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diff --git a/vignettes/FOCUS_Z.Rnw b/vignettes/FOCUS_Z.Rnw deleted file mode 100644 index 5abda0e1..00000000 --- a/vignettes/FOCUS_Z.Rnw +++ /dev/null @@ -1,274 +0,0 @@ -%\VignetteIndexEntry{Example evaluation of FOCUS dataset Z} -%\VignetteEngine{knitr::knitr} -\documentclass[12pt,a4paper]{article} -\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}, -} - -\begin{document} - -<<include=FALSE>>= -require(knitr) -opts_chunk$set(engine='R', tidy = FALSE, cache = TRUE) -options(width=70) -@ - -\title{Example evaluation of FOCUS dataset Z} -\author{\textbf{Johannes Ranke} \\[0.5cm] -%EndAName -Wissenschaftlicher Berater\\ -Kronacher Str. 8, 79639 Grenzach-Wyhlen, Germany\\[0.5cm] -and\\[0.5cm] -University of Bremen\\ -} -\maketitle - -\thispagestyle{empty} \setcounter{page}{0} - -\clearpage - -\tableofcontents - -\textbf{Key words}: Kinetics, FOCUS, nonlinear optimisation - -\section{The data} - -The following code defines the example dataset from Appendix 7 to the FOCUS kinetics -report \citep{FOCUSkinetics2011}, p.350. - -<<FOCUS_2006_Z_data, echo=TRUE, eval=TRUE>>= -require(mkin) -LOD = 0.5 -FOCUS_2006_Z = data.frame( - t = c(0, 0.04, 0.125, 0.29, 0.54, 1, 2, 3, 4, 7, 10, 14, 21, - 42, 61, 96, 124), - Z0 = c(100, 81.7, 70.4, 51.1, 41.2, 6.6, 4.6, 3.9, 4.6, 4.3, 6.8, - 2.9, 3.5, 5.3, 4.4, 1.2, 0.7), - Z1 = c(0, 18.3, 29.6, 46.3, 55.1, 65.7, 39.1, 36, 15.3, 5.6, 1.1, - 1.6, 0.6, 0.5 * LOD, NA, NA, NA), - Z2 = c(0, NA, 0.5 * LOD, 2.6, 3.8, 15.3, 37.2, 31.7, 35.6, 14.5, - 0.8, 2.1, 1.9, 0.5 * LOD, NA, NA, NA), - Z3 = c(0, NA, NA, NA, NA, 0.5 * LOD, 9.2, 13.1, 22.3, 28.4, 32.5, - 25.2, 17.2, 4.8, 4.5, 2.8, 4.4)) - -FOCUS_2006_Z_mkin <- mkin_wide_to_long(FOCUS_2006_Z) -@ - -\section{Parent compound and one metabolite} - -The next step is to set up the models used for the kinetic analysis. As the -simultaneous fit of parent and the first metabolite is usually straightforward, -Step 1 (SFO for parent only) is skipped here. We start with the model 2a, -with formation and decline of metabolite Z1 and the pathway from parent -directly to sink included (default in mkin). - -<<FOCUS_2006_Z_fits_1, echo=TRUE, fig.height=6>>= -Z.2a <- mkinmod(Z0 = mkinsub("SFO", "Z1"), - Z1 = mkinsub("SFO")) -m.Z.2a <- mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE) -plot_sep(m.Z.2a) -summary(m.Z.2a, data = FALSE)$bpar -@ - -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: - -<<FOCUS_2006_Z_fits_2, echo=TRUE, fig.height=6>>= -Z.2a.ff <- mkinmod(Z0 = mkinsub("SFO", "Z1"), - Z1 = mkinsub("SFO"), - use_of_ff = "max") - -m.Z.2a.ff <- mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE) -plot_sep(m.Z.2a.ff) -summary(m.Z.2a.ff, data = FALSE)$bpar -@ - -Here, the ilr transformed formation fraction fitted in the model takes a very -large value, and the backtransformed formation fraction from parent Z to Z1 is -practically unity. Again, the covariance matrix is not returned as the model is -overparameterised. - -The simplified model is obtained by setting the list component \texttt{sink} to -\texttt{FALSE}.\footnote{If the model formulation without formation fractions -is used, the same effect can be obtained by fixing the parameter \texttt{k\_Z\_sink} -to a value of zero.} - -In the following, we use the parameterisation with formation fractions in order -to be able to compare with the results in the FOCUS guidance, and as it -makes it easier to use parameters obtained in a previous fit when adding a further -metabolite. - -<<FOCUS_2006_Z_fits_3, echo=TRUE, fig.height=6>>= -Z.3 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE), - Z1 = mkinsub("SFO"), use_of_ff = "max") -m.Z.3 <- mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE) -plot_sep(m.Z.3) -summary(m.Z.3, data = FALSE)$bpar -@ - -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. - -<<FOCUS_2006_Z_fits_5, echo=TRUE, fig.height=7>>= -Z.5 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE), - Z1 = mkinsub("SFO", "Z2", sink = FALSE), - Z2 = mkinsub("SFO"), use_of_ff = "max") -m.Z.5 <- mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE) -plot_sep(m.Z.5) -@ - -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. - -<<FOCUS_2006_Z_fits_6, echo=TRUE, fig.height=8>>= -Z.FOCUS <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE), - Z1 = mkinsub("SFO", "Z2", sink = FALSE), - Z2 = mkinsub("SFO", "Z3"), - Z3 = mkinsub("SFO"), - use_of_ff = "max") -m.Z.FOCUS <- mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, - parms.ini = m.Z.5$bparms.ode, - quiet = TRUE) -plot_sep(m.Z.FOCUS) -summary(m.Z.FOCUS, data = FALSE)$bpar -endpoints(m.Z.FOCUS) -@ - -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. - -<<FOCUS_2006_Z_fits_7, echo=TRUE, fig.height=8>>= -Z.mkin.1 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE), - Z1 = mkinsub("SFO", "Z2", sink = FALSE), - Z2 = mkinsub("SFO", "Z3"), - Z3 = mkinsub("SFORB")) -m.Z.mkin.1 <- mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE) -plot_sep(m.Z.mkin.1) -summary(m.Z.mkin.1, data = FALSE)$cov.unscaled -@ - -Therefore, a further stepwise model building is performed starting from the -stage of parent and two metabolites, starting from the assumption that the model -fit for the parent compound can be improved by using the SFORB model. - -<<FOCUS_2006_Z_fits_9, echo=TRUE, fig.height=8>>= -Z.mkin.3 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE), - Z1 = mkinsub("SFO", "Z2", sink = FALSE), - Z2 = mkinsub("SFO")) -m.Z.mkin.3 <- mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE) -plot_sep(m.Z.mkin.3) -@ - -This results in a much better representation of the behaviour of the parent -compound Z0. - -Finally, Z3 is added as well. These models appear overparameterised (no -covariance matrix returned) if the sink for Z1 is left in the models. - -<<FOCUS_2006_Z_fits_10, echo=TRUE, fig.height=8>>= -Z.mkin.4 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE), - Z1 = mkinsub("SFO", "Z2", sink = FALSE), - Z2 = mkinsub("SFO", "Z3"), - Z3 = mkinsub("SFO")) -m.Z.mkin.4 <- mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, - parms.ini = m.Z.mkin.3$bparms.ode, - quiet = TRUE) -plot_sep(m.Z.mkin.4) -@ - -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. - -<<FOCUS_2006_Z_fits_11, echo=TRUE, fig.height=8>>= -Z.mkin.5 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE), - Z1 = mkinsub("SFO", "Z2", sink = FALSE), - Z2 = mkinsub("SFO", "Z3"), - Z3 = mkinsub("SFORB")) -m.Z.mkin.5 <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, - parms.ini = m.Z.mkin.4$bparms.ode[1:4], - quiet = TRUE) -plot_sep(m.Z.mkin.5) -@ - -The summary view of the backtransformed parameters shows that we get no -confidence intervals due to overparameterisation. As the optimized -\texttt{k\_Z3\_bound\_free} is excessively small, it seems reasonable to fix it to -zero. - -<<FOCUS_2006_Z_fits_11a, echo=TRUE>>= -m.Z.mkin.5a <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, - parms.ini = c(m.Z.mkin.5$bparms.ode[1:7], - k_Z3_bound_free = 0), - fixed_parms = "k_Z3_bound_free", - quiet = TRUE) -plot_sep(m.Z.mkin.5a) -@ - -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. - -<<FOCUS_2006_Z_fits_11b, echo=TRUE>>= -mkinparplot(m.Z.mkin.5a) -@ - -The endpoints obtained with this model are - -<<FOCUS_2006_Z_fits_11b_endpoints, echo=TRUE>>= -endpoints(m.Z.mkin.5a) -@ - -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: |