diff options
30 files changed, 2059 insertions, 11 deletions
diff --git a/DESCRIPTION b/DESCRIPTION index 0ef8ba6..c76ca01 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -2,8 +2,8 @@ Package: mkin Type: Package Title: Routines for fitting kinetic models with one or more state variables to chemical degradation data -Version: 0.9-09 -Date: 2013-02-05 +Version: 0.9-10 +Date: 2013-02-16 Author: Johannes Ranke, Katrin Lindenberger, René Lehmann Maintainer: Johannes Ranke <jranke@uni-bremen.de> Description: Calculation routines based on the FOCUS Kinetics Report (2006). diff --git a/R/mkinfit.R b/R/mkinfit.R index f574b6e..411cb40 100644 --- a/R/mkinfit.R +++ b/R/mkinfit.R @@ -158,7 +158,7 @@ mkinfit <- function(mkinmod, observed, points(subset(observed, name == obs_var, c(time, value)),
pch = pch_obs[obs_var], col = col_obs[obs_var])
}
- matlines(out_plot$time, out_plot[-1], co = col_obs, lty = lty_obs)
+ matlines(out_plot$time, out_plot[-1], col = col_obs, lty = lty_obs)
legend("topright", inset=c(0.05, 0.05), legend=obs_vars,
col=col_obs, pch=pch_obs, lty=1:length(pch_obs))
}
diff --git a/R/mkinresplot.R b/R/mkinresplot.R index 6392794..b348278 100644 --- a/R/mkinresplot.R +++ b/R/mkinresplot.R @@ -19,7 +19,7 @@ # this program. If not, see <http://www.gnu.org/licenses/>
mkinresplot <- function (object, obs_vars = vector(),
- xlab = "Time [days]", ylab = "Residual [% of applied radioactivity]",
+ xlab = "Time", ylab = "Residual",
maxabs = "auto", legend= TRUE, lpos = "topright", ...)
{
obs_vars_all <- as.character(unique(object$data$variable))
diff --git a/R/plot.mkinfit.R b/R/plot.mkinfit.R index 1858aa8..b47678b 100644 --- a/R/plot.mkinfit.R +++ b/R/plot.mkinfit.R @@ -1,8 +1,8 @@ plot.mkinfit <- function(x, fit = x, xlab = "Time", ylab = "Observed", - xlim = range(fit$data$time), ylim = range(fit$data$observed, na.rm = TRUE), + xlim = range(fit$data$time), ylim = c(0, max(fit$data$observed, na.rm = TRUE)), col_obs = 1:length(fit$mkinmod$map), - pch_obs = col_obs, lty_obs = rep(1, length(fit$mkinmod$map)), + pch_obs = col_obs, lty_obs = 1, add = FALSE, legend = !add, ...) { solution_type = fit$solution_type diff --git a/man/mkin_long_to_wide.Rd b/man/mkin_long_to_wide.Rd index 6fa1860..e583664 100644 --- a/man/mkin_long_to_wide.Rd +++ b/man/mkin_long_to_wide.Rd @@ -13,8 +13,9 @@ mkin_long_to_wide(long_data, time = "time", outtime = "time") } \arguments{ \item{long_data}{ - The dataframe must contain one variable with the time values specified by the - \code{time} argument and one column of observed values named "value". + The dataframe must contain one variable called "time" with the time values specified by the + \code{time} argument, one column called "name" with the grouping of the observed values, and + finally one column of observed values called "value". } \item{time}{ The name of the time variable in the long input data. diff --git a/man/mkinfit.Rd b/man/mkinfit.Rd index 181da4b..319b1b3 100644 --- a/man/mkinfit.Rd +++ b/man/mkinfit.Rd @@ -26,7 +26,7 @@ mkinfit(mkinmod, observed, } \item{observed}{ The observed data. It has to be in the long format as described in - \code{\link{modFit}}, i.e. the first column must contain the name of the + \code{\link{modFit}}, i.e. the first column called "name" must contain the name of the observed variable for each data point. The second column must contain the times of observation, named "time". The third column must be named "value" and contain the observed values. Optionally, a further column can contain diff --git a/man/mkinresplot.Rd b/man/mkinresplot.Rd index 0b48692..8e3f18a 100644 --- a/man/mkinresplot.Rd +++ b/man/mkinresplot.Rd @@ -9,7 +9,7 @@ }
\usage{
mkinresplot(object, obs_vars = vector(),
- xlab = "Time [days]", ylab = "Residual [\% of applied radioactivity]",
+ xlab = "Time", ylab = "Residual",
maxabs = "auto", legend = TRUE, lpos = "topright", ...)
}
\arguments{
diff --git a/man/plot.mkinfit.Rd b/man/plot.mkinfit.Rd index 01b8cec..56ee551 100644 --- a/man/plot.mkinfit.Rd +++ b/man/plot.mkinfit.Rd @@ -10,7 +10,7 @@ } \usage{ \method{plot}{mkinfit}(x, fit = x, xlab = "Time", ylab = "Observed", - xlim = range(fit$data$time), ylim = range(fit$data$observed, na.rm = TRUE), + xlim = range(fit$data$time), ylim = c(0, max(fit$data$observed, na.rm = TRUE)), col_obs = 1:length(fit$mkinmod$map), pch_obs = col_obs, lty_obs = 1, add = FALSE, legend = !add, ...) } diff --git a/vignettes/examples-L1_SFO_plot.pdf b/vignettes/examples-L1_SFO_plot.pdf Binary files differnew file mode 100644 index 0000000..d4f8834 --- /dev/null +++ b/vignettes/examples-L1_SFO_plot.pdf diff --git a/vignettes/examples-L1_SFO_plots.pdf b/vignettes/examples-L1_SFO_plots.pdf Binary files differnew file mode 100644 index 0000000..d34116f --- /dev/null +++ b/vignettes/examples-L1_SFO_plots.pdf diff --git a/vignettes/examples-L1_SFO_residuals.pdf b/vignettes/examples-L1_SFO_residuals.pdf Binary files differnew file mode 100644 index 0000000..35907df --- /dev/null +++ b/vignettes/examples-L1_SFO_residuals.pdf diff --git a/vignettes/examples-L2_DFOP.pdf b/vignettes/examples-L2_DFOP.pdf Binary files differnew file mode 100644 index 0000000..8bbfdf6 --- /dev/null +++ b/vignettes/examples-L2_DFOP.pdf diff --git a/vignettes/examples-L2_DFOP_2.pdf b/vignettes/examples-L2_DFOP_2.pdf Binary files differnew file mode 100644 index 0000000..3437f5d --- /dev/null +++ b/vignettes/examples-L2_DFOP_2.pdf diff --git a/vignettes/examples-L2_FOMC.pdf b/vignettes/examples-L2_FOMC.pdf Binary files differnew file mode 100644 index 0000000..763d617 --- /dev/null +++ b/vignettes/examples-L2_FOMC.pdf diff --git a/vignettes/examples-L2_SFO_plot.pdf b/vignettes/examples-L2_SFO_plot.pdf Binary files differnew file mode 100644 index 0000000..c8831b9 --- /dev/null +++ b/vignettes/examples-L2_SFO_plot.pdf diff --git a/vignettes/examples-L2_SFO_residuals.pdf b/vignettes/examples-L2_SFO_residuals.pdf Binary files differnew file mode 100644 index 0000000..d56b0d1 --- /dev/null +++ b/vignettes/examples-L2_SFO_residuals.pdf diff --git a/vignettes/examples-L3_DFOP.pdf b/vignettes/examples-L3_DFOP.pdf Binary files differnew file mode 100644 index 0000000..c747d79 --- /dev/null +++ b/vignettes/examples-L3_DFOP.pdf diff --git a/vignettes/examples-L3_FOMC.pdf b/vignettes/examples-L3_FOMC.pdf Binary files differnew file mode 100644 index 0000000..322dbeb --- /dev/null +++ b/vignettes/examples-L3_FOMC.pdf diff --git a/vignettes/examples-L3_SFO.pdf b/vignettes/examples-L3_SFO.pdf Binary files differnew file mode 100644 index 0000000..7057333 --- /dev/null +++ b/vignettes/examples-L3_SFO.pdf diff --git a/vignettes/examples-L4_FOMC.pdf b/vignettes/examples-L4_FOMC.pdf Binary files differnew file mode 100644 index 0000000..3f164e7 --- /dev/null +++ b/vignettes/examples-L4_FOMC.pdf diff --git a/vignettes/examples-L4_SFO.pdf b/vignettes/examples-L4_SFO.pdf Binary files differnew file mode 100644 index 0000000..42cdf34 --- /dev/null +++ b/vignettes/examples-L4_SFO.pdf diff --git a/vignettes/examples.Rnw b/vignettes/examples.Rnw new file mode 100644 index 0000000..24e1b57 --- /dev/null +++ b/vignettes/examples.Rnw @@ -0,0 +1,289 @@ +% $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},
+}
+\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{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
+
+<<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 \Robject{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>>=
+plot(m.L1.SFO)
+@
+
+The residual plot can be easily obtained by
+
+<<L1_SFO_residuals, fig=TRUE, echo=TRUE>>=
+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)
+s.m.L1.FOMC <- summary(m.L1.FOMC)
+s.m.L1.FOMC$errmin
+@
+
+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
+
+<<FOCUS_2006_L2_data, echo=TRUE, eval=TRUE>>=
+library("mkin")
+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>>=
+plot(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.
+
+<<L2_SFO_residuals, fig=TRUE, echo=TRUE>>=
+mkinresplot(m.L2.SFO, ylab = "Observed", xlab = "Time")
+@
+
+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.
+
+<<L2_FOMC, echo=TRUE, fig=TRUE>>=
+m.L2.FOMC <- mkinfit(FOMC, FOCUS_2006_L2_mkin, quiet=TRUE)
+plot(m.L2.FOMC)
+s.m.L2.FOMC <- summary(m.L2.FOMC)
+s.m.L2.FOMC$errmin
+@
+
+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.
+
+<<L2_DFOP, echo=TRUE, fig=TRUE>>=
+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>>=
+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)
+s.m.L2.DFOP <- summary(m.L2.DFOP)
+s.m.L2.DFOP$errmin
+@
+
+Therefore, the FOMC model is clearly the best-fit model based on the
+$\chi^2$ error level criterion.
+
+\subsection{Laboratory Data L3}
+
+The following code defines example dataset L3 from the FOCUS kinetics
+report, p. 290
+
+<<FOCUS_2006_L3_data, echo=TRUE, eval=TRUE>>=
+library("mkin")
+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>>=
+m.L3.SFO <- mkinfit(SFO, FOCUS_2006_L3_mkin, quiet=TRUE)
+summary(m.L3.SFO)
+plot(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>>=
+m.L3.FOMC <- mkinfit(FOMC, FOCUS_2006_L3_mkin, quiet=TRUE)
+plot(m.L3.FOMC)
+s.m.L3.FOMC <- summary(m.L3.FOMC)
+s.m.L3.FOMC$errmin
+endpoints(m.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:
+
+<<L3_DFOP, echo=TRUE, fig=TRUE>>=
+m.L3.DFOP <- mkinfit(DFOP, FOCUS_2006_L3_mkin, quiet=TRUE)
+plot(m.L3.DFOP)
+s.m.L3.DFOP <- summary(m.L3.DFOP)
+s.m.L3.DFOP$errmin
+@
+
+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
+
+<<FOCUS_2006_L4_data, echo=TRUE, eval=TRUE>>=
+library("mkin")
+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>>=
+m.L4.SFO <- mkinfit(SFO, FOCUS_2006_L4_mkin, quiet=TRUE)
+summary(m.L4.SFO)
+plot(m.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
+
+<<L4_FOMC, echo=TRUE, fig=TRUE>>=
+m.L4.FOMC <- mkinfit(FOMC, FOCUS_2006_L4_mkin, quiet=TRUE)
+plot(m.L4.FOMC)
+s.m.L4.FOMC <- summary(m.L4.FOMC)
+s.m.L4.FOMC$errmin
+@
+
+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.aux b/vignettes/examples.aux new file mode 100644 index 0000000..3770338 --- /dev/null +++ b/vignettes/examples.aux @@ -0,0 +1,29 @@ +\relax +\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} +\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined +\global\let\oldcontentsline\contentsline +\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} +\global\let\oldnewlabel\newlabel +\gdef\newlabel#1#2{\newlabelxx{#1}#2} +\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} +\AtEndDocument{\ifx\hyper@anchor\@undefined +\let\contentsline\oldcontentsline +\let\newlabel\oldnewlabel +\fi} +\fi} +\global\let\hyper@last\relax +\gdef\HyperFirstAtBeginDocument#1{#1} +\providecommand\HyField@AuxAddToFields[1]{} +\citation{pkg:kinfit} +\citation{FOCUS2006,FOCUSkinetics2011} +\@writefile{toc}{\contentsline {section}{\numberline {1}Kinetic evaluations for parent compounds}{1}{section.1}} +\newlabel{intro}{{1}{1}{Kinetic evaluations for parent compounds\relax }{section.1}{}} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Laboratory Data L1}{1}{subsection.1.1}} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Laboratory Data L2}{6}{subsection.1.2}} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.3}Laboratory Data L3}{14}{subsection.1.3}} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.4}Laboratory Data L4}{20}{subsection.1.4}} +\bibstyle{plainnat} +\bibdata{references} +\bibcite{FOCUS2006}{{1}{2006}{{FOCUS Work Group on Degradation Kinetics}}{{}}} +\bibcite{FOCUSkinetics2011}{{2}{2011}{{FOCUS Work Group on Degradation Kinetics}}{{}}} +\bibcite{pkg:kinfit}{{3}{2012}{{Ranke}}{{}}} diff --git a/vignettes/examples.bbl b/vignettes/examples.bbl new file mode 100644 index 0000000..3f240cf --- /dev/null +++ b/vignettes/examples.bbl @@ -0,0 +1,29 @@ +\begin{thebibliography}{3} +\providecommand{\natexlab}[1]{#1} +\providecommand{\url}[1]{\texttt{#1}} +\expandafter\ifx\csname urlstyle\endcsname\relax + \providecommand{\doi}[1]{doi: #1}\else + \providecommand{\doi}{doi: \begingroup \urlstyle{rm}\Url}\fi + +\bibitem[{FOCUS Work Group on Degradation Kinetics}(2006)]{FOCUS2006} +{FOCUS Work Group on Degradation Kinetics}. +\newblock \emph{Guidance Document on Estimating Persistence and Degradation + Kinetics from Environmental Fate Studies on Pesticides in EU Registration. + Report of the FOCUS Work Group on Degradation Kinetics}, 2006. +\newblock URL \url{http://focus.jrc.ec.europa.eu/dk}. +\newblock EC Document Reference Sanco/10058/2005 version 2.0. + +\bibitem[{FOCUS Work Group on Degradation Kinetics}(2011)]{FOCUSkinetics2011} +{FOCUS Work Group on Degradation Kinetics}. +\newblock \emph{Generic guidance for estimating persistence and degradation + kinetics from environmental fate studies on pesticides in EU registration}, + 1.0 edition, November 2011. +\newblock URL \url{http://focus.jrc.ec.europa.eu/dk}. + +\bibitem[Ranke(2012)]{pkg:kinfit} +Johannes Ranke. +\newblock \emph{kinfit: {R}outines for fitting simple kinetic models to + chemical degradation data}, 2012. +\newblock URL \url{http://CRAN.R-project.org}. + +\end{thebibliography} diff --git a/vignettes/examples.blg b/vignettes/examples.blg new file mode 100644 index 0000000..61ca3d2 --- /dev/null +++ b/vignettes/examples.blg @@ -0,0 +1,46 @@ +This is BibTeX, Version 0.99d (TeX Live 2012/Debian) +Capacity: max_strings=35307, hash_size=35307, hash_prime=30011 +The top-level auxiliary file: examples.aux +The style file: plainnat.bst +Database file #1: references.bib +You've used 3 entries, + 2773 wiz_defined-function locations, + 609 strings with 5481 characters, +and the built_in function-call counts, 895 in all, are: += -- 82 +> -- 30 +< -- 3 ++ -- 12 +- -- 9 +* -- 57 +:= -- 151 +add.period$ -- 10 +call.type$ -- 3 +change.case$ -- 10 +chr.to.int$ -- 3 +cite$ -- 6 +duplicate$ -- 51 +empty$ -- 76 +format.name$ -- 12 +if$ -- 173 +int.to.chr$ -- 1 +int.to.str$ -- 1 +missing$ -- 0 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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 differnew file mode 100644 index 0000000..be0d96e --- /dev/null +++ b/vignettes/examples.pdf diff --git a/vignettes/examples.tex b/vignettes/examples.tex new file mode 100644 index 0000000..4f59aa2 --- /dev/null +++ b/vignettes/examples.tex @@ -0,0 +1,700 @@ +% $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 new file mode 100644 index 0000000..f25aa62 --- /dev/null +++ b/vignettes/examples.toc @@ -0,0 +1,5 @@ +\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} |