From f18213520f20aba947093e53113c44b689e8b98d Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Tue, 16 Jan 2018 06:11:54 +0100 Subject: Updates in the FOCUS Z vignette To make the text consistent with the results produced by the current mkin version. Static documentation articles rebuilt by pkgdown::build_articles() --- docs/articles/FOCUS_D.html | 2 +- docs/articles/FOCUS_L.html | 44 ++++++++--------- docs/articles/FOCUS_Z.R | 1 + docs/articles/FOCUS_Z.html | 92 ++++++++++++++++-------------------- docs/articles/FOCUS_Z.pdf | Bin 240270 -> 384032 bytes docs/articles/compiled_models.html | 12 ++--- docs/articles/mkin.html | 2 +- docs/articles/twa.html | 2 +- vignettes/FOCUS_Z.Rmd | 17 +++---- vignettes/FOCUS_Z.html | 94 ++++++++++++++++--------------------- vignettes/FOCUS_Z.pdf | Bin 0 -> 384032 bytes 11 files changed, 122 insertions(+), 144 deletions(-) create mode 100644 vignettes/FOCUS_Z.pdf diff --git a/docs/articles/FOCUS_D.html b/docs/articles/FOCUS_D.html index e3f87eae..d9dd8ad5 100644 --- a/docs/articles/FOCUS_D.html +++ b/docs/articles/FOCUS_D.html @@ -77,7 +77,7 @@

Example evaluation of FOCUS Example Dataset D

Johannes Ranke

-

2018-01-14

+

2018-01-16

diff --git a/docs/articles/FOCUS_L.html b/docs/articles/FOCUS_L.html index bc2b9947..42ec2df1 100644 --- a/docs/articles/FOCUS_L.html +++ b/docs/articles/FOCUS_L.html @@ -77,7 +77,7 @@

Example evaluation of FOCUS Laboratory Data L1 to L3

Johannes Ranke

-

2018-01-14

+

2018-01-16

@@ -100,15 +100,15 @@ FOCUS_2006_L1_mkin <- summary(m.L1.SFO) 
## mkin version:    0.9.47.1 
 ## R version:       3.4.3 
-## Date of fit:     Sun Jan 14 18:36:12 2018 
-## Date of summary: Sun Jan 14 18:36:12 2018 
+## Date of fit:     Tue Jan 16 06:11:06 2018 
+## Date of summary: Tue Jan 16 06:11:06 2018 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 37 model solutions performed in 0.258 s
+## Fitted with method Port using 37 model solutions performed in 0.245 s
 ## 
 ## Weighting: none
 ## 
@@ -193,8 +193,8 @@ FOCUS_2006_L1_mkin <- 
summary(m.L1.FOMC, data = FALSE)

 
## mkin version:    0.9.47.1 
 ## R version:       3.4.3 
-## Date of fit:     Sun Jan 14 18:36:13 2018 
-## Date of summary: Sun Jan 14 18:36:13 2018 
+## Date of fit:     Tue Jan 16 06:11:07 2018 
+## Date of summary: Tue Jan 16 06:11:07 2018 
 ## 
 ## 
 ## Warning: Optimisation by method Port did not converge.
@@ -206,7 +206,7 @@ FOCUS_2006_L1_mkin <-  
summary(m.L2.FOMC, data = FALSE)

 
## mkin version:    0.9.47.1 
 ## R version:       3.4.3 
-## Date of fit:     Sun Jan 14 18:36:14 2018 
-## Date of summary: Sun Jan 14 18:36:14 2018 
+## Date of fit:     Tue Jan 16 06:11:08 2018 
+## Date of summary: Tue Jan 16 06:11:08 2018 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 81 model solutions performed in 0.177 s
+## Fitted with method Port using 81 model solutions performed in 0.168 s
 ## 
 ## Weighting: none
 ## 
@@ -364,8 +364,8 @@ FOCUS_2006_L2_mkin <- 
summary(m.L2.DFOP, data = FALSE)

 
## mkin version:    0.9.47.1 
 ## R version:       3.4.3 
-## Date of fit:     Sun Jan 14 18:36:15 2018 
-## Date of summary: Sun Jan 14 18:36:15 2018 
+## Date of fit:     Tue Jan 16 06:11:09 2018 
+## Date of summary: Tue Jan 16 06:11:09 2018 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) *
@@ -374,7 +374,7 @@ FOCUS_2006_L2_mkin <-  
summary(mm.L3[["DFOP", 1]])

 
## mkin version:    0.9.47.1 
 ## R version:       3.4.3 
-## Date of fit:     Sun Jan 14 18:36:16 2018 
-## Date of summary: Sun Jan 14 18:36:16 2018 
+## Date of fit:     Tue Jan 16 06:11:10 2018 
+## Date of summary: Tue Jan 16 06:11:10 2018 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) *
@@ -466,7 +466,7 @@ mm.L3 <-  
summary(mm.L4[["SFO", 1]], data = FALSE)

 
## mkin version:    0.9.47.1 
 ## R version:       3.4.3 
-## Date of fit:     Sun Jan 14 18:36:16 2018 
-## Date of summary: Sun Jan 14 18:36:17 2018 
+## Date of fit:     Tue Jan 16 06:11:10 2018 
+## Date of summary: Tue Jan 16 06:11:10 2018 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 46 model solutions performed in 0.097 s
+## Fitted with method Port using 46 model solutions performed in 0.094 s
 ## 
 ## Weighting: none
 ## 
@@ -617,15 +617,15 @@ mm.L4 <- 
summary(mm.L4[["FOMC", 1]], data = FALSE)

 
## mkin version:    0.9.47.1 
 ## R version:       3.4.3 
-## Date of fit:     Sun Jan 14 18:36:17 2018 
-## Date of summary: Sun Jan 14 18:36:17 2018 
+## Date of fit:     Tue Jan 16 06:11:10 2018 
+## Date of summary: Tue Jan 16 06:11:10 2018 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 66 model solutions performed in 0.138 s
+## Fitted with method Port using 66 model solutions performed in 0.139 s
 ## 
 ## Weighting: none
 ## 
diff --git a/docs/articles/FOCUS_Z.R b/docs/articles/FOCUS_Z.R
index 65ddbeba..4d2dffca 100644
--- a/docs/articles/FOCUS_Z.R
+++ b/docs/articles/FOCUS_Z.R
@@ -1,5 +1,6 @@
 ## ---- include = FALSE----------------------------------------------------
 require(knitr)
+options(digits = 5)
 opts_chunk$set(engine='R', tidy = FALSE)
 
 ## ---- echo = TRUE, fig = TRUE, fig.width = 8, fig.height = 7-------------
diff --git a/docs/articles/FOCUS_Z.html b/docs/articles/FOCUS_Z.html
index 7a37c66d..a5cfc616 100644
--- a/docs/articles/FOCUS_Z.html
+++ b/docs/articles/FOCUS_Z.html
@@ -77,7 +77,7 @@
       
Example evaluation of FOCUS dataset Z

                         
Johannes Ranke

             
-            
2018-01-14

+            
2018-01-16

           
 
     
@@ -115,17 +115,12 @@ FOCUS_2006_Z_mkin <- plot_sep(m.Z.2a)

 

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

-
##               Estimate se_notrans      t value       Pr(>t)      Lower
-## Z0_0      9.701488e+01 3.55313531 2.730402e+01 1.679194e-21 91.4013833
-## k_Z0_sink 6.213452e-10 0.22689429 2.738479e-09 5.000000e-01  0.0000000
-## k_Z0_Z1   2.236006e+00 0.16507349 1.354552e+01 7.393893e-14  1.8374087
-## k_Z1_sink 4.821248e-01 0.06585366 7.321154e+00 3.551981e-08  0.4005976
-##                 Upper
-## Z0_0      102.6283792
-## k_Z0_sink         Inf
-## k_Z0_Z1     2.7210739
-## k_Z1_sink   0.5802439

-
As obvious from the parameter summary (the  component of the summary), the kinetic rate constant from parent compound Z to sink is negligible. Accordingly, the exact magnitude of the fitted parameter  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.

+
##             Estimate se_notrans    t value     Pr(>t)   Lower     Upper
+## Z0_0      9.7015e+01   3.553135 2.7304e+01 1.6792e-21 91.4014 102.62838
+## k_Z0_sink 6.2135e-10   0.226894 2.7385e-09 5.0000e-01  0.0000       Inf
+## k_Z0_Z1   2.2360e+00   0.165073 1.3546e+01 7.3939e-14  1.8374   2.72107
+## k_Z1_sink 4.8212e-01   0.065854 7.3212e+00 3.5520e-08  0.4006   0.58024

+
As obvious from the parameter summary (the  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:

 
Z.2a.ff <- mkinmod(Z0 = mkinsub("SFO", "Z1"),
                    Z1 = mkinsub("SFO"),
@@ -135,13 +130,13 @@ FOCUS_2006_Z_mkin <- plot_sep(m.Z.2a.ff)

 

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

-
##              Estimate se_notrans   t value       Pr(>t) Lower Upper
-## Z0_0       97.0148813 3.55314638 27.303936 1.679331e-21    NA    NA
-## k_Z0        2.2360064 0.21684717 10.311439 3.661734e-11    NA    NA
-## k_Z1        0.4821248 0.06585372  7.321147 3.552046e-08    NA    NA
-## f_Z0_to_Z1  1.0000000 0.10147344  9.854795 9.707117e-11    NA    NA

-
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  to .

+
##            Estimate se_notrans t value     Pr(>t) Lower Upper
+## Z0_0       97.01488   3.553146 27.3039 1.6793e-21    NA    NA
+## k_Z0        2.23601   0.216847 10.3114 3.6617e-11    NA    NA
+## k_Z1        0.48212   0.065854  7.3211 3.5520e-08    NA    NA
+## f_Z0_to_Z1  1.00000   0.101473  9.8548 9.7071e-11    NA    NA

+
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. 

 
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.

 
Z.3 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
                Z1 = mkinsub("SFO"), use_of_ff = "max")

@@ -150,10 +145,10 @@ FOCUS_2006_Z_mkin <- plot_sep(m.Z.3)

 

 
summary(m.Z.3, data = FALSE)$bpar

-
##        Estimate se_notrans  t value       Pr(>t)      Lower       Upper
-## Z0_0 97.0148816 2.68177104 36.17568 2.363590e-25 91.5215232 102.5082401
-## k_Z0  2.2360064 0.14686238 15.22518 2.247007e-15  1.9545318   2.5580166
-## k_Z1  0.4821248 0.04268711 11.29439 3.068559e-12  0.4021552   0.5779966

+
##      Estimate se_notrans t value     Pr(>t)    Lower   Upper
+## Z0_0 97.01488   2.681771  36.176 2.3636e-25 91.52152 102.508
+## k_Z0  2.23601   0.146862  15.225 2.2470e-15  1.95453   2.558
+## k_Z1  0.48212   0.042687  11.294 3.0686e-12  0.40216   0.578

 
As there is only one transformation product for Z0 and no pathway to sink, the formation fraction is internally fixed to unity.

 
 

@@ -182,34 +177,27 @@ FOCUS_2006_Z_mkin <- 
plot_sep(m.Z.FOCUS)

 

 
summary(m.Z.FOCUS, data = FALSE)$bpar

-
##               Estimate se_notrans   t value       Pr(>t)       Lower
-## Z0_0       96.84024413 2.05881366 47.036916 5.572278e-44 92.70685169
-## k_Z0        2.21540096 0.11812759 18.754306 7.736886e-25  1.99050408
-## k_Z1        0.47835870 0.02929353 16.329843 3.344317e-22  0.42303496
-## k_Z2        0.45166296 0.04418624 10.221801 3.036447e-14  0.37106537
-## k_Z3        0.05868971 0.01428961  4.107158 7.256030e-05  0.03598292
-## f_Z2_to_Z3  0.47147387 0.05702672  8.267596 2.779011e-11  0.36029541
-##                   Upper
-## Z0_0       100.97363656
-## k_Z0         2.46570780
-## k_Z1         0.54091758
-## k_Z2         0.54976682
-## k_Z3         0.09572548
-## f_Z2_to_Z3   0.58555627

+
##            Estimate se_notrans t value     Pr(>t)     Lower      Upper
+## Z0_0       96.84024   2.058814 47.0369 5.5723e-44 92.706852 100.973637
+## k_Z0        2.21540   0.118128 18.7543 7.7369e-25  1.990504   2.465708
+## k_Z1        0.47836   0.029294 16.3298 3.3443e-22  0.423035   0.540918
+## k_Z2        0.45166   0.044186 10.2218 3.0364e-14  0.371065   0.549767
+## k_Z3        0.05869   0.014290  4.1072 7.2560e-05  0.035983   0.095725
+## f_Z2_to_Z3  0.47147   0.057027  8.2676 2.7790e-11  0.360295   0.585556

 
endpoints(m.Z.FOCUS)

 
## $ff
-##     Z2_Z3   Z2_sink 
-## 0.4714739 0.5285261 
+##   Z2_Z3 Z2_sink 
+## 0.47147 0.52853 
 ## 
 ## $SFORB
 ## logical(0)
 ## 
 ## $distimes
-##          DT50      DT90
-## Z0  0.3128766  1.039354
-## Z1  1.4490113  4.813512
-## Z2  1.5346558  5.098016
-## Z3 11.8103701 39.233200

+##        DT50    DT90
+## Z0  0.31288  1.0394
+## Z1  1.44901  4.8135
+## Z2  1.53466  5.0980
+## Z3 11.81037 39.2332

 
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.

 
 

@@ -274,18 +262,18 @@ FOCUS_2006_Z_mkin <- 
endpoints(m.Z.mkin.5a)

 
## $ff
 ##   Z0_free_Z1        Z1_Z2      Z2_sink   Z2_Z3_free Z3_free_sink 
-##    1.0000000    1.0000000    0.4634423    0.5365577    1.0000000 
+##      1.00000      1.00000      0.46344      0.53656      1.00000 
 ## 
 ## $SFORB
-##       Z0_b1       Z0_b2       Z3_b1       Z3_b2 
-## 2.447137325 0.007512576 0.080007563 0.000000000 
+##     Z0_b1     Z0_b2     Z3_b1     Z3_b2 
+## 2.4471373 0.0075126 0.0800076 0.0000000 
 ## 
 ## $distimes
-##         DT50     DT90 DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2
-## Z0 0.3042974 1.184810  0.2832482   92.26492         NA         NA
-## Z1 1.5147780 5.031984         NA         NA         NA         NA
-## Z2 1.6413852 5.452564         NA         NA         NA         NA
-## Z3        NA       NA         NA         NA   8.663521        Inf

+##      DT50   DT90 DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2
+## Z0 0.3043 1.1848    0.28325     92.265         NA         NA
+## Z1 1.5148 5.0320         NA         NA         NA         NA
+## Z2 1.6414 5.4526         NA         NA         NA         NA
+## Z3     NA     NA         NA         NA     8.6635        Inf

 
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.

 
 

diff --git a/docs/articles/FOCUS_Z.pdf b/docs/articles/FOCUS_Z.pdf
index 8a87e874..975ad17f 100644
Binary files a/docs/articles/FOCUS_Z.pdf and b/docs/articles/FOCUS_Z.pdf differ
diff --git a/docs/articles/compiled_models.html b/docs/articles/compiled_models.html
index 4c850d14..d5d29a1a 100644
--- a/docs/articles/compiled_models.html
+++ b/docs/articles/compiled_models.html
@@ -77,7 +77,7 @@
       
Performance benefit by using compiled model definitions in mkin

                         
Johannes Ranke

             
-            
2018-01-14

+            
2018-01-16

           

 
     
@@ -115,9 +115,9 @@ SFO_SFO <-  Johannes Ranke
             
-            
2018-01-14

+            
2018-01-16

           
 
     
diff --git a/docs/articles/twa.html b/docs/articles/twa.html
index f141ce63..086c8593 100644
--- a/docs/articles/twa.html
+++ b/docs/articles/twa.html
@@ -77,7 +77,7 @@
       
Calculation of time weighted average concentrations with mkin

                         
Johannes Ranke

             
-            
2018-01-14

+            
2018-01-16

           
 
     
diff --git a/vignettes/FOCUS_Z.Rmd b/vignettes/FOCUS_Z.Rmd
index b1ac7d42..951d5eee 100644
--- a/vignettes/FOCUS_Z.Rmd
+++ b/vignettes/FOCUS_Z.Rmd
@@ -20,6 +20,7 @@ vignette: >
 
 ```{r, include = FALSE}
 require(knitr)
+options(digits = 5)
 opts_chunk$set(engine='R', tidy = FALSE)
 ```
 
@@ -64,11 +65,10 @@ 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.
+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:
@@ -85,11 +85,12 @@ 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
+practically unity. Here, the covariance matrix used for the calculation
+of confidence intervals 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
+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.}
 
diff --git a/vignettes/FOCUS_Z.html b/vignettes/FOCUS_Z.html
index 1428ea85..95a67f94 100644
--- a/vignettes/FOCUS_Z.html
+++ b/vignettes/FOCUS_Z.html
@@ -11,7 +11,7 @@
 
 
 
-
+
 
 Example evaluation of FOCUS dataset Z
 
@@ -234,7 +234,7 @@ div.tocify {
 
 
Example evaluation of FOCUS dataset Z

 
Johannes Ranke

-
2018-01-14

+
2018-01-16

 
 
 
@@ -269,17 +269,12 @@ FOCUS_2006_Z_mkin <- mkin_wide_to_long(FOCUS_2006_Z)

 plot_sep(m.Z.2a)

 

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

-
##               Estimate se_notrans      t value       Pr(>t)      Lower
-## Z0_0      9.701488e+01 3.55313531 2.730402e+01 1.679194e-21 91.4013833
-## k_Z0_sink 6.213452e-10 0.22689429 2.738479e-09 5.000000e-01  0.0000000
-## k_Z0_Z1   2.236006e+00 0.16507349 1.354552e+01 7.393893e-14  1.8374087
-## k_Z1_sink 4.821248e-01 0.06585366 7.321154e+00 3.551981e-08  0.4005976
-##                 Upper
-## Z0_0      102.6283792
-## k_Z0_sink         Inf
-## k_Z0_Z1     2.7210739
-## k_Z1_sink   0.5802439

-
As obvious from the parameter summary (the  component of the summary), the kinetic rate constant from parent compound Z to sink is negligible. Accordingly, the exact magnitude of the fitted parameter  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.

+
##             Estimate se_notrans    t value     Pr(>t)   Lower     Upper
+## Z0_0      9.7015e+01   3.553135 2.7304e+01 1.6792e-21 91.4014 102.62838
+## k_Z0_sink 6.2135e-10   0.226894 2.7385e-09 5.0000e-01  0.0000       Inf
+## k_Z0_Z1   2.2360e+00   0.165073 1.3546e+01 7.3939e-14  1.8374   2.72107
+## k_Z1_sink 4.8212e-01   0.065854 7.3212e+00 3.5520e-08  0.4006   0.58024

+
As obvious from the parameter summary (the  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:

 
Z.2a.ff <- mkinmod(Z0 = mkinsub("SFO", "Z1"),
                    Z1 = mkinsub("SFO"),
@@ -289,13 +284,13 @@ plot_sep(m.Z.2a)

 plot_sep(m.Z.2a.ff)

summary(m.Z.2a.ff, data = FALSE)$bpar
-
##              Estimate se_notrans   t value       Pr(>t) Lower Upper
-## Z0_0       97.0148813 3.55314638 27.303936 1.679331e-21    NA    NA
-## k_Z0        2.2360064 0.21684717 10.311439 3.661734e-11    NA    NA
-## k_Z1        0.4821248 0.06585372  7.321147 3.552046e-08    NA    NA
-## f_Z0_to_Z1  1.0000000 0.10147344  9.854795 9.707117e-11    NA    NA
-

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 to .

+
##            Estimate se_notrans t value     Pr(>t) Lower Upper
+## Z0_0       97.01488   3.553146 27.3039 1.6793e-21    NA    NA
+## k_Z0        2.23601   0.216847 10.3114 3.6617e-11    NA    NA
+## k_Z1        0.48212   0.065854  7.3211 3.5520e-08    NA    NA
+## f_Z0_to_Z1  1.00000   0.101473  9.8548 9.7071e-11    NA    NA
+

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.

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.

Z.3 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
                Z1 = mkinsub("SFO"), use_of_ff = "max")
@@ -304,10 +299,10 @@ plot_sep(m.Z.2a.ff) plot_sep(m.Z.3) 

summary(m.Z.3, data = FALSE)$bpar
-
##        Estimate se_notrans  t value       Pr(>t)      Lower       Upper
-## Z0_0 97.0148816 2.68177104 36.17568 2.363590e-25 91.5215232 102.5082401
-## k_Z0  2.2360064 0.14686238 15.22518 2.247007e-15  1.9545318   2.5580166
-## k_Z1  0.4821248 0.04268711 11.29439 3.068559e-12  0.4021552   0.5779966
+
##      Estimate se_notrans t value     Pr(>t)    Lower   Upper
+## Z0_0 97.01488   2.681771  36.176 2.3636e-25 91.52152 102.508
+## k_Z0  2.23601   0.146862  15.225 2.2470e-15  1.95453   2.558
+## k_Z1  0.48212   0.042687  11.294 3.0686e-12  0.40216   0.578

As there is only one transformation product for Z0 and no pathway to sink, the formation fraction is internally fixed to unity.

@@ -335,34 +330,27 @@ plot_sep(m.Z.5) 
plot_sep(m.Z.FOCUS)

summary(m.Z.FOCUS, data = FALSE)$bpar
-
##               Estimate se_notrans   t value       Pr(>t)       Lower
-## Z0_0       96.84024413 2.05881366 47.036916 5.572278e-44 92.70685169
-## k_Z0        2.21540096 0.11812759 18.754306 7.736886e-25  1.99050408
-## k_Z1        0.47835870 0.02929353 16.329843 3.344317e-22  0.42303496
-## k_Z2        0.45166296 0.04418624 10.221801 3.036447e-14  0.37106537
-## k_Z3        0.05868971 0.01428961  4.107158 7.256030e-05  0.03598292
-## f_Z2_to_Z3  0.47147387 0.05702672  8.267596 2.779011e-11  0.36029541
-##                   Upper
-## Z0_0       100.97363656
-## k_Z0         2.46570780
-## k_Z1         0.54091758
-## k_Z2         0.54976682
-## k_Z3         0.09572548
-## f_Z2_to_Z3   0.58555627
+
##            Estimate se_notrans t value     Pr(>t)     Lower      Upper
+## Z0_0       96.84024   2.058814 47.0369 5.5723e-44 92.706852 100.973637
+## k_Z0        2.21540   0.118128 18.7543 7.7369e-25  1.990504   2.465708
+## k_Z1        0.47836   0.029294 16.3298 3.3443e-22  0.423035   0.540918
+## k_Z2        0.45166   0.044186 10.2218 3.0364e-14  0.371065   0.549767
+## k_Z3        0.05869   0.014290  4.1072 7.2560e-05  0.035983   0.095725
+## f_Z2_to_Z3  0.47147   0.057027  8.2676 2.7790e-11  0.360295   0.585556
endpoints(m.Z.FOCUS)
## $ff
-##     Z2_Z3   Z2_sink 
-## 0.4714739 0.5285261 
+##   Z2_Z3 Z2_sink 
+## 0.47147 0.52853 
 ## 
 ## $SFORB
 ## logical(0)
 ## 
 ## $distimes
-##          DT50      DT90
-## Z0  0.3128766  1.039354
-## Z1  1.4490113  4.813512
-## Z2  1.5346558  5.098016
-## Z3 11.8103701 39.233200
+## DT50 DT90 +## Z0 0.31288 1.0394 +## Z1 1.44901 4.8135 +## Z2 1.53466 5.0980 +## Z3 11.81037 39.2332

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.

@@ -426,18 +414,18 @@ plot_sep(m.Z.mkin.5a) 
endpoints(m.Z.mkin.5a)
## $ff
 ##   Z0_free_Z1        Z1_Z2      Z2_sink   Z2_Z3_free Z3_free_sink 
-##    1.0000000    1.0000000    0.4634423    0.5365577    1.0000000 
+##      1.00000      1.00000      0.46344      0.53656      1.00000 
 ## 
 ## $SFORB
-##       Z0_b1       Z0_b2       Z3_b1       Z3_b2 
-## 2.447137325 0.007512576 0.080007563 0.000000000 
+##     Z0_b1     Z0_b2     Z3_b1     Z3_b2 
+## 2.4471373 0.0075126 0.0800076 0.0000000 
 ## 
 ## $distimes
-##         DT50     DT90 DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2
-## Z0 0.3042974 1.184810  0.2832482   92.26492         NA         NA
-## Z1 1.5147780 5.031984         NA         NA         NA         NA
-## Z2 1.6413852 5.452564         NA         NA         NA         NA
-## Z3        NA       NA         NA         NA   8.663521        Inf
+## DT50 DT90 DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2 +## Z0 0.3043 1.1848 0.28325 92.265 NA NA +## Z1 1.5148 5.0320 NA NA NA NA +## Z2 1.6414 5.4526 NA NA NA NA +## Z3 NA NA NA NA 8.6635 Inf

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.

diff --git a/vignettes/FOCUS_Z.pdf b/vignettes/FOCUS_Z.pdf new file mode 100644 index 00000000..975ad17f Binary files /dev/null and b/vignettes/FOCUS_Z.pdf differ -- cgit v1.2.1