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-%\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}
-\usepackage[utf8]{inputenc}
-\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
-Wissenschaftlicher Berater\\
-Kronacher Str. 8, 79639 Grenzach-Wyhlen, Germany\\[0.5cm]
-and\\[0.5cm]
-Privatdozent at the 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{rcore2014} 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 transformation products, commonly termed metabolites, and to more than one
-compartment. It is also possible to include back reactions, so equilibrium reactions
-and equilibrium partitioning can be specified, although this oftentimes leads 
-to an overparameterisation of the model.
-
-When mkin was first published in May 2010, the most commonly used tools
-for fitting more complex kinetic degradation models to experimental data were KinGUI
-\citep{schaefer2007}, a MATLAB$^\circledR$ based tool with a graphical user
-interface that was specifically tailored to the task and included some output
-as proposed by the FOCUS Kinetics Workgroup, and ModelMaker, a general purpose
-compartment based tool providing infrastructure for fitting dynamic simulation
-models based on differential equations to data.
-
-At that time, the R package \Rpackage{FME} (Flexible Modelling Environment) 
-\citep{soetaert2010} was already available, and provided a good basis for
-developing a package specifically tailored to the task. The remaining challenge
-was to make it as easy as possible for the users (including the author of this
-vignette) to specify the system of differential equations and to include the
-output requested by the FOCUS guidance, such as the relative standard deviation
-that has to be assumed for the residuals, such that the $\chi^2$
-goodness-of-fit test as defined by the FOCUS kinetics workgroup would pass
-using an significance level $\alpha$ of 0.05.
-
-Also, mkin introduced using analytical solutions for parent only kinetics for
-improved optimization speed. Later, Eigenvalue based solutions were
-introduced to mkin for the case of linear differential equations (\textit{i.e.}
-where the FOMC or DFOP models were not used for the parent compound), greatly
-improving the optimization speed for these cases.
-
-Soon after the publication of mkin, two derived tools were published, namely
-KinGUII (available from Bayer Crop Science) and CAKE (commissioned to Tessella
-by Syngenta), which added a graphical user interface (GUI), and added fitting by
-iteratively reweighted least squares (IRLS) and characterisation of likely
-parameter distributions by Markov Chain Monte Carlo (MCMC) sampling.
-
-CAKE focuses on a smooth use experience, sacrificing some flexibility in the model
-definition, allowing only two primary metabolites in parallel. KinGUI offers
-quite a flexible widget for specifying complex kinetic models. Back-reactions
-(non-instanteneous equilibria) were not present in the first version of
-KinGUII, and only simple first-order models could be specified for
-transformation products.  As of May 2014 (KinGUII version 2.1), back-reactions
-and biphasic modelling of metabolites are also available in KinGUII.
-
-Currently (May 2014), the main feature available in \Rpackage{mkin} which is
-not present in KinGUII or CAKE, is the estimation of parameter confidence
-intervals based on transformed parameters. For rate constants, the log
-transformation is used, as proposed by Bates and Watts \citep[p. 77, p.
-149]{bates1988}. Approximate intervals are constructed for the transformed rate
-constants \citep[compare][p. 153]{bates1988}, \textit{i.e.} for their logarithms.
-Confidence intervals for the rate constants are then obtained using the
-appropriate backtransformation using the exponential function.
-
-In the first version of \Rpackage{mkin} allowing for specifying models using 
-formation fractions, a home-made reparameterisation was used in order to ensure
-that the sum of formation fractions would not exceed unity. 
-
-This method is still used in the current version of KinGUII (v2.1), with a
-modification that allows for fixing the pathway to sink to zero. CAKE uses
-penalties in the objective function in order to enforce this constraint.
-
-In 2012, an alternative reparameterisation of the formation fractions was
-proposed together with René Lehmann \citep{ranke2012}, based on isometric
-logratio transformation (ILR). The aim was to improve the validity of the
-linear approximation of the objective function during the parameter
-estimation procedure as well as in the subsequent calculation of parameter
-confidence intervals.
-
-In the first attempt at providing improved parameter confidence intervals
-introduced to \Rpackage{mkin} in 2013, confidence intervals obtained from 
-FME on the transformed parameters were simply all backtransformed one by one
-to yield asymetric confidence intervals for the backtransformed parameters.
-
-However, while there is a 1:1 relation between the rate constants in the model
-and the transformed parameters fitted in the model, the parameters obtained by the
-isometric logratio transformation are calculated from the set of formation
-fractions that quantify the paths to each of the compounds formed from a
-specific parent compound, and no such 1:1 relation exists.
-
-Therefore, parameter confidence intervals for formation fractions obtained with
-this method only appear valid for the case of a single transformation product, where 
-only one formation fraction is to be estimated, directly corresponding to one
-component of the ilr transformed parameter.
-
-The confidence intervals obtained by backtransformation for the cases where a 
-1:1 relation between transformed and original parameter exist are considered by 
-the author of this vignette to be more accurate than those obtained using a
-re-estimation of the Hessian matrix after backtransformation, as implemented 
-in the FME package.
-
-\bibliographystyle{plainnat}
-\bibliography{references}
-
-\end{document}
-% vim: set foldmethod=syntax: