diff options
Diffstat (limited to 'vignettes')
| -rw-r--r-- | vignettes/header.tex | 1 | ||||
| -rw-r--r-- | vignettes/mkin.Rnw | 95 | ||||
| -rw-r--r-- | vignettes/mkin.pdf | bin | 124442 -> 160326 bytes | |||
| -rw-r--r-- | vignettes/references.bib | 35 |
4 files changed, 112 insertions, 19 deletions
diff --git a/vignettes/header.tex b/vignettes/header.tex index 476415e5..e0775d34 100644 --- a/vignettes/header.tex +++ b/vignettes/header.tex @@ -8,7 +8,6 @@ \usepackage[round]{natbib}
\usepackage{amstext}
\usepackage{hyperref}
-\usepackage[utf8]{inputenc}
\newcommand{\Rpackage}[1]{{\normalfont\fontseries{b}\selectfont #1}}
\newcommand{\Robject}[1]{\texttt{#1}}
diff --git a/vignettes/mkin.Rnw b/vignettes/mkin.Rnw index 0ac114ed..1befe009 100644 --- a/vignettes/mkin.Rnw +++ b/vignettes/mkin.Rnw @@ -2,6 +2,7 @@ %\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}, @@ -29,7 +30,7 @@ chemical degradation data} Wissenschaftlicher Berater\\ Kronacher Str. 8, 79639 Grenzach-Wyhlen, Germany\\[0.5cm] and\\[0.5cm] -University of Bremen\\ +Privatdozent at the University of Bremen\\ } \maketitle @@ -58,14 +59,100 @@ metabolites. 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 +\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 metabolites and more than one compartment and includes the possibility -for back reactions. +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} diff --git a/vignettes/mkin.pdf b/vignettes/mkin.pdf Binary files differindex 0e4d1be8..12293506 100644 --- a/vignettes/mkin.pdf +++ b/vignettes/mkin.pdf diff --git a/vignettes/references.bib b/vignettes/references.bib index e069daf2..88caea60 100644 --- a/vignettes/references.bib +++ b/vignettes/references.bib @@ -1,7 +1,7 @@ % This file was originally created with JabRef 2.7b. % Encoding: ISO8859_1 -@BOOK{bates88, +@BOOK{bates1988, title = {Nonlinear regression and its applications}, publisher = {Wiley-Interscience}, year = {1988}, @@ -29,12 +29,12 @@ url = {http://focus.jrc.ec.europa.eu/dk} } -@MANUAL{rcore2013, +@MANUAL{rcore2014, title = {\textsf{R}: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, - year = {2013}, + year = {2014}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org} } @@ -52,21 +52,20 @@ variables to chemical degradation data}, author = {Johannes Ranke}, year = {2013}, - url = {http://CRAN.R-project.org/package/kinfit} + url = {http://CRAN.R-project.org/package=mkin} } -@INPROCEEDINGS{schaefer2007, - author = {D. Sch\"{a}fer and M. Mikolasch and P. Rainbird and B. Harvey}, - title = {{KinGUI}: a new kinetic software tool for evaluations according to - FOCUS degradation kinetics}, - booktitle = {Proceedings of the XIII Symposium Pesticide Chemistry}, - year = {2007}, - editor = {Del Re A. A. M. and Capri E. and Fragoulis G. and Trevisan M.}, - pages = {916--923}, - address = {Piacenza} +@Inproceedings{ schaefer2007, + title = {{KinGUI}: a new kinetic software tool for evaluations according to {FOCUS} degradation kinetics}, + author = {D. Sch\"{a}fer and B. Mikolasch and P. Rainbird and B. Harvey}, + booktitle = {Proceedings of the XIII Symposium Pesticide Chemistry}, + editor = {Del Re A. A. M. and Capri E. and Fragoulis G. and Trevisan M.}, + year = {2007}, + address = {Piacenza}, + pages = {916--923} } -@ARTICLE{soetaert10, +@ARTICLE{soetaert2010, author = {Karline Soetaert and Thomas Petzoldt}, title = {Inverse Modelling, Sensitivity and Monte Carlo Analysis in {R} Using Package {FME}}, @@ -77,3 +76,11 @@ number = {3}, url = {http://www.jstatsoft.org/v33/i03/} } + +@Inproceedings{ ranke2012, + title = {Parameter reliability in kinetic evaluation of environmental metabolism data - Assessment and the influence of model specification}, + author = {J. Ranke and R. Lehmann}, + booktitle = {SETAC World 20-24 May}, + year = {2012}, + address = {Berlin} +} |