Functions to transform and backtransform kinetic parameters for fitting

+ +

The transformations are intended to map parameters that should only take on +restricted values to the full scale of real numbers. For kinetic rate +constants and other parameters that can only take on positive values, a +simple log transformation is used. For compositional parameters, such as the +formations fractions that should always sum up to 1 and can not be negative, +the ilr transformation is used.

+ +

Usage

transform_odeparms(
+  parms,
+  mkinmod,
+  transform_rates = TRUE,
+  transform_fractions = TRUE
+)
+
+backtransform_odeparms(
+  transparms,
+  mkinmod,
+  transform_rates = TRUE,
+  transform_fractions = TRUE
+)

+ +

Arguments

+ + +

parms: Parameters of kinetic models as used in the differential +equations.
mkinmod: The kinetic model of class mkinmod, containing +the names of the model variables that are needed for grouping the +formation fractions before ilr transformation, the parameter +names and the information if the pathway to sink is included in the model.
transform_rates: Boolean specifying if kinetic rate constants should +be transformed in the model specification used in the fitting for better +compliance with the assumption of normal distribution of the estimator. If +TRUE, also alpha and beta parameters of the FOMC model are +log-transformed, as well as k1 and k2 rate constants for the DFOP and HS +models and the break point tb of the HS model.
transform_fractions: Boolean specifying if formation fractions +constants should be transformed in the model specification used in the +fitting for better compliance with the assumption of normal distribution +of the estimator. The default (TRUE) is to do transformations. +The g parameter of the DFOP model is also seen as a fraction. +If a single fraction is transformed (g parameter of DFOP or only a single +target variable e.g. a single metabolite plus a pathway to sink), a +logistic transformation is used stats::qlogis(). In other cases, i.e. if +two or more formation fractions need to be transformed whose sum cannot +exceed one, the ilr transformation is used.
transparms: Transformed parameters of kinetic models as used in the +fitting procedure.

Value

A vector of transformed or backtransformed parameters

Details

The transformation of sets of formation fractions is fragile, as it supposes +the same ordering of the components in forward and backward transformation. +This is no problem for the internal use in mkinfit.

Author

Johannes Ranke

+ +

Examples


+SFO_SFO <- mkinmod(
+  parent = list(type = "SFO", to = "m1", sink = TRUE),
+  m1 = list(type = "SFO"), use_of_ff = "min")
+#> Temporary DLL for differentials generated and loaded
+
+# Fit the model to the FOCUS example dataset D using defaults
+FOCUS_D <- subset(FOCUS_2006_D, value != 0) # remove zero values to avoid warning
+fit <- mkinfit(SFO_SFO, FOCUS_D, quiet = TRUE)
+fit.s <- summary(fit)
+# Transformed and backtransformed parameters
+print(fit.s$par, 3)
+#>                   Estimate Std. Error Lower  Upper
+#> parent_0             99.60     1.5702 96.40 102.79
+#> log_k_parent_sink    -3.04     0.0763 -3.19  -2.88
+#> log_k_parent_m1      -2.98     0.0403 -3.06  -2.90
+#> log_k_m1_sink        -5.25     0.1332 -5.52  -4.98
+#> sigma                 3.13     0.3585  2.40   3.85
+print(fit.s$bpar, 3)
+#>               Estimate se_notrans t value   Pr(>t)    Lower    Upper
+#> parent_0      99.59848    1.57022   63.43 2.30e-36 96.40384 102.7931
+#> k_parent_sink  0.04792    0.00365   13.11 6.13e-15  0.04103   0.0560
+#> k_parent_m1    0.05078    0.00205   24.80 3.27e-23  0.04678   0.0551
+#> k_m1_sink      0.00526    0.00070    7.51 6.16e-09  0.00401   0.0069
+#> sigma          3.12550    0.35852    8.72 2.24e-10  2.39609   3.8549
+
+# \dontrun{
+# Compare to the version without transforming rate parameters (does not work
+# with analytical solution, we get NA values for m1 in predictions)
+fit.2 <- mkinfit(SFO_SFO, FOCUS_D, transform_rates = FALSE,
+  solution_type = "deSolve", quiet = TRUE)
+fit.2.s <- summary(fit.2)
+print(fit.2.s$par, 3)
+#>               Estimate Std. Error    Lower    Upper
+#> parent_0      99.59848    1.57022 96.40384 1.03e+02
+#> k_parent_sink  0.04792    0.00365  0.04049 5.54e-02
+#> k_parent_m1    0.05078    0.00205  0.04661 5.49e-02
+#> k_m1_sink      0.00526    0.00070  0.00384 6.69e-03
+#> sigma          3.12550    0.35852  2.39609 3.85e+00
+print(fit.2.s$bpar, 3)
+#>               Estimate se_notrans t value   Pr(>t)    Lower    Upper
+#> parent_0      99.59848    1.57022   63.43 2.30e-36 96.40384 1.03e+02
+#> k_parent_sink  0.04792    0.00365   13.11 6.13e-15  0.04049 5.54e-02
+#> k_parent_m1    0.05078    0.00205   24.80 3.27e-23  0.04661 5.49e-02
+#> k_m1_sink      0.00526    0.00070    7.51 6.16e-09  0.00384 6.69e-03
+#> sigma          3.12550    0.35852    8.72 2.24e-10  2.39609 3.85e+00
+# }
+
+initials <- fit$start$value
+names(initials) <- rownames(fit$start)
+transformed <- fit$start_transformed$value
+names(transformed) <- rownames(fit$start_transformed)
+transform_odeparms(initials, SFO_SFO)
+#>          parent_0 log_k_parent_sink   log_k_parent_m1     log_k_m1_sink 
+#>        100.750000         -2.302585         -2.301586         -2.300587 
+backtransform_odeparms(transformed, SFO_SFO)
+#>      parent_0 k_parent_sink   k_parent_m1     k_m1_sink 
+#>      100.7500        0.1000        0.1001        0.1002 
+
+# \dontrun{
+# The case of formation fractions (this is now the default)
+SFO_SFO.ff <- mkinmod(
+  parent = list(type = "SFO", to = "m1", sink = TRUE),
+  m1 = list(type = "SFO"),
+  use_of_ff = "max")
+#> Temporary DLL for differentials generated and loaded
+
+fit.ff <- mkinfit(SFO_SFO.ff, FOCUS_D, quiet = TRUE)
+fit.ff.s <- summary(fit.ff)
+print(fit.ff.s$par, 3)
+#>                 Estimate Std. Error  Lower  Upper
+#> parent_0         99.5985     1.5702 96.404 102.79
+#> log_k_parent     -2.3157     0.0409 -2.399  -2.23
+#> log_k_m1         -5.2475     0.1332 -5.518  -4.98
+#> f_parent_qlogis   0.0579     0.0893 -0.124   0.24
+#> sigma             3.1255     0.3585  2.396   3.85
+print(fit.ff.s$bpar, 3)
+#>                Estimate se_notrans t value   Pr(>t)    Lower    Upper
+#> parent_0       99.59848    1.57022   63.43 2.30e-36 96.40383 102.7931
+#> k_parent        0.09870    0.00403   24.47 4.96e-23  0.09082   0.1073
+#> k_m1            0.00526    0.00070    7.51 6.16e-09  0.00401   0.0069
+#> f_parent_to_m1  0.51448    0.02230   23.07 3.10e-22  0.46912   0.5596
+#> sigma           3.12550    0.35852    8.72 2.24e-10  2.39609   3.8549
+initials <- c("f_parent_to_m1" = 0.5)
+transformed <- transform_odeparms(initials, SFO_SFO.ff)
+backtransform_odeparms(transformed, SFO_SFO.ff)
+#> f_parent_to_m1 
+#>            0.5 
+
+# And without sink
+SFO_SFO.ff.2 <- mkinmod(
+  parent = list(type = "SFO", to = "m1", sink = FALSE),
+  m1 = list(type = "SFO"),
+  use_of_ff = "max")
+#> Temporary DLL for differentials generated and loaded
+
+
+fit.ff.2 <- mkinfit(SFO_SFO.ff.2, FOCUS_D, quiet = TRUE)
+fit.ff.2.s <- summary(fit.ff.2)
+print(fit.ff.2.s$par, 3)
+#>              Estimate Std. Error Lower Upper
+#> parent_0        84.79      3.012 78.67 90.91
+#> log_k_parent    -2.76      0.082 -2.92 -2.59
+#> log_k_m1        -4.21      0.123 -4.46 -3.96
+#> sigma            8.22      0.943  6.31 10.14
+print(fit.ff.2.s$bpar, 3)
+#>          Estimate se_notrans t value   Pr(>t)   Lower  Upper
+#> parent_0  84.7916    3.01203   28.15 1.92e-25 78.6704 90.913
+#> k_parent   0.0635    0.00521   12.19 2.91e-14  0.0538  0.075
+#> k_m1       0.0148    0.00182    8.13 8.81e-10  0.0115  0.019
+#> sigma      8.2229    0.94323    8.72 1.73e-10  6.3060 10.140
+# }
+
+