOCUS_2006_D)
-summary(SFO_SFO.fit, data=FALSE)
-SFORB_SFO.fit <- mkinfit(SFORB_SFO, FOCUS_2006_D)
-summary(SFORB_SFO.fit, data=FALSE)
-@
-
-\section{Acknowledgements}
-
-This package would not have been written without me being introduced to regulatory
-fate modelling of pesticides by Adrian Gurney during my time at Harlan Laboratories Ltd
-(formerly RCC Ltd). Parts of the package were written during my employment at Harlan.
-
-\bibliographystyle{plainnat}
-\bibliography{references}
-
-\end{document}
-% vim: set foldmethod=syntax:
+%\VignetteIndexEntry{Routines for fitting kinetic models with one or more state variables to chemical degradation data} +%\VignetteEngine{knitr::knitr} +\documentclass[12pt,a4paper]{article} +\usepackage{a4wide} +\input{header} +\hypersetup{ + pdftitle = {mkin - Routines for fitting kinetic models with one or more state variables to chemical degradation data}, + pdfsubject = {Manuscript}, + pdfauthor = {Johannes Ranke}, + colorlinks = {true}, + linkcolor = {blue}, + citecolor = {blue}, + urlcolor = {red}, + linktocpage = {true}, +} + +\begin{document} + +<<include=FALSE>>= +require(knitr) +opts_chunk$set(engine='R', tidy=FALSE) +@ + +\title{mkin -\\ +Routines for fitting kinetic models with one or more state variables to +chemical degradation data} +\author{\textbf{Johannes Ranke} \\[0.5cm] +%EndAName +Eurofins Regulatory AG\\ +Weidenweg 15, CH--4310 Rheinfelden, Switzerland\\[0.5cm] +and\\[0.5cm] +University of Bremen\\ +} +\maketitle + +\begin{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 \RR{} add-on package \Rpackage{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. +\end{abstract} + + +\thispagestyle{empty} \setcounter{page}{0} + +\clearpage + +\tableofcontents + +\textbf{Key words}: Kinetics, FOCUS, nonlinear optimisation + +\section{Introduction} +\label{intro} + +Many approaches are possible regarding the evaluation of chemical degradation +data. The \Rpackage{kinfit} package \citep{pkg:kinfit} in \RR{} +\citep{rcore2013} implements the approach recommended in the kinetics report +provided by the FOrum for Co-ordination of pesticide fate models and their +USe \citep{FOCUS2006, FOCUSkinetics2011} for simple data series for one parent +compound in one compartment. + +The \Rpackage{mkin} package \citep{pkg:mkin} extends this approach to data series +with metabolites and more than one compartment and includes the possibility +for back reactions. + +\bibliographystyle{plainnat} +\bibliography{references} + +\end{document} +% vim: set foldmethod=syntax: diff --git a/vignettes/mkin.pdf b/vignettes/mkin.pdf Binary files differnew file mode 100644 index 0000000..6849fb4 --- /dev/null +++ b/vignettes/mkin.pdf diff --git a/vignettes/references.bib b/vignettes/references.bib index 7796000..e069daf 100644 --- a/vignettes/references.bib +++ b/vignettes/references.bib @@ -1,4 +1,4 @@ -% This file was created with JabRef 2.7b. +% This file was originally created with JabRef 2.7b. % Encoding: ISO8859_1 @BOOK{bates88, @@ -16,8 +16,6 @@ month = {November}, year = {2011}, file = {FOCUS kinetics 2011 Generic guidance:/home/ranke/dok/orgs/focus/FOCUSkineticsvc_1_0_Nov23.pdf:PDF}, - owner = {ranke}, - timestamp = {2012.09.20}, url = {http://focus.jrc.ec.europa.eu/dk} } @@ -46,7 +44,7 @@ degradation data}, author = {Johannes Ranke}, year = {2013}, - url = {http://CRAN.R-project.org} + url = {http://CRAN.R-project.org/package=kinfit} } @MANUAL{pkg:mkin, @@ -54,7 +52,7 @@ variables to chemical degradation data}, author = {Johannes Ranke}, year = {2013}, - url = {http://CRAN.R-project.org} + url = {http://CRAN.R-project.org/package/kinfit} } @INPROCEEDINGS{schaefer2007, @@ -79,4 +77,3 @@ number = {3}, url = {http://www.jstatsoft.org/v33/i03/} } - |
