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diff --git a/vignettes/examples.tex b/vignettes/examples.tex new file mode 100644 index 0000000..4d92a06 --- /dev/null +++ b/vignettes/examples.tex @@ -0,0 +1,657 @@ +% $Id: $ +%%\VignetteIndexEntry{Examples for kinetic evaluations using kinfit} +%%\usepackage{Sweave} +\documentclass[12pt,a4paper]{article} +\usepackage{a4wide} +%%\usepackage[lists,heads]{endfloat} +\input{header} +\hypersetup{ + pdftitle = {Examples for kinetic evaluations using kinfit}, + 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 kinfit} +\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{mkin} package \citep{pkg:mkin}. The datasets are from Appendix 3, +of the FOCUS kinetics report \citep{FOCUS2006, FOCUSkinetics2011}. + +\subsection{Laboratory Data L1} + +The following code defines an object containing the example dataset L1 from the +FOCUS kinetics report, p. 284 + +\begin{Schunk} +\begin{Sinput} +R> library("kinfit") +R> FOCUS_2006_L1 = kinobject("Parent", "Degradation data", "") +R> FOCUS_2006_L1$data = data.frame( ++ t = rep(c(0, 1, 2, 3, 5, 7, 14, 21, 30), each = 2), ++ parent = c(88.3, 91.4, 85.6, 84.5, 78.9, 77.6, ++ 72.0, 71.9, 50.3, 59.4, 47.0, 45.1, ++ 27.7, 27.3, 10.0, 10.4, 2.9, 4.0)) +\end{Sinput} +\end{Schunk} + +The following two lines fit the model and produce the summary report +of the model fit. This covers the numerical analyses given in the +FOCUS report. + +\begin{Schunk} +\begin{Sinput} +R> FOCUS_2006_L1$fits <- kinfit(FOCUS_2006_L1$data, ++ kinmodels = c("SFO", "FOMC", "DFOP")) +R> FOCUS_2006_L1$results <- kinresults(FOCUS_2006_L1$fits) +R> kinreport(FOCUS_2006_L1) +\end{Sinput} +\begin{Soutput} +Parent compound: Parent +Study type: Degradation data +System: +kinfit version: 1.1.10 +R version: 2.15.2 +Report generated: Sun Feb 17 21:07:59 2013 + +Data: + t parent +1 0 88.3 +2 0 91.4 +3 1 85.6 +4 1 84.5 +5 2 78.9 +6 2 77.6 +7 3 72.0 +8 3 71.9 +9 5 50.3 +10 5 59.4 +11 7 47.0 +12 7 45.1 +13 14 27.7 +14 14 27.3 +15 21 10.0 +16 21 10.4 +17 30 2.9 +18 30 4.0 + + + +--- +Nonlinear least squares fit of the SFO model + +Parameter estimation: + Estimate Std. Error t value Pr(>t) +parent.0 92.4710 1.36830 67.6 0.00e+00 +k 0.0956 0.00388 24.6 1.87e-14 + +Chi2 error estimation: 3.42 % + + + +--- +Endpoint estimates + + DT50 DT90 +SFO 7.2 24.1 +\end{Soutput} +\end{Schunk} + +Obviously, the FOMC model and the DFOP model were not fitted. As discussed in the +kinfit vignette of this package, this occurs when the SFO model fits very well. + +We can try to force the FOMC fit using the parameters obtained using mkin. + +\begin{Schunk} +\begin{Sinput} +R> FOCUS_2006_L1$fits <- kinfit(FOCUS_2006_L1$data, ++ kinmodels = c("SFO", "FOMC", "DFOP"), ++ start.FOMC = list(parent.0 = 92.47, alpha = 1.35e11, beta = 1.41e12)) +R> FOCUS_2006_L1$results <- kinresults(FOCUS_2006_L1$fits) +R> kinreport(FOCUS_2006_L1) +\end{Sinput} +\begin{Soutput} +Parent compound: Parent +Study type: Degradation data +System: +kinfit version: 1.1.10 +R version: 2.15.2 +Report generated: Sun Feb 17 21:08:00 2013 + +Data: + t parent +1 0 88.3 +2 0 91.4 +3 1 85.6 +4 1 84.5 +5 2 78.9 +6 2 77.6 +7 3 72.0 +8 3 71.9 +9 5 50.3 +10 5 59.4 +11 7 47.0 +12 7 45.1 +13 14 27.7 +14 14 27.3 +15 21 10.0 +16 21 10.4 +17 30 2.9 +18 30 4.0 + + + +--- +Nonlinear least squares fit of the SFO model + +Parameter estimation: + Estimate Std. Error t value Pr(>t) +parent.0 92.4710 1.36830 67.6 0.00e+00 +k 0.0956 0.00388 24.6 1.87e-14 + +Chi2 error estimation: 3.42 % + + + +--- +Endpoint estimates + + DT50 DT90 +SFO 7.2 24.1 +\end{Soutput} +\end{Schunk} + +It still does not converge. As discussed in the kinfit vignette, the FOMC model usually +is not returned by kinfit when the SFO model fits very well. This should be seen as +a feature, not a bug, as the FOMC model is ill-defined in such cases. + +A plot of the fit is obtained with the kinplot function. + +\begin{Schunk} +\begin{Sinput} +R> kinplot(FOCUS_2006_L1, ylab = "Observed") +\end{Sinput} +\end{Schunk} +\includegraphics{examples-L1_SFO_plot} + +The residual plot can be easily obtained by + +\begin{Schunk} +\begin{Sinput} +R> kinresplot(FOCUS_2006_L1, "SFO", ylab = "Observed") +\end{Sinput} +\end{Schunk} +\includegraphics{examples-L1_SFO_residuals} + +\subsection{Laboratory Data L2} + +The following code defines example dataset L2 from the FOCUS kinetics +report, p. 287 + +\begin{Schunk} +\begin{Sinput} +R> FOCUS_2006_L2 = kinobject("Parent", "Degradation data", "") +R> FOCUS_2006_L2$data = 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)) +\end{Sinput} +\end{Schunk} + +Again, the SFO, FOMC and DFOP models are fitted and a report is printed. + +\begin{Schunk} +\begin{Sinput} +R> FOCUS_2006_L2$fits <- kinfit(FOCUS_2006_L2$data, ++ kinmodels = c("SFO", "FOMC", "DFOP")) +R> FOCUS_2006_L2$results <- kinresults(FOCUS_2006_L2$fits) +R> kinreport(FOCUS_2006_L2) +\end{Sinput} +\begin{Soutput} +Parent compound: Parent +Study type: Degradation data +System: +kinfit version: 1.1.10 +R version: 2.15.2 +Report generated: Sun Feb 17 21:08:00 2013 + +Data: + t parent +1 0 96.1 +2 0 91.8 +3 1 41.4 +4 1 38.7 +5 3 19.3 +6 3 22.3 +7 7 4.6 +8 7 4.6 +9 14 2.6 +10 14 1.2 +11 28 0.3 +12 28 0.6 + + + +--- +Nonlinear least squares fit of the SFO model + +Parameter estimation: + Estimate Std. Error t value Pr(>t) +parent.0 91.466 3.8065 24.03 1.77e-10 +k 0.663 0.0712 9.31 1.52e-06 + +Chi2 error estimation: 14.38 % + + + +--- +Nonlinear least squares fit of the FOMC model + +Parameter estimation: + Estimate Std. Error t value Pr(>t) +parent.0 93.77 1.856 50.51 1.17e-12 +alpha 1.37 0.257 5.36 2.30e-04 +beta 1.23 0.363 3.40 3.95e-03 + +Chi2 error estimation: 6.2 % + + + +--- +Endpoint estimates + + DT50 DT90 +SFO 1.0 3.5 +FOMC 0.8 5.4 +\end{Soutput} +\end{Schunk} + +Here, only the DFOP did not converge using default parameters. The DFOP fit can be +obtained using refined starting parameters: + +\begin{Schunk} +\begin{Sinput} +R> FOCUS_2006_L2$fits <- kinfit(FOCUS_2006_L2$data, ++ kinmodels = c("SFO", "FOMC", "DFOP"), ++ start.DFOP = list(parent.0 = 94, g = 0.4, k1 = 142, k2 = 0.34)) +R> FOCUS_2006_L2$results <- kinresults(FOCUS_2006_L2$fits) +R> kinreport(FOCUS_2006_L2) +\end{Sinput} +\begin{Soutput} +Parent compound: Parent +Study type: Degradation data +System: +kinfit version: 1.1.10 +R version: 2.15.2 +Report generated: Sun Feb 17 21:08:00 2013 + +Data: + t parent +1 0 96.1 +2 0 91.8 +3 1 41.4 +4 1 38.7 +5 3 19.3 +6 3 22.3 +7 7 4.6 +8 7 4.6 +9 14 2.6 +10 14 1.2 +11 28 0.3 +12 28 0.6 + + + +--- +Nonlinear least squares fit of the SFO model + +Parameter estimation: + Estimate Std. Error t value Pr(>t) +parent.0 91.466 3.8065 24.03 1.77e-10 +k 0.663 0.0712 9.31 1.52e-06 + +Chi2 error estimation: 14.38 % + + + +--- +Nonlinear least squares fit of the FOMC model + +Parameter estimation: + Estimate Std. Error t value Pr(>t) +parent.0 93.77 1.856 50.51 1.17e-12 +alpha 1.37 0.257 5.36 2.30e-04 +beta 1.23 0.363 3.40 3.95e-03 + +Chi2 error estimation: 6.2 % + + + +--- +Endpoint estimates + + DT50 DT90 +SFO 1.0 3.5 +FOMC 0.8 5.4 +\end{Soutput} +\end{Schunk} + +Again, even with starting parameters very close to the optimum obtained using mkin, +there is no convergence with kinfit. However, when looking at the fit obtained using +mkin plotted in the mkin vignette, it is clear that the point where the break point +of the curve, caused by the large difference between k1 and k2, is not clearly defined +by the data. Therefore, it should be seen as a desirable feature of the +underlying nls() function that no solution is returned. + +Comparison of $\chi^2$ error levels of the two models shows that the FOMC model allows +for a better representation of the data. This is also obvious from the plot +of the fits. + +\begin{Schunk} +\begin{Sinput} +R> kinplot(FOCUS_2006_L2, ylab = "Observed") +\end{Sinput} +\end{Schunk} +\includegraphics{examples-L2_plot} + +Residual plots are obtained using kinresplot. + +\begin{Schunk} +\begin{Sinput} +R> par(mfrow=c(2,1)) +R> kinresplot(FOCUS_2006_L2, "SFO", ylab = "Observed") +R> kinresplot(FOCUS_2006_L2, "FOMC", ylab = "Observed") +\end{Sinput} +\end{Schunk} +\includegraphics{examples-L2_resplot} + +\subsection{Laboratory Data L3} + +The following code defines example dataset L3 from the FOCUS kinetics +report, p. 290 and attempts to fit the SFO, FOMC and DFOP models. + +\begin{Schunk} +\begin{Sinput} +R> FOCUS_2006_L3 = kinobject("Parent", "Degradation data", "") +R> FOCUS_2006_L3$data = data.frame( ++ t = c(0, 3, 7, 14, 30, 60, 91, 120), ++ parent = c(97.8, 60, 51, 43, 35, 22, 15, 12)) +R> FOCUS_2006_L3$fits <- kinfit(FOCUS_2006_L3$data, ++ kinmodels = c("SFO", "FOMC", "DFOP")) +R> FOCUS_2006_L3$results <- kinresults(FOCUS_2006_L3$fits) +R> kinreport(FOCUS_2006_L3) +\end{Sinput} +\begin{Soutput} +Parent compound: Parent +Study type: Degradation data +System: +kinfit version: 1.1.10 +R version: 2.15.2 +Report generated: Sun Feb 17 21:08:00 2013 + +Data: + t parent +1 0 97.8 +2 3 60.0 +3 7 51.0 +4 14 43.0 +5 30 35.0 +6 60 22.0 +7 91 15.0 +8 120 12.0 + + + +--- +Nonlinear least squares fit of the SFO model + +Parameter estimation: + Estimate Std. Error t value Pr(>t) +parent.0 74.8718 8.45736 8.85 5.78e-05 +k 0.0253 0.00824 3.07 1.10e-02 + +Chi2 error estimation: 21.24 % + + + +--- +Nonlinear least squares fit of the DFOP model + +Parameter estimation: + Estimate Std. Error t value Pr(>t) +parent.0 97.7460 1.438160 68.0 1.40e-07 +k1 0.5162 0.068841 7.5 8.46e-04 +k2 0.0138 0.000812 16.9 3.56e-05 +g 0.4566 0.017970 25.4 7.12e-06 + +Chi2 error estimation: 2.22 % + + + +--- +Endpoint estimates + + DT50 DT90 +SFO 27.4 91.1 +DFOP 7.5 123.0 +\end{Soutput} +\end{Schunk} + +In this case, the FOMC model does not return a solution using kinfit. Trying with +closer starting parameters gives success this time. + +\begin{Schunk} +\begin{Sinput} +R> FOCUS_2006_L3$fits <- kinfit(FOCUS_2006_L3$data, ++ kinmodels = c("SFO", "FOMC", "DFOP"), ++ start.FOMC = list(parent.0 = 100, alpha = 0.5, beta = 2)) +R> FOCUS_2006_L3$results <- kinresults(FOCUS_2006_L3$fits) +R> kinreport(FOCUS_2006_L3) +\end{Sinput} +\begin{Soutput} +Parent compound: Parent +Study type: Degradation data +System: +kinfit version: 1.1.10 +R version: 2.15.2 +Report generated: Sun Feb 17 21:08:00 2013 + +Data: + t parent +1 0 97.8 +2 3 60.0 +3 7 51.0 +4 14 43.0 +5 30 35.0 +6 60 22.0 +7 91 15.0 +8 120 12.0 + + + +--- +Nonlinear least squares fit of the SFO model + +Parameter estimation: + Estimate Std. Error t value Pr(>t) +parent.0 74.8718 8.45736 8.85 5.78e-05 +k 0.0253 0.00824 3.07 1.10e-02 + +Chi2 error estimation: 21.24 % + + + +--- +Nonlinear least squares fit of the FOMC model + +Parameter estimation: + Estimate Std. Error t value Pr(>t) +parent.0 96.974 4.550 21.31 2.11e-06 +alpha 0.422 0.072 5.87 1.02e-03 +beta 1.858 0.881 2.11 4.44e-02 + +Chi2 error estimation: 7.32 % + + + +--- +Nonlinear least squares fit of the DFOP model + +Parameter estimation: + Estimate Std. Error t value Pr(>t) +parent.0 97.7460 1.438160 68.0 1.40e-07 +k1 0.5162 0.068841 7.5 8.46e-04 +k2 0.0138 0.000812 16.9 3.56e-05 +g 0.4566 0.017970 25.4 7.12e-06 + +Chi2 error estimation: 2.22 % + + + +--- +Endpoint estimates + + DT50 DT90 +SFO 27.4 91.1 +FOMC 7.7 431.2 +DFOP 7.5 123.0 +\end{Soutput} +\begin{Sinput} +R> kinplot(FOCUS_2006_L3, ylab = "Observed") +\end{Sinput} +\end{Schunk} +\includegraphics{examples-FOCUS_2006_L3_2} + +Based on the $\chi^2$ error level criterion and the visual analysis of the +fits, the DFOP model would be the best-fit model of choice for laboratory data +L3. + +\subsection{Laboratory Data L4} + +The following code defines example dataset L4 from the FOCUS kinetics +report, p. 293 and attempts to fit the SFO, FOMC and DFOP models. + +\begin{Schunk} +\begin{Sinput} +R> FOCUS_2006_L4 = kinobject("Parent", "Degradation data", "") +R> FOCUS_2006_L4$data = data.frame( ++ t = c(0, 3, 7, 14, 30, 60, 91, 120), ++ parent = c(96.6, 96.3, 94.3, 88.8, 74.9, 59.9, 53.5, 49.0)) +R> FOCUS_2006_L4$fits <- kinfit(FOCUS_2006_L4$data, ++ kinmodels = c("SFO", "FOMC", "DFOP")) +R> FOCUS_2006_L4$results <- kinresults(FOCUS_2006_L4$fits) +R> kinreport(FOCUS_2006_L4) +\end{Sinput} +\begin{Soutput} +Parent compound: Parent +Study type: Degradation data +System: +kinfit version: 1.1.10 +R version: 2.15.2 +Report generated: Sun Feb 17 21:08:00 2013 + +Data: + t parent +1 0 96.6 +2 3 96.3 +3 7 94.3 +4 14 88.8 +5 30 74.9 +6 60 59.9 +7 91 53.5 +8 120 49.0 + + + +--- +Nonlinear least squares fit of the SFO model + +Parameter estimation: + Estimate Std. Error t value Pr(>t) +parent.0 96.44152 1.948781 49.5 2.28e-09 +k 0.00654 0.000523 12.5 8.01e-06 + +Chi2 error estimation: 3.29 % + + + +--- +Nonlinear least squares fit of the FOMC model + +Parameter estimation: + Estimate Std. Error t value Pr(>t) +parent.0 99.143 1.680 59.02 1.32e-08 +alpha 0.704 0.262 2.68 2.18e-02 +beta 64.980 36.617 1.77 6.81e-02 + +Chi2 error estimation: 2.03 % + + + +--- +Nonlinear least squares fit of the DFOP model + +Parameter estimation: + Estimate Std. Error t value Pr(>t) +parent.0 98.7514 1.33707 73.857 1.01e-07 +k1 0.0105 0.00449 2.348 3.93e-02 +k2 -0.0112 0.01884 -0.596 7.08e-01 +g 0.9390 0.18530 5.068 3.57e-03 + +Chi2 error estimation: 1.63 % + + + +--- +Endpoint estimates + + DT50 DT90 +SFO 106.0 352.0 +FOMC 108.9 1644.1 +DFOP 118.7 122.8 +\end{Soutput} +\begin{Sinput} +R> kinplot(FOCUS_2006_L4, ylab = "Observed") +\end{Sinput} +\end{Schunk} +\includegraphics{examples-FOCUS_2006_L4} + +Although the $\chi^2$ error level is slightly smaller for the DFOP model and also +for the FOMC model, the differences are small, and the SFO model may appear to +be a suitable choice. The better fit of the DFOP model depends very much on the +last three data points. + +\bibliographystyle{plainnat} +\bibliography{references} + +\end{document} +% vim: set foldmethod=syntax: |