More work on the examples vignette

git-svn-id: svn+ssh://svn.r-forge.r-project.org/svnroot/kinfit/pkg/mkin@65 edb9625f-4e0d-4859-8d74-9fd3b1da38cb

1 files changed, 189 insertions, 1 deletions

diff --git a/vignettes/examples.Rnw b/vignettes/examples.Rnw
index 784eddfc..6d75e4ae 100644
--- a/vignettes/examples.Rnw
+++ b/vignettes/examples.Rnw
@@ -47,7 +47,6 @@ University of Bremen\\
 \textbf{Key words}: Kinetics, FOCUS, nonlinear optimisation

 

 \section{Kinetic evaluations for parent compounds}

-\label{intro}

 

 These examples are also evaluated in a parallel vignette of the

 \Rpackage{kinfit} package \citep{pkg:kinfit}. The datasets are from Appendix 3,

@@ -282,5 +281,194 @@ model. However, the difference appears negligible.
 \bibliographystyle{plainnat}

 \bibliography{references}

 

+\section{Kinetic evaluations for parent and metabolites}

+

+\subsection{Laboratory Data for example compound Z}

+

+The following code defines the example dataset from Appendix 7 to the FOCUS kinetics

+report, p.350 

+

+<<FOCUS_2006_Z_data, echo=TRUE, eval=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)

+@

+

+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=TRUE>>=

+debug(mkinmod)

+Z.2a <- mkinmod(Z0 = list(type = "SFO", to = "Z1"),

+                Z1 = list(type = "SFO"))

+m.Z.2a <- mkinfit(Z.2a, FOCUS_2006_Z_mkin)

+summary(m.Z.2a, data = FALSE)

+plot(m.Z.2a)

+@

+

+As obvious from 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\_Z\_sink} is ill-defined and the covariance matrix is not returned.

+This suggests, in agreement to 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=TRUE>>=

+Z.2a.ff <- mkinmod(Z0 = list(type = "SFO", to = "Z1"),

+                Z1 = list(type = "SFO"), use_of_ff = "max")

+

+m.Z.2a.ff <- mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin)

+summary(m.Z.2a.ff, data = FALSE)

+plot(m.Z.2a.ff)

+@

+

+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}. This model definition is not supported when formation fractions 

+are used.

+

+<<FOCUS_2006_Z_fits_3, echo=TRUE, fig=TRUE>>=

+Z.3 <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE),

+                Z1 = list(type = "SFO"))

+m.Z.3 <- mkinfit(Z.3, FOCUS_2006_Z_mkin)

+m.Z.3 <- mkinfit(Z.3, FOCUS_2006_Z_mkin, parms.ini = c(k_Z0_Z1 = 0.5))

+m.Z.3 <- mkinfit(Z.3, FOCUS_2006_Z_mkin, solution_type = "deSolve")

+summary(m.Z.2b, data = FALSE)

+plot(m.Z.2b)

+@

+

+The first attempt to fit the model fails, as the default solution type chosen

+by mkinfit is based on eigenvalues, and the system defined by the starting

+parameters is identified as being singular to the solver. This is caused by the

+fact that the rate constants for both state variables are the same using the

+default starting paramters. Setting a different starting value for one of the

+parameters overcomes this. Alternatively, the \Rpackage{deSolve} based model

+solution can be chosen, at the cost of a bit more computing time.

+

+<<FOCUS_2006_Z_fits_4, echo=TRUE, fig=TRUE>>=

+Z.4a <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE),

+                Z1 = list(type = "SFO", to = "Z2"),

+                Z2 = list(type = "SFO"))

+m.Z.4a <- mkinfit(Z.4a, FOCUS_2006_Z_mkin, parms.ini = c(k_Z0_Z1 = 0.5))

+summary(m.Z.4a, data = FALSE)

+plot(m.Z.4a)

+@

+

+As suggested in the FOCUS report, the pathway to sink was removed for metabolite Z1 as

+well. 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. Again, in order to avoid a singular system when using default starting

+parameters, the starting parameter for the pathway without sink term has to be adapted.

+

+<<FOCUS_2006_Z_fits_4, echo=TRUE, fig=TRUE>>=

+Z.5 <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE),

+                Z1 = list(type = "SFO", to = "Z2", sink = FALSE),

+                Z2 = list(type = "SFO"))

+m.Z.5 <- mkinfit(Z.5, FOCUS_2006_Z_mkin, 

+                  parms.ini = c(k_Z0_Z1 = 0.5, k_Z1_Z2 = 0.2))

+summary(m.Z.5, data = FALSE)

+plot(m.Z.5)

+@

+

+Finally, metabolite Z3 is added to the model.

+

+<<FOCUS_2006_Z_fits_5, echo=TRUE, fig=TRUE>>=

+Z.FOCUS <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE),

+                Z1 = list(type = "SFO", to = "Z2", sink = FALSE),

+                Z2 = list(type = "SFO", to = "Z3"),

+                Z3 = list(type = "SFO"))

+m.Z.FOCUS <- mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, 

+                  parms.ini = c(k_Z0_Z1 = 0.5, k_Z1_Z2 = 0.2, k_Z2_Z3 = 0.3))

+summary(m.Z.FOCUS, data = FALSE)

+plot(m.Z.FOCUS)

+@

+

+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. However, the $\chi^2$ error 

+level is higher for metabolite Z3 using this model, the covariance matrix is

+not returned, and graphically the fit is not significantly improved. Therefore,

+this appears to be a case of overparamterisation.

+

+<<FOCUS_2006_Z_fits_6, echo=TRUE, fig=TRUE>>=

+Z.mkin.1 <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE),

+                Z1 = list(type = "SFO", to = "Z2", sink = FALSE),

+                Z2 = list(type = "SFO", to = "Z3"),

+                Z3 = list(type = "SFORB"))

+m.Z.mkin.1 <- mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, 

+                  parms.ini = c(k_Z0_Z1 = 0.5, k_Z1_Z2 = 0.3, k_Z2_Z3 = 0.2))

+summary(m.Z.mkin.1, data = FALSE)

+plot(m.Z.mkin.1)

+@

+

+On the other hand, the model fit for the parent compound can be improved by

+using the SFORB model.

+

+<<FOCUS_2006_Z_fits_6, echo=TRUE, fig=TRUE>>=

+Z.mkin.2 <- mkinmod(Z0 = list(type = "SFORB", to = "Z1", sink = FALSE),

+                Z1 = list(type = "SFO"))

+m.Z.mkin.2 <- mkinfit(Z.mkin.2, FOCUS_2006_Z_mkin)

+summary(m.Z.mkin.2, data = FALSE)

+plot(m.Z.mkin.2)

+@

+

+The sink is for Z1 is turned off again, for the same reasons as in the original analysis.

+Then, metabolite Z2 is added.

+

+<<FOCUS_2006_Z_fits_6, echo=TRUE, fig=TRUE>>=

+Z.mkin.3 <- mkinmod(Z0 = list(type = "SFORB", to = "Z1", sink = FALSE),

+                Z1 = list(type = "SFO", to = "Z2"),

+                Z2 = list(type = "SFO"))

+m.Z.mkin.3 <- mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin)

+summary(m.Z.mkin.3, data = FALSE)

+plot(m.Z.mkin.3)

+@

+

+Finally, Z3 is added as well. This model appears overparameterised (no

+covariance matrix returned) if the sink for Z1 is left in the model.

+

+<<FOCUS_2006_Z_fits_6, echo=TRUE, fig=TRUE>>=

+Z.mkin.4 <- mkinmod(Z0 = list(type = "SFORB", to = "Z1", sink = FALSE),

+                Z1 = list(type = "SFO", to = "Z2", sink = FALSE),

+                Z2 = list(type = "SFO", to = "Z3"),

+                Z3 = list(type = "SFO"))

+m.Z.mkin.4 <- mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, 

+  parms.ini = c(k_Z1_Z2 = 0.05))

+summary(m.Z.mkin.4, data = FALSE)

+plot(m.Z.mkin.4)

+@

+

+<<FOCUS_2006_Z_fits_6, echo=TRUE, fig=TRUE>>=

+Z.mkin.5 <- mkinmod(Z0 = list(type = "SFORB", to = "Z1", sink = FALSE),

+                Z1 = list(type = "SFO", to = "Z2", sink = FALSE),

+                Z2 = list(type = "SFO", to = "Z3"),

+                Z3 = list(type = "SFORB"))

+m.Z.mkin.5 <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin) 

+summary(m.Z.mkin.5, data = FALSE)

+plot(m.Z.mkin.5)

+@

+

+

 \end{document}

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