From 218a9c55bd80fb708b15fa7196422f759bfe4b27 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Wed, 13 May 2020 16:20:23 +0200 Subject: Further formatting improvement of benchmark vignette Also, use .rmd extension instead of .Rmd for vignettes. --- vignettes/web_only/FOCUS_Z.Rmd | 255 ----------------------------------------- 1 file changed, 255 deletions(-) delete mode 100644 vignettes/web_only/FOCUS_Z.Rmd (limited to 'vignettes/web_only/FOCUS_Z.Rmd') diff --git a/vignettes/web_only/FOCUS_Z.Rmd b/vignettes/web_only/FOCUS_Z.Rmd deleted file mode 100644 index 2da7fde7..00000000 --- a/vignettes/web_only/FOCUS_Z.Rmd +++ /dev/null @@ -1,255 +0,0 @@ ---- -title: Example evaluation of FOCUS dataset Z -author: Johannes Ranke -date: "`r Sys.Date()`" -output: - html_document: - toc: true - toc_float: true - code_folding: show - fig_retina: null -bibliography: ../references.bib -vignette: > - %\VignetteEngine{knitr::rmarkdown} - %\VignetteEncoding{UTF-8} ---- - -[Wissenschaftlicher Berater, Kronacher Str. 12, 79639 Grenzach-Wyhlen, Germany](http://www.jrwb.de)
-[Privatdozent at the University of Bremen](http://chem.uft.uni-bremen.de/ranke) - -```{r, include = FALSE} -require(knitr) -options(digits = 5) -opts_chunk$set(engine='R', tidy = FALSE) -``` - -# The data - -The following code defines the example dataset from Appendix 7 to the FOCUS kinetics -report [@FOCUSkinetics2014, p. 354]. - -```{r, echo = TRUE, fig = TRUE, fig.width = 8, fig.height = 7} -library(mkin, quietly = TRUE) -LOD = 0.5 -FOCUS_2006_Z = data.frame( - t = c(0, 0.04, 0.125, 0.29, 0.54, 1, 2, 3, 4, 7, 10, 14, 21, - 42, 61, 96, 124), - Z0 = c(100, 81.7, 70.4, 51.1, 41.2, 6.6, 4.6, 3.9, 4.6, 4.3, 6.8, - 2.9, 3.5, 5.3, 4.4, 1.2, 0.7), - Z1 = c(0, 18.3, 29.6, 46.3, 55.1, 65.7, 39.1, 36, 15.3, 5.6, 1.1, - 1.6, 0.6, 0.5 * LOD, NA, NA, NA), - Z2 = c(0, NA, 0.5 * LOD, 2.6, 3.8, 15.3, 37.2, 31.7, 35.6, 14.5, - 0.8, 2.1, 1.9, 0.5 * LOD, NA, NA, NA), - Z3 = c(0, NA, NA, NA, NA, 0.5 * LOD, 9.2, 13.1, 22.3, 28.4, 32.5, - 25.2, 17.2, 4.8, 4.5, 2.8, 4.4)) - -FOCUS_2006_Z_mkin <- mkin_wide_to_long(FOCUS_2006_Z) -``` - -# Parent and one metabolite - -The next step is to set up the models used for the kinetic analysis. As the -simultaneous fit of parent and the first metabolite is usually straightforward, -Step 1 (SFO for parent only) is skipped here. We start with the model 2a, -with formation and decline of metabolite Z1 and the pathway from parent -directly to sink included (default in mkin). - -```{r FOCUS_2006_Z_fits_1, echo=TRUE, fig.height=6} -Z.2a <- mkinmod(Z0 = mkinsub("SFO", "Z1"), - Z1 = mkinsub("SFO")) -m.Z.2a <- mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE) -plot_sep(m.Z.2a) -summary(m.Z.2a, data = FALSE)$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 very small and the t-test for this parameter suggests that it is -not significantly different from zero. 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: - -```{r 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)$bpar -``` - -Here, the ilr transformed formation fraction fitted in the model takes a very -large value, and the backtransformed formation fraction from parent Z to Z1 is -practically unity. Here, the covariance matrix used for the calculation -of confidence intervals is not returned as the model is -overparameterised. - -A simplified model is obtained by removing the pathway to the sink. -\footnote{If the model formulation without formation fractions -is used, the same effect can be obtained by fixing the parameter \texttt{k\_Z\_sink} -to a value of zero.} - -In the following, we use the parameterisation with formation fractions in order -to be able to compare with the results in the FOCUS guidance, and as it -makes it easier to use parameters obtained in a previous fit when adding a further -metabolite. - -```{r FOCUS_2006_Z_fits_3, echo=TRUE, fig.height=6} -Z.3 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE), - Z1 = mkinsub("SFO"), use_of_ff = "max") -m.Z.3 <- mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE) -plot_sep(m.Z.3) -summary(m.Z.3, data = FALSE)$bpar -``` - -As there is only one transformation product for Z0 and no pathway -to sink, the formation fraction is internally fixed to unity. - -# 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. - -```{r 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. - -```{r 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. - -# Using the SFORB model - -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. - -```{r 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)$cov.unscaled -``` - -Therefore, a further stepwise model building is performed starting from the -stage of parent and two metabolites, starting from the assumption that the model -fit for the parent compound can be improved by using the SFORB model. - -```{r FOCUS_2006_Z_fits_9, echo=TRUE, fig.height=8} -Z.mkin.3 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE), - Z1 = mkinsub("SFO", "Z2", sink = FALSE), - Z2 = mkinsub("SFO")) -m.Z.mkin.3 <- mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE) -plot_sep(m.Z.mkin.3) -``` - -This results in a much better representation of the behaviour of the parent -compound Z0. - -Finally, Z3 is added as well. These models appear overparameterised (no -covariance matrix returned) if the sink for Z1 is left in the models. - -```{r FOCUS_2006_Z_fits_10, echo=TRUE, fig.height=8} -Z.mkin.4 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE), - Z1 = mkinsub("SFO", "Z2", sink = FALSE), - Z2 = mkinsub("SFO", "Z3"), - Z3 = mkinsub("SFO")) -m.Z.mkin.4 <- mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, - parms.ini = m.Z.mkin.3$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. - -```{r 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$bparms.ode[1:4], - quiet = TRUE) -plot_sep(m.Z.mkin.5) -``` - -The summary view of the backtransformed parameters shows that we get no -confidence intervals due to overparameterisation. As the optimized -\texttt{k\_Z3\_bound\_free} is excessively small, it seems reasonable to fix it to -zero. - -```{r FOCUS_2006_Z_fits_11a, echo=TRUE} -m.Z.mkin.5a <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, - parms.ini = c(m.Z.mkin.5$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. - -```{r FOCUS_2006_Z_fits_11b, echo=TRUE} -mkinparplot(m.Z.mkin.5a) -``` - -The endpoints obtained with this model are - -```{r 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. - - -# References - - -- cgit v1.2.1