Synthetic datasets for one parent compound with two metabolites

- - -

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.

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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

# \dontrun{
-# 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")
-#> Temporary DLL for differentials generated and loaded
-
-
-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")
-#> Temporary DLL for differentials generated and loaded
-
-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")
-#> Temporary DLL for differentials generated and loaded
-
-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")
-#> Temporary DLL for differentials generated and loaded
-
-# 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"))
-
-# Original function used or 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 %in% c("M1", "M2"), "value"] <- 0
-#   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 simplified version of 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)
-}
-
-# Add the errors.
-for (d_synth_name in d_synth_names)
-{
-  d_synth = get(d_synth_name)
-  assign(paste0(d_synth_name, "_a"), add_err(d_synth, function(value) 3))
-  assign(paste0(d_synth_name, "_b"), add_err(d_synth, function(value) 7))
-  assign(paste0(d_synth_name, "_c"), add_err(d_synth,
-                           function(value) sdfunc_twocomp(value, 0.5, 0.07)))
-
-}
-
-d_synth_err_names = c(
-  paste(rep(d_synth_names, each = 3), letters[1:3], sep = "_")
-)
-
-# This is just one example of an evaluation using the kinetic model used for
-# the generation of the data
-  fit <- mkinfit(m_synth_SFO_lin, synthetic_data_for_UBA_2014[[1]]$data,
-                 quiet = TRUE)
-  plot_sep(fit)
-
-  summary(fit)
-#> mkin version used for fitting:    1.2.3 
-#> R version used for fitting:       4.2.3 
-#> Date of fit:     Sun Apr 16 08:35:08 2023 
-#> Date of summary: Sun Apr 16 08:35:08 2023 
-#> 
-#> Equations:
-#> d_parent/dt = - k_parent * parent
-#> d_M1/dt = + f_parent_to_M1 * k_parent * parent - k_M1 * M1
-#> d_M2/dt = + f_M1_to_M2 * k_M1 * M1 - k_M2 * M2
-#> 
-#> Model predictions using solution type deSolve 
-#> 
-#> Fitted using 833 model solutions performed in 0.166 s
-#> 
-#> Error model: Constant variance 
-#> 
-#> Error model algorithm: OLS 
-#> 
-#> Starting values for parameters to be optimised:
-#>                   value   type
-#> parent_0       101.3500  state
-#> k_parent         0.1000 deparm
-#> k_M1             0.1001 deparm
-#> k_M2             0.1002 deparm
-#> f_parent_to_M1   0.5000 deparm
-#> f_M1_to_M2       0.5000 deparm
-#> 
-#> Starting values for the transformed parameters actually optimised:
-#>                      value lower upper
-#> parent_0        101.350000  -Inf   Inf
-#> log_k_parent     -2.302585  -Inf   Inf
-#> log_k_M1         -2.301586  -Inf   Inf
-#> log_k_M2         -2.300587  -Inf   Inf
-#> f_parent_qlogis   0.000000  -Inf   Inf
-#> f_M1_qlogis       0.000000  -Inf   Inf
-#> 
-#> Fixed parameter values:
-#>      value  type
-#> M1_0     0 state
-#> M2_0     0 state
-#> 
-#> Results:
-#> 
-#>        AIC      BIC    logLik
-#>   188.7274 200.3723 -87.36368
-#> 
-#> Optimised, transformed parameters with symmetric confidence intervals:
-#>                 Estimate Std. Error   Lower    Upper
-#> parent_0        102.1000    1.57000 98.8600 105.3000
-#> log_k_parent     -0.3020    0.03885 -0.3812  -0.2229
-#> log_k_M1         -1.2070    0.07123 -1.3520  -1.0620
-#> log_k_M2         -3.9010    0.06571 -4.0350  -3.7670
-#> f_parent_qlogis   1.2010    0.23530  0.7216   1.6800
-#> f_M1_qlogis       0.9589    0.24890  0.4520   1.4660
-#> sigma             2.2730    0.25740  1.7490   2.7970
-#> 
-#> Parameter correlation:
-#>                   parent_0 log_k_parent   log_k_M1   log_k_M2 f_parent_qlogis
-#> parent_0         1.000e+00    3.933e-01 -1.605e-01  2.819e-02      -4.624e-01
-#> log_k_parent     3.933e-01    1.000e+00 -4.082e-01  7.166e-02      -5.682e-01
-#> log_k_M1        -1.605e-01   -4.082e-01  1.000e+00 -3.929e-01       7.478e-01
-#> log_k_M2         2.819e-02    7.166e-02 -3.929e-01  1.000e+00      -2.658e-01
-#> f_parent_qlogis -4.624e-01   -5.682e-01  7.478e-01 -2.658e-01       1.000e+00
-#> f_M1_qlogis      1.614e-01    4.102e-01 -8.109e-01  5.419e-01      -8.605e-01
-#> sigma           -2.900e-08   -8.030e-09 -2.741e-08  3.938e-08      -2.681e-08
-#>                 f_M1_qlogis      sigma
-#> parent_0          1.614e-01 -2.900e-08
-#> log_k_parent      4.102e-01 -8.030e-09
-#> log_k_M1         -8.109e-01 -2.741e-08
-#> log_k_M2          5.419e-01  3.938e-08
-#> f_parent_qlogis  -8.605e-01 -2.681e-08
-#> f_M1_qlogis       1.000e+00  4.971e-08
-#> sigma             4.971e-08  1.000e+00
-#> 
-#> Backtransformed parameters:
-#> Confidence intervals for internally transformed parameters are asymmetric.
-#> t-test (unrealistically) based on the assumption of normal distribution
-#> for estimators of untransformed parameters.
-#>                 Estimate t value    Pr(>t)    Lower     Upper
-#> parent_0       102.10000  65.000 7.281e-36 98.86000 105.30000
-#> k_parent         0.73930  25.740 2.948e-23  0.68310   0.80020
-#> k_M1             0.29920  14.040 1.577e-15  0.25880   0.34590
-#> k_M2             0.02023  15.220 1.653e-16  0.01769   0.02312
-#> f_parent_to_M1   0.76870  18.370 7.295e-19  0.67300   0.84290
-#> f_M1_to_M2       0.72290  14.500 6.418e-16  0.61110   0.81240
-#> sigma            2.27300   8.832 2.161e-10  1.74900   2.79700
-#> 
-#> FOCUS Chi2 error levels in percent:
-#>          err.min n.optim df
-#> All data   8.454       6 17
-#> parent     8.660       2  6
-#> M1        10.583       2  5
-#> M2         3.586       2  6
-#> 
-#> Resulting formation fractions:
-#>                 ff
-#> parent_M1   0.7687
-#> parent_sink 0.2313
-#> M1_M2       0.7229
-#> M1_sink     0.2771
-#> 
-#> Estimated disappearance times:
-#>           DT50    DT90
-#> parent  0.9376   3.114
-#> M1      2.3170   7.697
-#> M2     34.2689 113.839
-#> 
-#> Data:
-#>  time variable observed  predicted residual
-#>     0   parent    101.5  1.021e+02 -0.56248
-#>     0   parent    101.2  1.021e+02 -0.86248
-#>     1   parent     53.9  4.873e+01  5.17118
-#>     1   parent     47.5  4.873e+01 -1.22882
-#>     3   parent     10.4  1.111e+01 -0.70773
-#>     3   parent      7.6  1.111e+01 -3.50773
-#>     7   parent      1.1  5.772e-01  0.52283
-#>     7   parent      0.3  5.772e-01 -0.27717
-#>    14   parent      3.5  3.264e-03  3.49674
-#>    28   parent      3.2  1.045e-07  3.20000
-#>    90   parent      0.6  9.530e-10  0.60000
-#>   120   parent      3.5 -5.940e-10  3.50000
-#>     1       M1     36.4  3.479e+01  1.61088
-#>     1       M1     37.4  3.479e+01  2.61088
-#>     3       M1     34.3  3.937e+01 -5.07027
-#>     3       M1     39.8  3.937e+01  0.42973
-#>     7       M1     15.1  1.549e+01 -0.38715
-#>     7       M1     17.8  1.549e+01  2.31285
-#>    14       M1      5.8  1.995e+00  3.80469
-#>    14       M1      1.2  1.995e+00 -0.79531
-#>    60       M1      0.5  2.111e-06  0.50000
-#>    90       M1      3.2 -9.670e-10  3.20000
-#>   120       M1      1.5  7.670e-10  1.50000
-#>   120       M1      0.6  7.670e-10  0.60000
-#>     1       M2      4.8  4.455e+00  0.34517
-#>     3       M2     20.9  2.153e+01 -0.62527
-#>     3       M2     19.3  2.153e+01 -2.22527
-#>     7       M2     42.0  4.192e+01  0.07941
-#>     7       M2     43.1  4.192e+01  1.17941
-#>    14       M2     49.4  4.557e+01  3.83353
-#>    14       M2     44.3  4.557e+01 -1.26647
-#>    28       M2     34.6  3.547e+01 -0.87275
-#>    28       M2     33.0  3.547e+01 -2.47275
-#>    60       M2     18.8  1.858e+01  0.21837
-#>    60       M2     17.6  1.858e+01 -0.98163
-#>    90       M2     10.6  1.013e+01  0.47130
-#>    90       M2     10.8  1.013e+01  0.67130
-#>   120       M2      9.8  5.521e+00  4.27893
-#>   120       M2      3.3  5.521e+00 -2.22107
-# }
-

- -