Example evaluation of FOCUS Laboratory Data L1 to L3

Johannes Ranke

Last change 18 May 2022 (rebuilt 2023-02-17)

- +

Last change 18 May 2023 (rebuilt 2023-05-18)

+ + +

Laboratory Data L1
Laboratory Data L2 +
- SFO fit for L2
- FOMC fit for L2
- DFOP fit for L2
Laboratory Data L3 +
- Fit multiple models
- Accessing mmkin objects
Laboratory Data L4
References

Laboratory Data L1

The following code defines example dataset L1 from the FOCUS kinetics report, p. 284:

library("mkin", quietly = TRUE)
-FOCUS_2006_L1 = data.frame(
-  t = rep(c(0, 1, 2, 3, 5, 7, 14, 21, 30), each = 2),
-  parent = c(88.3, 91.4, 85.6, 84.5, 78.9, 77.6,
-             72.0, 71.9, 50.3, 59.4, 47.0, 45.1,
-             27.7, 27.3, 10.0, 10.4, 2.9, 4.0))
-FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1)

library("mkin", quietly = TRUE)
+FOCUS_2006_L1 = data.frame(
+  t = rep(c(0, 1, 2, 3, 5, 7, 14, 21, 30), each = 2),
+  parent = c(88.3, 91.4, 85.6, 84.5, 78.9, 77.6,
+             72.0, 71.9, 50.3, 59.4, 47.0, 45.1,
+             27.7, 27.3, 10.0, 10.4, 2.9, 4.0))
+FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1)

Here we use the assumptions of simple first order (SFO), the case of declining rate constant over time (FOMC) and the case of two different phases of the kinetics (DFOP). For a more detailed discussion of the @@ -1559,12 +406,12 @@ like "SFO" for parent only degradation models. The following two lines fit the model and produce the summary report of the model fit. This covers the numerical analysis given in the FOCUS report.

m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet = TRUE)
-summary(m.L1.SFO)

## mkin version used for fitting:    1.2.2 
-## R version used for fitting:       4.2.2 
-## Date of fit:     Fri Feb 17 20:04:32 2023 
-## Date of summary: Fri Feb 17 20:04:32 2023 
+m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet = TRUE)
+summary(m.L1.SFO)
+## mkin version used for fitting:    1.2.4 
+## R version used for fitting:       4.3.0 
+## Date of fit:     Thu May 18 11:38:11 2023 
+## Date of summary: Thu May 18 11:38:11 2023 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent * parent
@@ -1647,27 +494,27 @@ summary(m.L1.SFO)
 ##    30   parent      4.0     5.251  -1.2513

A plot of the fit is obtained with the plot function for mkinfit objects.

plot(m.L1.SFO, show_errmin = TRUE, main = "FOCUS L1 - SFO")

plot(m.L1.SFO, show_errmin = TRUE, main = "FOCUS L1 - SFO")

The residual plot can be easily obtained by

mkinresplot(m.L1.SFO, ylab = "Observed", xlab = "Time")

mkinresplot(m.L1.SFO, ylab = "Observed", xlab = "Time")

For comparison, the FOMC model is fitted as well, and the χ² error level is checked.

m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE)

m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE)

## Warning in mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet = TRUE): Optimisation did not converge:
 ## false convergence (8)

plot(m.L1.FOMC, show_errmin = TRUE, main = "FOCUS L1 - FOMC")

plot(m.L1.FOMC, show_errmin = TRUE, main = "FOCUS L1 - FOMC")

summary(m.L1.FOMC, data = FALSE)

summary(m.L1.FOMC, data = FALSE)

## Warning in sqrt(diag(covar)): NaNs produced

## Warning in sqrt(1/diag(V)): NaNs produced

## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
-## doubtful

## mkin version used for fitting:    1.2.2 
-## R version used for fitting:       4.2.2 
-## Date of fit:     Fri Feb 17 20:04:32 2023 
-## Date of summary: Fri Feb 17 20:04:32 2023 
+## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result
+## is doubtful
+## mkin version used for fitting:    1.2.4 
+## R version used for fitting:       4.3.0 
+## Date of fit:     Thu May 18 11:38:11 2023 
+## Date of summary: Thu May 18 11:38:11 2023 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
@@ -1771,20 +618,20 @@ sponsored by the German Umweltbundesamt (Ranke
 Laboratory Data L2
 The following code defines example dataset L2 from the FOCUS kinetics
 report, p. 287:
-FOCUS_2006_L2 = data.frame(
-  t = rep(c(0, 1, 3, 7, 14, 28), each = 2),
-  parent = c(96.1, 91.8, 41.4, 38.7,
-             19.3, 22.3, 4.6, 4.6,
-             2.6, 1.2, 0.3, 0.6))
-FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2)
+FOCUS_2006_L2 = data.frame(
+  t = rep(c(0, 1, 3, 7, 14, 28), each = 2),
+  parent = c(96.1, 91.8, 41.4, 38.7,
+             19.3, 22.3, 4.6, 4.6,
+             2.6, 1.2, 0.3, 0.6))
+FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2)
 
 SFO fit for L2
 Again, the SFO model is fitted and the result is plotted. The
 residual plot can be obtained simply by adding the argument
 show_residuals to the plot command.
-m.L2.SFO <- mkinfit("SFO", FOCUS_2006_L2_mkin, quiet=TRUE)
-plot(m.L2.SFO, show_residuals = TRUE, show_errmin = TRUE,
-     main = "FOCUS L2 - SFO")
+m.L2.SFO <- mkinfit("SFO", FOCUS_2006_L2_mkin, quiet=TRUE)
+plot(m.L2.SFO, show_residuals = TRUE, show_errmin = TRUE,
+     main = "FOCUS L2 - SFO")
 
 The χ² error
 level of 14% suggests that the model does not fit very well. This is
@@ -1805,22 +652,22 @@ kinetics.
 FOMC fit for L2
 For comparison, the FOMC model is fitted as well, and the χ² error level is
 checked.
-m.L2.FOMC <- mkinfit("FOMC", FOCUS_2006_L2_mkin, quiet = TRUE)
-plot(m.L2.FOMC, show_residuals = TRUE,
-     main = "FOCUS L2 - FOMC")
+m.L2.FOMC <- mkinfit("FOMC", FOCUS_2006_L2_mkin, quiet = TRUE)
+plot(m.L2.FOMC, show_residuals = TRUE,
+     main = "FOCUS L2 - FOMC")
 
-summary(m.L2.FOMC, data = FALSE)
-## mkin version used for fitting:    1.2.2 
-## R version used for fitting:       4.2.2 
-## Date of fit:     Fri Feb 17 20:04:32 2023 
-## Date of summary: Fri Feb 17 20:04:32 2023 
+summary(m.L2.FOMC, data = FALSE)
+## mkin version used for fitting:    1.2.4 
+## R version used for fitting:       4.3.0 
+## Date of fit:     Thu May 18 11:38:11 2023 
+## Date of summary: Thu May 18 11:38:11 2023 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 239 model solutions performed in 0.014 s
+## Fitted using 239 model solutions performed in 0.015 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -1886,15 +733,15 @@ order to explain the data.
 
 DFOP fit for L2
 Fitting the four parameter DFOP model further reduces the χ² error level.
-m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin, quiet = TRUE)
-plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
-     main = "FOCUS L2 - DFOP")
+m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin, quiet = TRUE)
+plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
+     main = "FOCUS L2 - DFOP")
 
-summary(m.L2.DFOP, data = FALSE)
-## mkin version used for fitting:    1.2.2 
-## R version used for fitting:       4.2.2 
-## Date of fit:     Fri Feb 17 20:04:32 2023 
-## Date of summary: Fri Feb 17 20:04:32 2023 
+summary(m.L2.DFOP, data = FALSE)
+## mkin version used for fitting:    1.2.4 
+## R version used for fitting:       4.3.0 
+## Date of fit:     Thu May 18 11:38:11 2023 
+## Date of summary: Thu May 18 11:38:11 2023 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -1903,7 +750,7 @@ plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 581 model solutions performed in 0.039 s
+## Fitted using 581 model solutions performed in 0.041 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -1974,21 +821,21 @@ based on the chi^2 error level criterion.
 Laboratory Data L3
 The following code defines example dataset L3 from the FOCUS kinetics
 report, p. 290.
-FOCUS_2006_L3 = data.frame(
-  t = c(0, 3, 7, 14, 30, 60, 91, 120),
-  parent = c(97.8, 60, 51, 43, 35, 22, 15, 12))
-FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3)
+FOCUS_2006_L3 = data.frame(
+  t = c(0, 3, 7, 14, 30, 60, 91, 120),
+  parent = c(97.8, 60, 51, 43, 35, 22, 15, 12))
+FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3)
 
 Fit multiple models
 As of mkin version 0.9-39 (June 2015), we can fit several models to
 one or more datasets in one call to the function mmkin. The
 datasets have to be passed in a list, in this case a named list holding
 only the L3 dataset prepared above.
-# Only use one core here, not to offend the CRAN checks
-mm.L3 <- mmkin(c("SFO", "FOMC", "DFOP"), cores = 1,
-               list("FOCUS L3" = FOCUS_2006_L3_mkin), quiet = TRUE)
-plot(mm.L3)
-
+# Only use one core here, not to offend the CRAN checks
+mm.L3 <- mmkin(c("SFO", "FOMC", "DFOP"), cores = 1,
+               list("FOCUS L3" = FOCUS_2006_L3_mkin), quiet = TRUE)
+plot(mm.L3)
+
 The χ² error
 level of 21% as well as the plot suggest that the SFO model does not fit
 very well. The FOMC model performs better, with an error level at which
@@ -2003,11 +850,11 @@ as a row index and datasets as a column index.
 We can extract the summary and plot for e.g. the DFOP fit,
 using square brackets for indexing which will result in the use of the
 summary and plot functions working on mkinfit objects.
-summary(mm.L3[["DFOP", 1]])
-## mkin version used for fitting:    1.2.2 
-## R version used for fitting:       4.2.2 
-## Date of fit:     Fri Feb 17 20:04:33 2023 
-## Date of summary: Fri Feb 17 20:04:33 2023 
+summary(mm.L3[["DFOP", 1]])
+## mkin version used for fitting:    1.2.4 
+## R version used for fitting:       4.3.0 
+## Date of fit:     Thu May 18 11:38:12 2023 
+## Date of summary: Thu May 18 11:38:12 2023 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -2016,7 +863,7 @@ summary and plot functions working on mkinfit objects.
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 376 model solutions performed in 0.023 s
+## Fitted using 376 model solutions performed in 0.024 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -2090,8 +937,8 @@ summary and plot functions working on mkinfit objects.
 ##    60   parent     22.0     23.26 -1.25919
 ##    91   parent     15.0     15.18 -0.18181
 ##   120   parent     12.0     10.19  1.81395
-plot(mm.L3[["DFOP", 1]], show_errmin = TRUE)
-
+plot(mm.L3[["DFOP", 1]], show_errmin = TRUE)
+
 Here, a look to the model plot, the confidence intervals of the
 parameters and the correlation matrix suggest that the parameter
 estimates are reliable, and the DFOP model can be used as the best-fit
@@ -2108,35 +955,35 @@ parameter g is quite narrow.
 Laboratory Data L4
 The following code defines example dataset L4 from the FOCUS kinetics
 report, p. 293:
-FOCUS_2006_L4 = data.frame(
-  t = c(0, 3, 7, 14, 30, 60, 91, 120),
-  parent = c(96.6, 96.3, 94.3, 88.8, 74.9, 59.9, 53.5, 49.0))
-FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4)
+FOCUS_2006_L4 = data.frame(
+  t = c(0, 3, 7, 14, 30, 60, 91, 120),
+  parent = c(96.6, 96.3, 94.3, 88.8, 74.9, 59.9, 53.5, 49.0))
+FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4)
 Fits of the SFO and FOMC models, plots and summaries are produced
 below:
-# Only use one core here, not to offend the CRAN checks
-mm.L4 <- mmkin(c("SFO", "FOMC"), cores = 1,
-               list("FOCUS L4" = FOCUS_2006_L4_mkin),
-               quiet = TRUE)
-plot(mm.L4)
-
+# Only use one core here, not to offend the CRAN checks
+mm.L4 <- mmkin(c("SFO", "FOMC"), cores = 1,
+               list("FOCUS L4" = FOCUS_2006_L4_mkin),
+               quiet = TRUE)
+plot(mm.L4)
+
 The χ² error
 level of 3.3% as well as the plot suggest that the SFO model fits very
 well. The error level at which the χ² test passes is
 slightly lower for the FOMC model. However, the difference appears
 negligible.
-summary(mm.L4[["SFO", 1]], data = FALSE)
-## mkin version used for fitting:    1.2.2 
-## R version used for fitting:       4.2.2 
-## Date of fit:     Fri Feb 17 20:04:33 2023 
-## Date of summary: Fri Feb 17 20:04:33 2023 
+summary(mm.L4[["SFO", 1]], data = FALSE)
+## mkin version used for fitting:    1.2.4 
+## R version used for fitting:       4.3.0 
+## Date of fit:     Thu May 18 11:38:12 2023 
+## Date of summary: Thu May 18 11:38:12 2023 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 142 model solutions performed in 0.008 s
+## Fitted using 142 model solutions performed in 0.01 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -2189,11 +1036,11 @@ negligible.
 ## Estimated disappearance times:
 ##        DT50 DT90
 ## parent  106  352
-summary(mm.L4[["FOMC", 1]], data = FALSE)
-## mkin version used for fitting:    1.2.2 
-## R version used for fitting:       4.2.2 
-## Date of fit:     Fri Feb 17 20:04:33 2023 
-## Date of summary: Fri Feb 17 20:04:33 2023 
+summary(mm.L4[["FOMC", 1]], data = FALSE)
+## mkin version used for fitting:    1.2.4 
+## R version used for fitting:       4.3.0 
+## Date of fit:     Thu May 18 11:38:12 2023 
+## Date of summary: Thu May 18 11:38:12 2023 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
@@ -2272,69 +1119,8 @@ Validierung von Modellierungssoftware als Alternative zu ModelMaker
 
 
 
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diff --git a/vignettes/FOCUS_L.rmd b/vignettes/FOCUS_L.rmd
index 2dafa74d..69105e92 100644
--- a/vignettes/FOCUS_L.rmd
+++ b/vignettes/FOCUS_L.rmd
@@ -1,14 +1,11 @@
 ---
 title: "Example evaluation of FOCUS Laboratory Data L1 to L3"
 author: "Johannes Ranke"
-date: Last change 18 May 2022 (rebuilt `r Sys.Date()`)
+date: Last change 18 May 2023 (rebuilt `r Sys.Date()`)
 output:
-  html_document:
+  html_vignette:
     toc: true
-    toc_float:
-      collapsed: false
     mathjax: null
-    fig_retina: null
 references:
 - id: ranke2014
   title: Prüfung und Validierung von Modellierungssoftware als Alternative zu
diff --git a/vignettes/mkin.html b/vignettes/mkin.html
index a16f3074..12b8671e 100644
--- a/vignettes/mkin.html
+++ b/vignettes/mkin.html
@@ -8,1376 +8,36 @@
 
 
 
+
 
-
-
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-Introduction to mkin
-
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+@media print {
+pre > code.sourceCode { white-space: pre-wrap; }
+pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; }
+}
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+  { counter-reset: source-line 0; }
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+pre.numberSource code > span > a:first-child::before
+  { content: counter(source-line);
+    position: relative; left: -1em; text-align: right; vertical-align: baseline;
+    border: none; display: inline-block;
+    -webkit-touch-callout: none; -webkit-user-select: none;
+    -khtml-user-select: none; -moz-user-select: none;
+    -ms-user-select: none; user-select: none;
+    padding: 0 4px; width: 4em;
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+  }
+pre.numberSource { margin-left: 3em; border-left: 1px solid #aaaaaa;  padding-left: 4px; }
+div.sourceCode
+  {   }
+@media screen {
+pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
+}
+code span.al { color: #ff0000; font-weight: bold; } /* Alert */
+code span.an { color: #60a0b0; font-weight: bold; font-style: italic; } /* Annotation */
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+code span.dt { color: #902000; } /* DataType */
+code span.dv { color: #40a070; } /* DecVal */
+code span.er { color: #ff0000; font-weight: bold; } /* Error */
+code span.ex { } /* Extension */
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+code span.fu { color: #06287e; } /* Function */
+code span.im { color: #008000; font-weight: bold; } /* Import */
+code span.in { color: #60a0b0; font-weight: bold; font-style: italic; } /* Information */
+code span.kw { color: #007020; font-weight: bold; } /* Keyword */
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+code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
 
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+
 
 
 
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+
 
 
 
 
 
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+Short introduction to mkin
+Johannes Ranke
+Last change 18 May 2023 (rebuilt 2023-05-19)
 
-
 
-
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-Show All Code
-Hide All Code
+
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+Abstract
+Background
+
+Derived software tools
+
+Unique features
+Internal parameter
+transformations
+
+Confidence
+intervals based on transformed parameters
+Parameter
+t-test based on untransformed parameters
+
+References
 
 
 
-
-
-Introduction to mkin
-Johannes Ranke
-Last change 15 February 2021 (rebuilt 2023-02-17)
-
-
-
-
 Wissenschaftlicher Berater, Kronacher
 Str. 12, 79639 Grenzach-Wyhlen, Germany
 Privatdozent at the
 University of Freiburg
@@ -1633,34 +409,36 @@ nonlinear optimisation. The R add-on package
 this guidance from within R and calculates some statistical measures for
 data series within one or more compartments, for parent and
 metabolites.
-library("mkin", quietly = TRUE)
-# Define the kinetic model
-m_SFO_SFO_SFO <- mkinmod(parent = mkinsub("SFO", "M1"),
-                         M1 = mkinsub("SFO", "M2"),
-                         M2 = mkinsub("SFO"),
-                         use_of_ff = "max", quiet = TRUE)
-
-
-# Produce model predictions using some arbitrary parameters
-sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
-d_SFO_SFO_SFO <- mkinpredict(m_SFO_SFO_SFO,
-  c(k_parent = 0.03,
-    f_parent_to_M1 = 0.5, k_M1 = log(2)/100,
-    f_M1_to_M2 = 0.9, k_M2 = log(2)/50),
-  c(parent = 100, M1 = 0, M2 = 0),
-  sampling_times)
-
-# Generate a dataset by adding normally distributed errors with
-# standard deviation 3, for two replicates at each sampling time
-d_SFO_SFO_SFO_err <- add_err(d_SFO_SFO_SFO, reps = 2,
-                             sdfunc = function(x) 3,
-                             n = 1, seed = 123456789 )
-
-# Fit the model to the dataset
-f_SFO_SFO_SFO <- mkinfit(m_SFO_SFO_SFO, d_SFO_SFO_SFO_err[[1]], quiet = TRUE)
-
-# Plot the results separately for parent and metabolites
-plot_sep(f_SFO_SFO_SFO, lpos = c("topright", "bottomright", "bottomright"))
+Code
+library("mkin", quietly = TRUE)
+# Define the kinetic model
+m_SFO_SFO_SFO <- mkinmod(parent = mkinsub("SFO", "M1"),
+                         M1 = mkinsub("SFO", "M2"),
+                         M2 = mkinsub("SFO"),
+                         use_of_ff = "max", quiet = TRUE)
+
+
+# Produce model predictions using some arbitrary parameters
+sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
+d_SFO_SFO_SFO <- mkinpredict(m_SFO_SFO_SFO,
+  c(k_parent = 0.03,
+    f_parent_to_M1 = 0.5, k_M1 = log(2)/100,
+    f_M1_to_M2 = 0.9, k_M2 = log(2)/50),
+  c(parent = 100, M1 = 0, M2 = 0),
+  sampling_times)
+
+# Generate a dataset by adding normally distributed errors with
+# standard deviation 3, for two replicates at each sampling time
+d_SFO_SFO_SFO_err <- add_err(d_SFO_SFO_SFO, reps = 2,
+                             sdfunc = function(x) 3,
+                             n = 1, seed = 123456789 )
+
+# Fit the model to the dataset
+f_SFO_SFO_SFO <- mkinfit(m_SFO_SFO_SFO, d_SFO_SFO_SFO_err[[1]], quiet = TRUE)
+
+# Plot the results separately for parent and metabolites
+plot_sep(f_SFO_SFO_SFO, lpos = c("topright", "bottomright", "bottomright"))
+
 
 
 
@@ -1906,74 +684,8 @@ Sensitivity and Monte Carlo Analysis in R Using Package
 
 
 
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Example evaluation of FOCUS Example Dataset D

Johannes Ranke

Last change 31 January 2019 (rebuilt 2023-02-17)

Last change 31 January 2019 (rebuilt 2023-05-18)

Example evaluation of FOCUS Laboratory Data L1 to L3

Johannes Ranke

Last change 18 May 2022 (rebuilt 2023-02-17)

Last change 18 May 2023 (rebuilt 2023-05-18)

Laboratory Data L1

Laboratory Data L2

SFO fit for L2

FOMC fit for L2

DFOP fit for L2

Laboratory Data L3

Fit multiple models

Laboratory Data L4

Short introduction to mkin

Johannes Ranke

Last change 18 May 2023 (rebuilt 2023-05-19)