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 paramters 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.

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.

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.
transparms	Transformed parameters of kinetic models as used in the fitting procedure.
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 and HS models are also transformed, as they can also be seen as compositional data. The transformation used for these transformations is the ilr transformation.

Value

A vector of transformed or backtransformed parameters with the same names as the original parameters.

Examples

SFO_SFO <- mkinmod(
  parent = list(type = "SFO", to = "m1", sink = TRUE),
  m1 = list(type = "SFO"))
#> Successfully compiled differential equation model from auto-generated C code.
# Fit the model to the FOCUS example dataset D using defaults
fit <- mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE)
#> Warning: Observations with value of zero were removed from the data
fit.s <- summary(fit)
#> Warning: Could not calculate correlation; no covariance matrix
# Transformed and backtransformed parameters
print(fit.s$par, 3)
#>                   Estimate Std. Error Lower Upper
#> parent_0             99.60         NA    NA    NA
#> log_k_parent_sink    -3.04         NA    NA    NA
#> log_k_parent_m1      -2.98         NA    NA    NA
#> log_k_m1_sink        -5.25         NA    NA    NA
#> sigma                 3.13         NA    NA    NA
print(fit.s$bpar, 3)
#>               Estimate se_notrans t value Pr(>t) Lower Upper
#> parent_0      99.59848         NA      NA     NA    NA    NA
#> k_parent_sink  0.04792         NA      NA     NA    NA    NA
#> k_parent_m1    0.05078         NA      NA     NA    NA    NA
#> k_m1_sink      0.00526         NA      NA     NA    NA    NA
#> sigma          3.12550         NA      NA     NA    NA    NA

# Compare to the version without transforming rate parameters
fit.2 <- mkinfit(SFO_SFO, FOCUS_2006_D, transform_rates = FALSE, quiet = TRUE)
#> Warning: Observations with value of zero were removed from the data
fit.2.s <- summary(fit.2)
#> Warning: Could not calculate correlation; no covariance matrix
print(fit.2.s$par, 3)
#>               Estimate Std. Error Lower Upper
#> parent_0      99.59848         NA    NA    NA
#> k_parent_sink  0.04792         NA    NA    NA
#> k_parent_m1    0.05078         NA    NA    NA
#> k_m1_sink      0.00526         NA    NA    NA
#> sigma          3.12550         NA    NA    NA
print(fit.2.s$bpar, 3)
#>               Estimate se_notrans t value Pr(>t) Lower Upper
#> parent_0      99.59848         NA      NA     NA    NA    NA
#> k_parent_sink  0.04792         NA      NA     NA    NA    NA
#> k_parent_m1    0.05078         NA      NA     NA    NA    NA
#> k_m1_sink      0.00526         NA      NA     NA    NA    NA
#> sigma          3.12550         NA      NA     NA    NA    NA

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 

# The case of formation fractions
SFO_SFO.ff <- mkinmod(
  parent = list(type = "SFO", to = "m1", sink = TRUE),
  m1 = list(type = "SFO"),
  use_of_ff = "max")
#> Successfully compiled differential equation model from auto-generated C code.

fit.ff <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, quiet = TRUE)
#> Warning: Observations with value of zero were removed from the data
fit.ff.s <- summary(fit.ff)
#> Warning: Could not calculate correlation; no covariance matrix
print(fit.ff.s$par, 3)
#>                Estimate Std. Error Lower Upper
#> parent_0         99.598         NA    NA    NA
#> log_k_parent     -2.316         NA    NA    NA
#> log_k_m1         -5.248         NA    NA    NA
#> f_parent_ilr_1    0.041         NA    NA    NA
#> sigma             3.126         NA    NA    NA
print(fit.ff.s$bpar, 3)
#>                Estimate se_notrans t value Pr(>t) Lower Upper
#> parent_0       99.59848         NA      NA     NA    NA    NA
#> k_parent        0.09870         NA      NA     NA    NA    NA
#> k_m1            0.00526         NA      NA     NA    NA    NA
#> f_parent_to_m1  0.51448         NA      NA     NA    NA    NA
#> sigma           3.12550         NA      NA     NA    NA    NA
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")
#> Successfully compiled differential equation model from auto-generated C code.


fit.ff.2 <- mkinfit(SFO_SFO.ff.2, FOCUS_2006_D, quiet = TRUE)
#> Warning: Observations with value of zero were removed from the data
fit.ff.2.s <- summary(fit.ff.2)
#> Warning: Could not calculate correlation; no covariance matrix
print(fit.ff.2.s$par, 3)
#>              Estimate Std. Error Lower Upper
#> parent_0        84.79         NA    NA    NA
#> log_k_parent    -2.76         NA    NA    NA
#> log_k_m1        -4.21         NA    NA    NA
#> sigma            8.22         NA    NA    NA
print(fit.ff.2.s$bpar, 3)
#>          Estimate se_notrans t value Pr(>t) Lower Upper
#> parent_0  84.7916         NA      NA     NA    NA    NA
#> k_parent   0.0635         NA      NA     NA    NA    NA
#> k_m1       0.0148         NA      NA     NA    NA    NA
#> sigma      8.2229         NA      NA     NA    NA    NA