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-%\VignetteIndexEntry{Example evaluation of FOCUS dataset Z}
-%\VignetteEngine{knitr::knitr}
-\documentclass[12pt,a4paper]{article}\usepackage[]{graphicx}\usepackage[]{color}
-%% maxwidth is the original width if it is less than linewidth
-%% otherwise use linewidth (to make sure the graphics do not exceed the margin)
-\makeatletter
-\def\maxwidth{ %
-  \ifdim\Gin@nat@width>\linewidth
-    \linewidth
-  \else
-    \Gin@nat@width
-  \fi
-}
-\makeatother
-
-\definecolor{fgcolor}{rgb}{0.345, 0.345, 0.345}
-\newcommand{\hlnum}[1]{\textcolor[rgb]{0.686,0.059,0.569}{#1}}%
-\newcommand{\hlstr}[1]{\textcolor[rgb]{0.192,0.494,0.8}{#1}}%
-\newcommand{\hlcom}[1]{\textcolor[rgb]{0.678,0.584,0.686}{\textit{#1}}}%
-\newcommand{\hlopt}[1]{\textcolor[rgb]{0,0,0}{#1}}%
-\newcommand{\hlstd}[1]{\textcolor[rgb]{0.345,0.345,0.345}{#1}}%
-\newcommand{\hlkwa}[1]{\textcolor[rgb]{0.161,0.373,0.58}{\textbf{#1}}}%
-\newcommand{\hlkwb}[1]{\textcolor[rgb]{0.69,0.353,0.396}{#1}}%
-\newcommand{\hlkwc}[1]{\textcolor[rgb]{0.333,0.667,0.333}{#1}}%
-\newcommand{\hlkwd}[1]{\textcolor[rgb]{0.737,0.353,0.396}{\textbf{#1}}}%
-\let\hlipl\hlkwb
-
-\usepackage{framed}
-\makeatletter
-\newenvironment{kframe}{%
- \def\at@end@of@kframe{}%
- \ifinner\ifhmode%
-  \def\at@end@of@kframe{\end{minipage}}%
-  \begin{minipage}{\columnwidth}%
- \fi\fi%
- \def\FrameCommand##1{\hskip\@totalleftmargin \hskip-\fboxsep
- \colorbox{shadecolor}{##1}\hskip-\fboxsep
-     % There is no \\@totalrightmargin, so:
-     \hskip-\linewidth \hskip-\@totalleftmargin \hskip\columnwidth}%
- \MakeFramed {\advance\hsize-\width
-   \@totalleftmargin\z@ \linewidth\hsize
-   \@setminipage}}%
- {\par\unskip\endMakeFramed%
- \at@end@of@kframe}
-\makeatother
-
-\definecolor{shadecolor}{rgb}{.97, .97, .97}
-\definecolor{messagecolor}{rgb}{0, 0, 0}
-\definecolor{warningcolor}{rgb}{1, 0, 1}
-\definecolor{errorcolor}{rgb}{1, 0, 0}
-\newenvironment{knitrout}{}{} % an empty environment to be redefined in TeX
-
-\usepackage{alltt}
-\usepackage{a4wide}
-\input{header}
-\hypersetup{  
-  pdftitle = {Example evaluation of FOCUS dataset Z},
-  pdfsubject = {Manuscript},
-  pdfauthor = {Johannes Ranke},
-  colorlinks = {true},
-  linkcolor = {blue},
-  citecolor = {blue},
-  urlcolor = {red},
-  hyperindex = {true},
-  linktocpage = {true},
-}
-\IfFileExists{upquote.sty}{\usepackage{upquote}}{}
-\begin{document}
-
-
-
-\title{Example evaluation of FOCUS dataset Z}
-\author{\textbf{Johannes Ranke} \\[0.5cm]
-%EndAName
-Wissenschaftlicher Berater\\
-Kronacher Str. 8, 79639 Grenzach-Wyhlen, Germany\\[0.5cm]
-and\\[0.5cm]
-University of Bremen\\
-}
-\maketitle
-
-\thispagestyle{empty} \setcounter{page}{0}
-
-\clearpage
-
-\tableofcontents
-
-\textbf{Key words}: Kinetics, FOCUS, nonlinear optimisation
-
-\section{The data}
-
-The following code defines the example dataset from Appendix 7 to the FOCUS kinetics
-report \citep{FOCUSkinetics2011}, p.350.
-
-\begin{knitrout}
-\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe}
-\begin{alltt}
-\hlkwd{require}\hlstd{(mkin)}
-\end{alltt}
-
-
-{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Loading required package: mkin}}
-
-{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Loading required package: minpack.lm}}
-
-{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Loading required package: rootSolve}}
-
-{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Loading required package: inline}}
-
-{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Loading required package: methods}}
-
-{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Loading required package: parallel}}\begin{alltt}
-\hlstd{LOD} \hlkwb{=} \hlnum{0.5}
-\hlstd{FOCUS_2006_Z} \hlkwb{=} \hlkwd{data.frame}\hlstd{(}
-  \hlkwc{t} \hlstd{=} \hlkwd{c}\hlstd{(}\hlnum{0}\hlstd{,} \hlnum{0.04}\hlstd{,} \hlnum{0.125}\hlstd{,} \hlnum{0.29}\hlstd{,} \hlnum{0.54}\hlstd{,} \hlnum{1}\hlstd{,} \hlnum{2}\hlstd{,} \hlnum{3}\hlstd{,} \hlnum{4}\hlstd{,} \hlnum{7}\hlstd{,} \hlnum{10}\hlstd{,} \hlnum{14}\hlstd{,} \hlnum{21}\hlstd{,}
-        \hlnum{42}\hlstd{,} \hlnum{61}\hlstd{,} \hlnum{96}\hlstd{,} \hlnum{124}\hlstd{),}
-  \hlkwc{Z0} \hlstd{=} \hlkwd{c}\hlstd{(}\hlnum{100}\hlstd{,} \hlnum{81.7}\hlstd{,} \hlnum{70.4}\hlstd{,} \hlnum{51.1}\hlstd{,} \hlnum{41.2}\hlstd{,} \hlnum{6.6}\hlstd{,} \hlnum{4.6}\hlstd{,} \hlnum{3.9}\hlstd{,} \hlnum{4.6}\hlstd{,} \hlnum{4.3}\hlstd{,} \hlnum{6.8}\hlstd{,}
-         \hlnum{2.9}\hlstd{,} \hlnum{3.5}\hlstd{,} \hlnum{5.3}\hlstd{,} \hlnum{4.4}\hlstd{,} \hlnum{1.2}\hlstd{,} \hlnum{0.7}\hlstd{),}
-  \hlkwc{Z1} \hlstd{=} \hlkwd{c}\hlstd{(}\hlnum{0}\hlstd{,} \hlnum{18.3}\hlstd{,} \hlnum{29.6}\hlstd{,} \hlnum{46.3}\hlstd{,} \hlnum{55.1}\hlstd{,} \hlnum{65.7}\hlstd{,} \hlnum{39.1}\hlstd{,} \hlnum{36}\hlstd{,} \hlnum{15.3}\hlstd{,} \hlnum{5.6}\hlstd{,} \hlnum{1.1}\hlstd{,}
-         \hlnum{1.6}\hlstd{,} \hlnum{0.6}\hlstd{,} \hlnum{0.5} \hlopt{*} \hlstd{LOD,} \hlnum{NA}\hlstd{,} \hlnum{NA}\hlstd{,} \hlnum{NA}\hlstd{),}
-  \hlkwc{Z2} \hlstd{=} \hlkwd{c}\hlstd{(}\hlnum{0}\hlstd{,} \hlnum{NA}\hlstd{,} \hlnum{0.5} \hlopt{*} \hlstd{LOD,} \hlnum{2.6}\hlstd{,} \hlnum{3.8}\hlstd{,} \hlnum{15.3}\hlstd{,} \hlnum{37.2}\hlstd{,} \hlnum{31.7}\hlstd{,} \hlnum{35.6}\hlstd{,} \hlnum{14.5}\hlstd{,}
-         \hlnum{0.8}\hlstd{,} \hlnum{2.1}\hlstd{,} \hlnum{1.9}\hlstd{,} \hlnum{0.5} \hlopt{*} \hlstd{LOD,} \hlnum{NA}\hlstd{,} \hlnum{NA}\hlstd{,} \hlnum{NA}\hlstd{),}
-  \hlkwc{Z3} \hlstd{=} \hlkwd{c}\hlstd{(}\hlnum{0}\hlstd{,} \hlnum{NA}\hlstd{,} \hlnum{NA}\hlstd{,} \hlnum{NA}\hlstd{,} \hlnum{NA}\hlstd{,} \hlnum{0.5} \hlopt{*} \hlstd{LOD,} \hlnum{9.2}\hlstd{,} \hlnum{13.1}\hlstd{,} \hlnum{22.3}\hlstd{,} \hlnum{28.4}\hlstd{,} \hlnum{32.5}\hlstd{,}
-         \hlnum{25.2}\hlstd{,} \hlnum{17.2}\hlstd{,} \hlnum{4.8}\hlstd{,} \hlnum{4.5}\hlstd{,} \hlnum{2.8}\hlstd{,} \hlnum{4.4}\hlstd{))}
-
-\hlstd{FOCUS_2006_Z_mkin} \hlkwb{<-} \hlkwd{mkin_wide_to_long}\hlstd{(FOCUS_2006_Z)}
-\end{alltt}
-\end{kframe}
-\end{knitrout}
-
-\section{Parent compound and one metabolite}
-
-The next step is to set up the models used for the kinetic analysis. As the 
-simultaneous fit of parent and the first metabolite is usually straightforward,
-Step 1 (SFO for parent only) is skipped here. We start with the model 2a, 
-with formation and decline of metabolite Z1 and the pathway from parent
-directly to sink included (default in mkin).
-
-\begin{knitrout}
-\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe}
-\begin{alltt}
-\hlstd{Z.2a} \hlkwb{<-} \hlkwd{mkinmod}\hlstd{(}\hlkwc{Z0} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z1"}\hlstd{),}
-                \hlkwc{Z1} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{))}
-\end{alltt}
-\begin{verbatim}
-## make[1]: warning: jobserver unavailable: using -j1.  Add '+' to parent make rule.
-\end{verbatim}
-
-
-{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Successfully compiled differential equation model from auto-generated C code.}}\begin{alltt}
-\hlstd{m.Z.2a} \hlkwb{<-} \hlkwd{mkinfit}\hlstd{(Z.2a, FOCUS_2006_Z_mkin,} \hlkwc{quiet} \hlstd{=} \hlnum{TRUE}\hlstd{)}
-\hlkwd{plot_sep}\hlstd{(m.Z.2a)}
-\end{alltt}
-\end{kframe}
-\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_1-1} 
-\begin{kframe}\begin{alltt}
-\hlkwd{summary}\hlstd{(m.Z.2a,} \hlkwc{data} \hlstd{=} \hlnum{FALSE}\hlstd{)}\hlopt{$}\hlstd{bpar}
-\end{alltt}
-\begin{verbatim}
-##               Estimate se_notrans      t value       Pr(>t)
-## Z0_0      9.701488e+01 3.55313691 2.730401e+01 1.679214e-21
-## k_Z0_sink 1.281376e-11 0.22689470 5.647447e-11 5.000000e-01
-## k_Z0_Z1   2.236006e+00 0.16507604 1.354531e+01 7.396594e-14
-## k_Z1_sink 4.821248e-01 0.06585369 7.321150e+00 3.552015e-08
-##                Lower       Upper
-## Z0_0      91.4058170 102.6239462
-## k_Z0_sink  0.0000000         Inf
-## k_Z0_Z1    1.8419826   2.7143172
-## k_Z1_sink  0.4005856   0.5802613
-\end{verbatim}
-\end{kframe}
-\end{knitrout}
-
-As obvious from the parameter summary (the \texttt{bpar} component of the 
-summary), the kinetic rate constant from parent compound Z to sink
-is negligible. Accordingly, the exact magnitude of the fitted parameter 
-\texttt{log k\_Z0\_sink} is ill-defined and the covariance matrix is not
-returned (not shown, would be visible in the complete summary). 
-This suggests, in agreement with the analysis in the FOCUS kinetics report, to
-simplify the model by removing the pathway to sink.
-
-A similar result can be obtained when formation fractions are used in the model 
-formulation:
-
-\begin{knitrout}
-\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe}
-\begin{alltt}
-\hlstd{Z.2a.ff} \hlkwb{<-} \hlkwd{mkinmod}\hlstd{(}\hlkwc{Z0} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z1"}\hlstd{),}
-                   \hlkwc{Z1} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{),}
-                   \hlkwc{use_of_ff} \hlstd{=} \hlstr{"max"}\hlstd{)}
-\end{alltt}
-\begin{verbatim}
-## make[1]: warning: jobserver unavailable: using -j1.  Add '+' to parent make rule.
-\end{verbatim}
-
-
-{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Successfully compiled differential equation model from auto-generated C code.}}\begin{alltt}
-\hlstd{m.Z.2a.ff} \hlkwb{<-} \hlkwd{mkinfit}\hlstd{(Z.2a.ff, FOCUS_2006_Z_mkin,} \hlkwc{quiet} \hlstd{=} \hlnum{TRUE}\hlstd{)}
-\hlkwd{plot_sep}\hlstd{(m.Z.2a.ff)}
-\end{alltt}
-\end{kframe}
-\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_2-1} 
-\begin{kframe}\begin{alltt}
-\hlkwd{summary}\hlstd{(m.Z.2a.ff,} \hlkwc{data} \hlstd{=} \hlnum{FALSE}\hlstd{)}\hlopt{$}\hlstd{bpar}
-\end{alltt}
-\begin{verbatim}
-##              Estimate se_notrans   t value       Pr(>t)      Lower
-## Z0_0       97.0148812 3.55314944 27.303912 1.679369e-21 91.3287912
-## k_Z0        2.2360064 0.21684747 10.311425 3.661846e-11  1.8052909
-## k_Z1        0.4821248 0.06585372  7.321147 3.552045e-08  0.3996826
-## f_Z0_to_Z1  1.0000000 0.10147342  9.854798 9.707056e-11  0.0000000
-##                  Upper
-## Z0_0       102.7009713
-## k_Z0         2.7694843
-## k_Z1         0.5815722
-## f_Z0_to_Z1   1.0000000
-\end{verbatim}
-\end{kframe}
-\end{knitrout}
-
-Here, the ilr transformed formation fraction fitted in the model takes a very
-large value, and the backtransformed formation fraction from parent Z to Z1 is
-practically unity. Again, the covariance matrix is not returned as the model is
-overparameterised. 
-
-The simplified model is obtained by setting the list component \texttt{sink} to
-\texttt{FALSE}.\footnote{If the model formulation without formation fractions
-is used, the same effect can be obtained by fixing the parameter \texttt{k\_Z\_sink}
-to a value of zero.} 
-
-In the following, we use the parameterisation with formation fractions in order
-to be able to compare with the results in the FOCUS guidance, and as it 
-makes it easier to use parameters obtained in a previous fit when adding a further 
-metabolite.
-
-\begin{knitrout}
-\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe}
-\begin{alltt}
-\hlstd{Z.3} \hlkwb{<-} \hlkwd{mkinmod}\hlstd{(}\hlkwc{Z0} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z1"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),}
-               \hlkwc{Z1} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{),} \hlkwc{use_of_ff} \hlstd{=} \hlstr{"max"}\hlstd{)}
-\end{alltt}
-\begin{verbatim}
-## make[1]: warning: jobserver unavailable: using -j1.  Add '+' to parent make rule.
-\end{verbatim}
-
-
-{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Successfully compiled differential equation model from auto-generated C code.}}\begin{alltt}
-\hlstd{m.Z.3} \hlkwb{<-} \hlkwd{mkinfit}\hlstd{(Z.3, FOCUS_2006_Z_mkin,} \hlkwc{quiet} \hlstd{=} \hlnum{TRUE}\hlstd{)}
-\hlkwd{plot_sep}\hlstd{(m.Z.3)}
-\end{alltt}
-\end{kframe}
-\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_3-1} 
-\begin{kframe}\begin{alltt}
-\hlkwd{summary}\hlstd{(m.Z.3,} \hlkwc{data} \hlstd{=} \hlnum{FALSE}\hlstd{)}\hlopt{$}\hlstd{bpar}
-\end{alltt}
-\begin{verbatim}
-##        Estimate se_notrans  t value       Pr(>t)      Lower
-## Z0_0 97.0148815 2.68177093 36.17568 2.363587e-25 91.5215237
-## k_Z0  2.2360064 0.14686110 15.22531 2.246514e-15  1.9545310
-## k_Z1  0.4821248 0.04268712 11.29439 3.068581e-12  0.4021552
-##            Upper
-## Z0_0 102.5082392
-## k_Z0   2.5580177
-## k_Z1   0.5779966
-\end{verbatim}
-\end{kframe}
-\end{knitrout}
-
-As there is only one transformation product for Z0 and no pathway
-to sink, the formation fraction is internally fixed to unity.
-
-\section{Including metabolites Z2 and Z3}
-
-As suggested in the FOCUS report, the pathway to sink was removed for metabolite Z1 as
-well in the next step. While this step appears questionable on the basis of the above results, it 
-is followed here for the purpose of comparison. Also, in the FOCUS report, it is 
-assumed that there is additional empirical evidence that Z1 quickly and exclusively
-hydrolyses to Z2. 
-
-\begin{knitrout}
-\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe}
-\begin{alltt}
-\hlstd{Z.5} \hlkwb{<-} \hlkwd{mkinmod}\hlstd{(}\hlkwc{Z0} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z1"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),}
-               \hlkwc{Z1} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z2"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),}
-               \hlkwc{Z2} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{),} \hlkwc{use_of_ff} \hlstd{=} \hlstr{"max"}\hlstd{)}
-\end{alltt}
-\begin{verbatim}
-## make[1]: warning: jobserver unavailable: using -j1.  Add '+' to parent make rule.
-\end{verbatim}
-
-
-{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Successfully compiled differential equation model from auto-generated C code.}}\begin{alltt}
-\hlstd{m.Z.5} \hlkwb{<-} \hlkwd{mkinfit}\hlstd{(Z.5, FOCUS_2006_Z_mkin,} \hlkwc{quiet} \hlstd{=} \hlnum{TRUE}\hlstd{)}
-\hlkwd{plot_sep}\hlstd{(m.Z.5)}
-\end{alltt}
-\end{kframe}
-\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_5-1} 
-
-\end{knitrout}
-
-Finally, metabolite Z3 is added to the model. We use the optimised
-differential equation parameter values from the previous fit in order to
-accelerate the optimization.
-
-\begin{knitrout}
-\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe}
-\begin{alltt}
-\hlstd{Z.FOCUS} \hlkwb{<-} \hlkwd{mkinmod}\hlstd{(}\hlkwc{Z0} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z1"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),}
-                   \hlkwc{Z1} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z2"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),}
-                   \hlkwc{Z2} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z3"}\hlstd{),}
-                   \hlkwc{Z3} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{),}
-                   \hlkwc{use_of_ff} \hlstd{=} \hlstr{"max"}\hlstd{)}
-\end{alltt}
-\begin{verbatim}
-## make[1]: warning: jobserver unavailable: using -j1.  Add '+' to parent make rule.
-\end{verbatim}
-
-
-{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Successfully compiled differential equation model from auto-generated C code.}}\begin{alltt}
-\hlstd{m.Z.FOCUS} \hlkwb{<-} \hlkwd{mkinfit}\hlstd{(Z.FOCUS, FOCUS_2006_Z_mkin,}
-                     \hlkwc{parms.ini} \hlstd{= m.Z.5}\hlopt{$}\hlstd{bparms.ode,}
-                     \hlkwc{quiet} \hlstd{=} \hlnum{TRUE}\hlstd{)}
-\hlkwd{plot_sep}\hlstd{(m.Z.FOCUS)}
-\end{alltt}
-\end{kframe}
-\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_6-1} 
-\begin{kframe}\begin{alltt}
-\hlkwd{summary}\hlstd{(m.Z.FOCUS,} \hlkwc{data} \hlstd{=} \hlnum{FALSE}\hlstd{)}\hlopt{$}\hlstd{bpar}
-\end{alltt}
-\begin{verbatim}
-##               Estimate se_notrans   t value       Pr(>t)       Lower
-## Z0_0       96.83849566 2.05886133 47.034977 5.583742e-44 92.70517559
-## k_Z0        2.21540897 0.11813046 18.753919 7.744034e-25  1.99051134
-## k_Z1        0.47829896 0.02928763 16.331089 3.333376e-22  0.42297603
-## k_Z2        0.45161653 0.04421268 10.214638 3.110936e-14  0.37103495
-## k_Z3        0.05869343 0.01429485  4.105914 7.285393e-05  0.03599566
-## f_Z2_to_Z3  0.47150952 0.05705233  8.264510 2.809889e-11  0.36038193
-##                   Upper
-## Z0_0       100.97181573
-## k_Z0         2.46571661
-## k_Z1         0.54085782
-## k_Z2         0.54969886
-## k_Z3         0.09570371
-## f_Z2_to_Z3   0.58553462
-\end{verbatim}
-\begin{alltt}
-\hlkwd{endpoints}\hlstd{(m.Z.FOCUS)}
-\end{alltt}
-\begin{verbatim}
-## $ff
-##     Z2_Z3   Z2_sink 
-## 0.4715095 0.5284905 
-## 
-## $SFORB
-## logical(0)
-## 
-## $distimes
-##          DT50      DT90
-## Z0  0.3128755  1.039350
-## Z1  1.4491923  4.814113
-## Z2  1.5348136  5.098540
-## Z3 11.8096217 39.230714
-\end{verbatim}
-\end{kframe}
-\end{knitrout}
-
-This fit corresponds to the final result chosen in Appendix 7 of the FOCUS
-report. Confidence intervals returned by mkin are based on internally
-transformed parameters, however.
-
-\section{Using the SFORB model for parent and metabolites}
-
-As the FOCUS report states, there is a certain tailing of the time course of metabolite 
-Z3. Also, the time course of the parent compound is not fitted very well using the 
-SFO model, as residues at a certain low level remain.
-
-Therefore, an additional model is offered here, using the single first-order 
-reversible binding (SFORB) model for metabolite Z3. As expected, the $\chi^2$
-error level is lower for metabolite Z3 using this model and the graphical 
-fit for Z3 is improved. However, the covariance matrix is not returned.
-
-\begin{knitrout}
-\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe}
-\begin{alltt}
-\hlstd{Z.mkin.1} \hlkwb{<-} \hlkwd{mkinmod}\hlstd{(}\hlkwc{Z0} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z1"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),}
-                    \hlkwc{Z1} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z2"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),}
-                    \hlkwc{Z2} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z3"}\hlstd{),}
-                    \hlkwc{Z3} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFORB"}\hlstd{))}
-\end{alltt}
-\begin{verbatim}
-## make[1]: warning: jobserver unavailable: using -j1.  Add '+' to parent make rule.
-\end{verbatim}
-
-
-{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Successfully compiled differential equation model from auto-generated C code.}}\begin{alltt}
-\hlstd{m.Z.mkin.1} \hlkwb{<-} \hlkwd{mkinfit}\hlstd{(Z.mkin.1, FOCUS_2006_Z_mkin,} \hlkwc{quiet} \hlstd{=} \hlnum{TRUE}\hlstd{)}
-\hlkwd{plot_sep}\hlstd{(m.Z.mkin.1)}
-\end{alltt}
-\end{kframe}
-\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_7-1} 
-\begin{kframe}\begin{alltt}
-\hlkwd{summary}\hlstd{(m.Z.mkin.1,} \hlkwc{data} \hlstd{=} \hlnum{FALSE}\hlstd{)}\hlopt{$}\hlstd{cov.unscaled}
-\end{alltt}
-\begin{verbatim}
-## NULL
-\end{verbatim}
-\end{kframe}
-\end{knitrout}
-
-Therefore, a further stepwise model building is performed starting from the
-stage of parent and two metabolites, starting from the assumption that the model
-fit for the parent compound can be improved by using the SFORB model.
-
-\begin{knitrout}
-\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe}
-\begin{alltt}
-\hlstd{Z.mkin.3} \hlkwb{<-} \hlkwd{mkinmod}\hlstd{(}\hlkwc{Z0} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFORB"}\hlstd{,} \hlstr{"Z1"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),}
-                    \hlkwc{Z1} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z2"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),}
-                    \hlkwc{Z2} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{))}
-\end{alltt}
-\begin{verbatim}
-## make[1]: warning: jobserver unavailable: using -j1.  Add '+' to parent make rule.
-\end{verbatim}
-
-
-{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Successfully compiled differential equation model from auto-generated C code.}}\begin{alltt}
-\hlstd{m.Z.mkin.3} \hlkwb{<-} \hlkwd{mkinfit}\hlstd{(Z.mkin.3, FOCUS_2006_Z_mkin,} \hlkwc{quiet} \hlstd{=} \hlnum{TRUE}\hlstd{)}
-\hlkwd{plot_sep}\hlstd{(m.Z.mkin.3)}
-\end{alltt}
-\end{kframe}
-\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_9-1} 
-
-\end{knitrout}
-
-This results in a much better representation of the behaviour of the parent 
-compound Z0.
-
-Finally, Z3 is added as well. These models appear overparameterised (no
-covariance matrix returned) if the sink for Z1 is left in the models.
-
-\begin{knitrout}
-\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe}
-\begin{alltt}
-\hlstd{Z.mkin.4} \hlkwb{<-} \hlkwd{mkinmod}\hlstd{(}\hlkwc{Z0} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFORB"}\hlstd{,} \hlstr{"Z1"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),}
-                    \hlkwc{Z1} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z2"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),}
-                    \hlkwc{Z2} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z3"}\hlstd{),}
-                    \hlkwc{Z3} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{))}
-\end{alltt}
-\begin{verbatim}
-## make[1]: warning: jobserver unavailable: using -j1.  Add '+' to parent make rule.
-\end{verbatim}
-
-
-{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Successfully compiled differential equation model from auto-generated C code.}}\begin{alltt}
-\hlstd{m.Z.mkin.4} \hlkwb{<-} \hlkwd{mkinfit}\hlstd{(Z.mkin.4, FOCUS_2006_Z_mkin,}
-                      \hlkwc{parms.ini} \hlstd{= m.Z.mkin.3}\hlopt{$}\hlstd{bparms.ode,}
-                      \hlkwc{quiet} \hlstd{=} \hlnum{TRUE}\hlstd{)}
-\hlkwd{plot_sep}\hlstd{(m.Z.mkin.4)}
-\end{alltt}
-\end{kframe}
-\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_10-1} 
-
-\end{knitrout}
-
-The error level of the fit, but especially of metabolite Z3, can be improved if
-the SFORB model is chosen for this metabolite, as this model is capable of
-representing the tailing of the metabolite decline phase.
-
-\begin{knitrout}
-\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe}
-\begin{alltt}
-\hlstd{Z.mkin.5} \hlkwb{<-} \hlkwd{mkinmod}\hlstd{(}\hlkwc{Z0} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFORB"}\hlstd{,} \hlstr{"Z1"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),}
-                    \hlkwc{Z1} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z2"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),}
-                    \hlkwc{Z2} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z3"}\hlstd{),}
-                    \hlkwc{Z3} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFORB"}\hlstd{))}
-\end{alltt}
-\begin{verbatim}
-## make[1]: warning: jobserver unavailable: using -j1.  Add '+' to parent make rule.
-\end{verbatim}
-
-
-{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Successfully compiled differential equation model from auto-generated C code.}}\begin{alltt}
-\hlstd{m.Z.mkin.5} \hlkwb{<-} \hlkwd{mkinfit}\hlstd{(Z.mkin.5, FOCUS_2006_Z_mkin,}
-                      \hlkwc{parms.ini} \hlstd{= m.Z.mkin.4}\hlopt{$}\hlstd{bparms.ode[}\hlnum{1}\hlopt{:}\hlnum{4}\hlstd{],}
-                      \hlkwc{quiet} \hlstd{=} \hlnum{TRUE}\hlstd{)}
-\hlkwd{plot_sep}\hlstd{(m.Z.mkin.5)}
-\end{alltt}
-\end{kframe}
-\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_11-1} 
-
-\end{knitrout}
-
-The summary view of the backtransformed parameters shows that we get no
-confidence intervals due to overparameterisation. As the optimized
-\texttt{k\_Z3\_bound\_free} is excessively small, it seems reasonable to fix it to
-zero. 
-
-\begin{knitrout}
-\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe}
-\begin{alltt}
-\hlstd{m.Z.mkin.5a} \hlkwb{<-} \hlkwd{mkinfit}\hlstd{(Z.mkin.5, FOCUS_2006_Z_mkin,}
-                       \hlkwc{parms.ini} \hlstd{=} \hlkwd{c}\hlstd{(m.Z.mkin.5}\hlopt{$}\hlstd{bparms.ode[}\hlnum{1}\hlopt{:}\hlnum{7}\hlstd{],}
-                                     \hlkwc{k_Z3_bound_free} \hlstd{=} \hlnum{0}\hlstd{),}
-                       \hlkwc{fixed_parms} \hlstd{=} \hlstr{"k_Z3_bound_free"}\hlstd{,}
-                       \hlkwc{quiet} \hlstd{=} \hlnum{TRUE}\hlstd{)}
-\hlkwd{plot_sep}\hlstd{(m.Z.mkin.5a)}
-\end{alltt}
-\end{kframe}
-\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_11a-1} 
-
-\end{knitrout}
-
-As expected, the residual plots for Z0 and Z3 are more random than in the case of the 
-all SFO model for which they were shown above. In conclusion, the model
-\texttt{Z.mkin.5a} is proposed as the best-fit model for the dataset from
-Appendix 7 of the FOCUS report.
-
-A graphical representation of the confidence intervals can finally be obtained.
-
-\begin{knitrout}
-\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe}
-\begin{alltt}
-\hlkwd{mkinparplot}\hlstd{(m.Z.mkin.5a)}
-\end{alltt}
-\end{kframe}
-\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_11b-1} 
-
-\end{knitrout}
-
-The endpoints obtained with this model are
-
-\begin{knitrout}
-\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe}
-\begin{alltt}
-\hlkwd{endpoints}\hlstd{(m.Z.mkin.5a)}
-\end{alltt}
-\begin{verbatim}
-## $ff
-##   Z0_free_Z1        Z1_Z2      Z2_sink   Z2_Z3_free Z3_free_sink 
-##    1.0000000    1.0000000    0.4634431    0.5365569    1.0000000 
-## 
-## $SFORB
-##       Z0_b1       Z0_b2       Z3_b1       Z3_b2 
-## 2.447138640 0.007512589 0.080007099 0.000000000 
-## 
-## $distimes
-##         DT50     DT90 DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2
-## Z0 0.3042972 1.184811   0.283248   92.26476         NA         NA
-## Z1 1.5147787 5.031986         NA         NA         NA         NA
-## Z2 1.6413857 5.452565         NA         NA         NA         NA
-## Z3        NA       NA         NA         NA   8.663571        Inf
-\end{verbatim}
-\end{kframe}
-\end{knitrout}
-
-It is clear the degradation rate of Z3 towards the end of the experiment 
-is very low as DT50\_Z3\_b2 (the second Eigenvalue of the system of two differential 
-equations representing the SFORB system for Z3, corresponding to the slower rate
-constant of the DFOP model) is reported to be infinity.  However, this appears
-to be a feature of the data.
-
-\bibliographystyle{plainnat}
-\bibliography{references}
-
-\end{document}
-% vim: set foldmethod=syntax: