The 12 datasets were generated using four different models and three different variance components. The four models are either the SFO or the DFOP model with either two sequential or two parallel metabolites.

Variance component 'a' is based on a normal distribution with standard deviation of 3, Variance component 'b' is also based on a normal distribution, but with a standard deviation of 7. Variance component 'c' is based on the error model from Rocke and Lorenzato (1995), with the minimum standard deviation (for small y values) of 0.5, and a proportionality constant of 0.07 for the increase of the standard deviation with y. Note that this is a simplified version of the error model proposed by Rocke and Lorenzato (1995), as in their model the error of the measured values approximates lognormal distribution for high values, whereas we are using normally distributed error components all along.

Initial concentrations for metabolites and all values where adding the variance component resulted in a value below the assumed limit of detection of 0.1 were set to NA.

As an example, the first dataset has the title SFO_lin_a and is based on the SFO model with two sequential metabolites (linear pathway), with added variance component 'a'.

Compare also the code in the example section to see the degradation models.

synthetic_data_for_UBA_2014

## Format

A list containing twelve datasets as an R6 class defined by mkinds, each containing, among others, the following components

title

The name of the dataset, e.g. SFO_lin_a

data

A data frame with the data in the form expected by mkinfit

## Source

Ranke (2014) Prüfung und Validierung von Modellierungssoftware als Alternative zu ModelMaker 4.0, Umweltbundesamt Projektnummer 27452

Rocke, David M. und Lorenzato, Stefan (1995) A two-component model for measurement error in analytical chemistry. Technometrics 37(2), 176-184.

## Examples

# The data have been generated using the following kinetic models
m_synth_SFO_lin <- mkinmod(parent = list(type = "SFO", to = "M1"),
M1 = list(type = "SFO", to = "M2"),
M2 = list(type = "SFO"), use_of_ff = "max")

m_synth_SFO_par <- mkinmod(parent = list(type = "SFO", to = c("M1", "M2"),
sink = FALSE),
M1 = list(type = "SFO"),
M2 = list(type = "SFO"), use_of_ff = "max")

m_synth_DFOP_lin <- mkinmod(parent = list(type = "DFOP", to = "M1"),
M1 = list(type = "SFO", to = "M2"),
M2 = list(type = "SFO"), use_of_ff = "max")

m_synth_DFOP_par <- mkinmod(parent = list(type = "DFOP", to = c("M1", "M2"),
sink = FALSE),
M1 = list(type = "SFO"),
M2 = list(type = "SFO"), use_of_ff = "max")

# The model predictions without intentional error were generated as follows
sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)

d_synth_SFO_lin <- mkinpredict(m_synth_SFO_lin,
c(k_parent = 0.7, f_parent_to_M1 = 0.8,
k_M1 = 0.3, f_M1_to_M2 = 0.7,
k_M2 = 0.02),
c(parent = 100, M1 = 0, M2 = 0),
sampling_times)

d_synth_DFOP_lin <- mkinpredict(m_synth_DFOP_lin,
c(k1 = 0.2, k2 = 0.02, g = 0.5,
f_parent_to_M1 = 0.5, k_M1 = 0.3,
f_M1_to_M2 = 0.7, k_M2 = 0.02),
c(parent = 100, M1 = 0, M2 = 0),
sampling_times)

d_synth_SFO_par <- mkinpredict(m_synth_SFO_par,
c(k_parent = 0.2,
f_parent_to_M1 = 0.8, k_M1 = 0.01,
f_parent_to_M2 = 0.2, k_M2 = 0.02),
c(parent = 100, M1 = 0, M2 = 0),
sampling_times)

d_synth_DFOP_par <- mkinpredict(m_synth_DFOP_par,
c(k1 = 0.3, k2 = 0.02, g = 0.7,
f_parent_to_M1 = 0.6, k_M1 = 0.04,
f_parent_to_M2 = 0.4, k_M2 = 0.01),
c(parent = 100, M1 = 0, M2 = 0),
sampling_times)

# Construct names for datasets with errors
d_synth_names = paste0("d_synth_", c("SFO_lin", "SFO_par",
"DFOP_lin", "DFOP_par"))

# Function for adding errors. The add_err function now published with this
# package is a slightly generalised version where the names of secondary
# compartments that should have an initial value of zero (M1 and M2 in this
# case) are not hardcoded any more.
add_err = function(d, sdfunc, LOD = 0.1, reps = 2, seed = 123456789)
{
set.seed(seed)
d_long = mkin_wide_to_long(d, time = "time")
d_rep = data.frame(lapply(d_long, rep, each = 2))
d_rep$value = rnorm(length(d_rep$value), d_rep$value, sdfunc(d_rep$value))

d_rep[d_rep$time == 0 & d_rep$name
d_NA <- transform(d_rep, value = ifelse(value < LOD, NA, value))
d_NA$value <- round(d_NA$value, 1)
return(d_NA)
}

# The following is the two-component model of Rocke and Lorenzato (1995)
sdfunc_twocomp = function(value, sd_low, rsd_high) {
sqrt(sd_low^2 + value^2 * rsd_high^2)
}

for (d_synth_name in d_synth_names)
{
d_synth = get(d_synth_name)
fit <- mkinfit(m_synth_SFO_lin, synthetic_data_for_UBA_2014[[1]]$data, quiet = TRUE) plot_sep(fit) summary(fit) #> Error: <text>:67:43: Unerwartete(s) SPECIAL #> 66: #> 67: d_rep[d_rep$time == 0 & d_rep\$name <!-- %in%
#>                                               ^