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L1}{section.1}% 2 -\BOOKMARK [2][-]{subsection.1.2}{Laboratory Data L2}{section.1}% 3 -\BOOKMARK [2][-]{subsection.1.3}{Laboratory Data L3}{section.1}% 4 -\BOOKMARK [2][-]{subsection.1.4}{Laboratory Data L4}{section.1}% 5 diff --git a/vignettes/examples.pdf b/vignettes/examples.pdf Binary files differindex be0d96e..ff71a42 100644 --- a/vignettes/examples.pdf +++ b/vignettes/examples.pdf diff --git a/vignettes/examples.tex b/vignettes/examples.tex deleted file mode 100644 index 4f59aa2..0000000 --- a/vignettes/examples.tex +++ /dev/null @@ -1,700 +0,0 @@ -% $Id: examples.Rnw 66 2010-09-03 08:50:26Z jranke $ -%%\VignetteIndexEntry{Examples for kinetic evaluations using mkin} -%%VignetteDepends{FME} -%%\usepackage{Sweave} -\documentclass[12pt,a4paper]{article} -\usepackage{a4wide} -%%\usepackage[lists,heads]{endfloat} -\input{header} -\hypersetup{ - pdftitle = {Examples for kinetic evaluations using mkin}, - pdfsubject = {Manuscript}, - pdfauthor = {Johannes Ranke}, - colorlinks = {true}, - linkcolor = {blue}, - citecolor = {blue}, - urlcolor = {red}, - hyperindex = {true}, - linktocpage = {true}, -} - -\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} -\label{intro} - -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 - -\begin{Schunk} -\begin{Sinput} -R> library("mkin") -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, -+ 72.0, 71.9, 50.3, 59.4, 47.0, 45.1, -+ 27.7, 27.3, 10.0, 10.4, 2.9, 4.0)) -R> FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1) -\end{Sinput} -\end{Schunk} - -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 \Robject{parent}. - -\begin{Schunk} -\begin{Sinput} -R> SFO <- mkinmod(parent = list(type = "SFO")) -R> FOMC <- mkinmod(parent = list(type = "FOMC")) -R> DFOP <- mkinmod(parent = list(type = "DFOP")) -\end{Sinput} -\end{Schunk} - -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. - -\begin{Schunk} -\begin{Sinput} -R> m.L1.SFO <- mkinfit(SFO, FOCUS_2006_L1_mkin, quiet=TRUE) -R> summary(m.L1.SFO) -\end{Sinput} -\begin{Soutput} -mkin version: 0.9.10 -R version: 2.15.2 -Date of fit: Sat Feb 16 21:38:15 2013 -Date of summary: Sat Feb 16 21:38:15 2013 - -Equations: -[1] d_parent = - k_parent_sink * parent - -Starting values for optimised parameters: - initial type transformed -parent_0 100.0 state 100.000000 -k_parent_sink 0.1 deparm -2.302585 - -Fixed parameter values: -None - -Optimised, transformed parameters: - Estimate Std. Error -parent_0 92.471 1.368 -k_parent_sink -2.347 0.041 - -Backtransformed parameters: - Estimate -parent_0 92.471 -k_parent_sink 0.096 - -Residual standard error: 2.948 on 16 degrees of freedom - -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 - -Estimated formation fractions: - ff -parent_sink 1 - -Parameter correlation: - parent_0 k_parent_sink -parent_0 1.0000 0.6248 -k_parent_sink 0.6248 1.0000 - -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 3.4527 - 14 parent 27.3 24.247 3.0527 - 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 -\end{Soutput} -\end{Schunk} - -A plot of the fit is obtained with the plot function for mkinfit objects. - -\begin{Schunk} -\begin{Sinput} -R> plot(m.L1.SFO) -\end{Sinput} -\end{Schunk} -\includegraphics{examples-L1_SFO_plot} - -The residual plot can be obtained using the information contained in the -mkinfit object, which is in fact a derivative of an modFit object defined by -the \Rpackage{FME} package. - -\begin{Schunk} -\begin{Sinput} -R> plot(m.L1.SFO$data$time, m.L1.SFO$data$residual, -+ xlab = "Time", ylab = "Residual", ylim = c(-8, 8)) -R> abline(h = 0, lty = 2) -\end{Sinput} -\end{Schunk} -\includegraphics{examples-L1_SFO_residuals} - -For comparison, the FOMC model is fitted as well, and the $\chi^2$ error level -is checked. - -\begin{Schunk} -\begin{Sinput} -R> m.L1.FOMC <- mkinfit(FOMC, FOCUS_2006_L1_mkin, quiet=TRUE) -R> s.m.L1.FOMC <- summary(m.L1.FOMC) -R> s.m.L1.FOMC$errmin -\end{Sinput} -\begin{Soutput} - err.min n.optim df -All data 0.03618911 3 6 -parent 0.03618911 3 6 -\end{Soutput} -\end{Schunk} - -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\%). - -\subsection{Laboratory Data L2} - -The following code defines example dataset L2 from the FOCUS kinetics -report, p. 287 - -\begin{Schunk} -\begin{Sinput} -R> library("mkin") -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)) -R> FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2) -\end{Sinput} -\end{Schunk} - -Again, the SFO model is fitted and a summary is obtained. - -\begin{Schunk} -\begin{Sinput} -R> m.L2.SFO <- mkinfit(SFO, FOCUS_2006_L2_mkin, quiet=TRUE) -R> summary(m.L2.SFO) -\end{Sinput} -\begin{Soutput} -mkin version: 0.9.10 -R version: 2.15.2 -Date of fit: Sat Feb 16 21:38:15 2013 -Date of summary: Sat Feb 16 21:38:15 2013 - -Equations: -[1] d_parent = - k_parent_sink * parent - -Starting values for optimised parameters: - initial type transformed -parent_0 100.0 state 100.000000 -k_parent_sink 0.1 deparm -2.302585 - -Fixed parameter values: -None - -Optimised, transformed parameters: - Estimate Std. Error -parent_0 91.4656 3.807 -k_parent_sink -0.4112 0.107 - -Backtransformed parameters: - Estimate -parent_0 91.466 -k_parent_sink 0.663 - -Residual standard error: 5.51 on 10 degrees of freedom - -Chi2 error levels in percent: - err.min n.optim df -All data 14.38 2 4 -parent 14.38 2 4 - -Estimated disappearance times: - DT50 DT90 -parent 1.046 3.474 - -Estimated formation fractions: - ff -parent_sink 1 - -Parameter correlation: - parent_0 k_parent_sink -parent_0 1.0000 0.4295 -k_parent_sink 0.4295 1.0000 - -Data: - time variable observed predicted residual - 0 parent 96.1 91.4656079103 4.6344 - 0 parent 91.8 91.4656079103 0.3344 - 1 parent 41.4 47.1395280371 -5.7395 - 1 parent 38.7 47.1395280371 -8.4395 - 3 parent 19.3 12.5210295280 6.7790 - 3 parent 22.3 12.5210295280 9.7790 - 7 parent 4.6 0.8833842647 3.7166 - 7 parent 4.6 0.8833842647 3.7166 - 14 parent 2.6 0.0085318162 2.5915 - 14 parent 1.2 0.0085318162 1.1915 - 28 parent 0.3 0.0000007958 0.3000 - 28 parent 0.6 0.0000007958 0.6000 -\end{Soutput} -\end{Schunk} - -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. - -\begin{Schunk} -\begin{Sinput} -R> plot(m.L2.SFO) -\end{Sinput} -\end{Schunk} -\includegraphics{examples-L2_SFO_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. - -\begin{Schunk} -\begin{Sinput} -R> plot(m.L2.SFO$data$time, m.L2.SFO$data$residual, -+ xlab = "Time", ylab = "Residual", ylim = c(-10, 10)) -R> abline(h = 0, lty = 2) -\end{Sinput} -\end{Schunk} -\includegraphics{examples-L2_SFO_residuals} - -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 why a -consistent underestimation after the approximate DT90 should be irrelevant. - -For comparison, the FOMC model is fitted as well, and the $\chi^2$ error level -is checked. - -\begin{Schunk} -\begin{Sinput} -R> m.L2.FOMC <- mkinfit(FOMC, FOCUS_2006_L2_mkin, quiet=TRUE) -R> plot(m.L2.FOMC) -R> s.m.L2.FOMC <- summary(m.L2.FOMC) -R> s.m.L2.FOMC$errmin -\end{Sinput} -\begin{Soutput} - err.min n.optim df -All data 0.06204245 3 3 -parent 0.06204245 3 3 -\end{Soutput} -\end{Schunk} -\includegraphics{examples-L2_FOMC} - -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 does not further reduce the -$\chi^2$ error level. - -\begin{Schunk} -\begin{Sinput} -R> m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin, quiet=TRUE) -R> plot(m.L2.DFOP) -\end{Sinput} -\end{Schunk} -\includegraphics{examples-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. - -\begin{Schunk} -\begin{Sinput} -R> m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin, -+ parms.ini = c(k1 = 1, k2 = 0.01, g = 0.8), -+ quiet=TRUE) -R> plot(m.L2.DFOP) -R> summary(m.L2.DFOP) -\end{Sinput} -\begin{Soutput} -mkin version: 0.9.10 -R version: 2.15.2 -Date of fit: Sat Feb 16 21:38:16 2013 -Date of summary: Sat Feb 16 21:38:16 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 - -Starting values for optimised parameters: - initial type transformed -parent_0 1e+02 state 100.0000000 -k1 1e+00 deparm 0.0000000 -k2 1e-02 deparm -4.6051702 -g 8e-01 deparm 0.9802581 - -Fixed parameter values: -None - -Optimised, transformed parameters: - Estimate Std. Error -parent_0 93.9500 NA -k1 4.9589 NA -k2 -1.0880 NA -g -0.2821 NA - -Backtransformed parameters: - Estimate -parent_0 93.950 -k1 142.434 -k2 0.337 -g 0.402 - -Residual standard error: 1.732 on 8 degrees of freedom - -Chi2 error levels in percent: - err.min n.optim df -All data 2.529 4 2 -parent 2.529 4 2 - -Estimated disappearance times: - DT50 DT90 -parent NA NA - -Estimated formation fractions: -[1] ff -<0 rows> (or 0-length row.names) - -Data: - time variable observed predicted residual - 0 parent 96.1 93.950000 2.1500 - 0 parent 91.8 93.950000 -2.1500 - 1 parent 41.4 40.143423 1.2566 - 1 parent 38.7 40.143423 -1.4434 - 3 parent 19.3 20.464500 -1.1645 - 3 parent 22.3 20.464500 1.8355 - 7 parent 4.6 5.318322 -0.7183 - 7 parent 4.6 5.318322 -0.7183 - 14 parent 2.6 0.503070 2.0969 - 14 parent 1.2 0.503070 0.6969 - 28 parent 0.3 0.004501 0.2955 - 28 parent 0.6 0.004501 0.5955 -\end{Soutput} -\begin{Sinput} -R> s.m.L2.DFOP <- summary(m.L2.DFOP) -R> s.m.L2.DFOP$errmin -\end{Sinput} -\begin{Soutput} - err.min n.optim df -All data 0.02528763 4 2 -parent 0.02528763 4 2 -\end{Soutput} -\end{Schunk} -\includegraphics{examples-L2_DFOP_2} - -Therefore, the FOMC model is clearly the best-fit model based on the -$\chi^2$ error level criterion. - -\subsection{Laboratory Data L3} - -The following code defines example dataset L3 from the FOCUS kinetics -report, p. 290 - -\begin{Schunk} -\begin{Sinput} -R> library("mkin") -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)) -R> FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3) -\end{Sinput} -\end{Schunk} - -SFO model, summary and plot: - -\begin{Schunk} -\begin{Sinput} -R> m.L3.SFO <- mkinfit(SFO, FOCUS_2006_L3_mkin, quiet=TRUE) -R> summary(m.L3.SFO) -\end{Sinput} -\begin{Soutput} -mkin version: 0.9.10 -R version: 2.15.2 -Date of fit: Sat Feb 16 21:38:16 2013 -Date of summary: Sat Feb 16 21:38:16 2013 - -Equations: -[1] d_parent = - k_parent_sink * parent - -Starting values for optimised parameters: - initial type transformed -parent_0 100.0 state 100.000000 -k_parent_sink 0.1 deparm -2.302585 - -Fixed parameter values: -None - -Optimised, transformed parameters: - Estimate Std. Error -parent_0 74.873 8.458 -k_parent_sink -3.678 0.326 - -Backtransformed parameters: - Estimate -parent_0 74.873 -k_parent_sink 0.025 - -Residual standard error: 12.91 on 6 degrees of freedom - -Chi2 error levels in percent: - err.min n.optim df -All data 21.24 2 6 -parent 21.24 2 6 - -Estimated disappearance times: - DT50 DT90 -parent 27.43 91.12 - -Estimated formation fractions: - ff -parent_sink 1 - -Parameter correlation: - parent_0 k_parent_sink -parent_0 1.0000 0.5484 -k_parent_sink 0.5484 1.0000 - -Data: - time variable observed predicted residual - 0 parent 97.8 74.873 22.92734 - 3 parent 60.0 69.407 -9.40654 - 7 parent 51.0 62.734 -11.73403 - 14 parent 43.0 52.563 -9.56336 - 30 parent 35.0 35.083 -0.08281 - 60 parent 22.0 16.439 5.56137 - 91 parent 15.0 7.510 7.48961 - 120 parent 12.0 3.609 8.39083 -\end{Soutput} -\begin{Sinput} -R> plot(m.L3.SFO) -\end{Sinput} -\end{Schunk} -\includegraphics{examples-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: - -\begin{Schunk} -\begin{Sinput} -R> m.L3.FOMC <- mkinfit(FOMC, FOCUS_2006_L3_mkin, quiet=TRUE) -R> plot(m.L3.FOMC) -R> s.m.L3.FOMC <- summary(m.L3.FOMC) -R> s.m.L3.FOMC$errmin -\end{Sinput} -\begin{Soutput} - err.min n.optim df -All data 0.07321867 3 5 -parent 0.07321867 3 5 -\end{Soutput} -\begin{Sinput} -R> endpoints(m.L3.FOMC) -\end{Sinput} -\begin{Soutput} -$distimes - DT50 DT90 -parent 7.729478 431.2428 - -$ff -logical(0) - -$SFORB -logical(0) -\end{Soutput} -\end{Schunk} -\includegraphics{examples-L3_FOMC} - -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: - -\begin{Schunk} -\begin{Sinput} -R> m.L3.DFOP <- mkinfit(DFOP, FOCUS_2006_L3_mkin, quiet=TRUE) -R> plot(m.L3.DFOP) -R> s.m.L3.DFOP <- summary(m.L3.DFOP) -R> s.m.L3.DFOP$errmin -\end{Sinput} -\begin{Soutput} - err.min n.optim df -All data 0.02223992 4 4 -parent 0.02223992 4 4 -\end{Soutput} -\end{Schunk} -\includegraphics{examples-L3_DFOP} - -Therefore, the DFOP model is 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 - -\begin{Schunk} -\begin{Sinput} -R> library("mkin") -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)) -R> FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4) -\end{Sinput} -\end{Schunk} - -SFO model, summary and plot: - -\begin{Schunk} -\begin{Sinput} -R> m.L4.SFO <- mkinfit(SFO, FOCUS_2006_L4_mkin, quiet=TRUE) -R> summary(m.L4.SFO) -\end{Sinput} -\begin{Soutput} -mkin version: 0.9.10 -R version: 2.15.2 -Date of fit: Sat Feb 16 21:38:17 2013 -Date of summary: Sat Feb 16 21:38:17 2013 - -Equations: -[1] d_parent = - k_parent_sink * parent - -Starting values for optimised parameters: - initial type transformed -parent_0 100.0 state 100.000000 -k_parent_sink 0.1 deparm -2.302585 - -Fixed parameter values: -None - -Optimised, transformed parameters: - Estimate Std. Error -parent_0 96.44 1.949 -k_parent_sink -5.03 0.080 - -Backtransformed parameters: - Estimate -parent_0 96.442 -k_parent_sink 0.007 - -Residual standard error: 3.651 on 6 degrees of freedom - -Chi2 error levels in percent: - err.min n.optim df -All data 3.288 2 6 -parent 3.288 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 1.0000 0.5865 -k_parent_sink 0.5865 1.0000 - -Data: - time variable observed predicted residual - 0 parent 96.6 96.44 0.1585 - 3 parent 96.3 94.57 1.7324 - 7 parent 94.3 92.13 2.1744 - 14 parent 88.8 88.00 0.7972 - 30 parent 74.9 79.26 -4.3589 - 60 parent 59.9 65.14 -5.2376 - 91 parent 53.5 53.18 0.3167 - 120 parent 49.0 43.99 5.0054 -\end{Soutput} -\begin{Sinput} -R> plot(m.L4.SFO) -\end{Sinput} -\end{Schunk} -\includegraphics{examples-L4_SFO} - -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 - -\begin{Schunk} -\begin{Sinput} -R> m.L4.FOMC <- mkinfit(FOMC, FOCUS_2006_L4_mkin, quiet=TRUE) -R> plot(m.L4.FOMC) -R> s.m.L4.FOMC <- summary(m.L4.FOMC) -R> s.m.L4.FOMC$errmin -\end{Sinput} -\begin{Soutput} - err.min n.optim df -All data 0.02027643 3 5 -parent 0.02027643 3 5 -\end{Soutput} -\end{Schunk} -\includegraphics{examples-L4_FOMC} - -The error level at which the $\chi^2$ test passes is slightly lower for the FOMC -model. However, the difference appears negligible. - -\bibliographystyle{plainnat} -\bibliography{references} - -\end{document} -% vim: set foldmethod=syntax: diff --git a/vignettes/examples.toc b/vignettes/examples.toc deleted file mode 100644 index f25aa62..0000000 --- a/vignettes/examples.toc +++ /dev/null @@ -1,5 +0,0 @@ -\contentsline {section}{\numberline {1}Kinetic evaluations for parent compounds}{1}{section.1} -\contentsline {subsection}{\numberline {1.1}Laboratory Data L1}{1}{subsection.1.1} -\contentsline {subsection}{\numberline {1.2}Laboratory Data L2}{6}{subsection.1.2} -\contentsline {subsection}{\numberline {1.3}Laboratory Data L3}{14}{subsection.1.3} -\contentsline {subsection}{\numberline {1.4}Laboratory Data L4}{20}{subsection.1.4} diff --git a/vignettes/mkin.pdf b/vignettes/mkin.pdf Binary files differindex e1fe352..9738230 100644 --- a/vignettes/mkin.pdf +++ b/vignettes/mkin.pdf |