mkin (version 1.2.6)

transform_odeparms: Functions to transform and backtransform kinetic parameters for fitting

Description

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
)

Value

A vector of transformed or backtransformed parameters

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.

Author

Johannes Ranke

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.

Examples

SFO_SFO <- mkinmod(
  parent = list(type = "SFO", to = "m1", sink = TRUE),
  m1 = list(type = "SFO"), use_of_ff = "min")

# 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$par, 3)
print(fit.s$bpar, 3)

if (FALSE) {
# 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$par, 3)
print(fit.2.s$bpar, 3)
}

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)
backtransform_odeparms(transformed, SFO_SFO)

if (FALSE) {
# 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")

fit.ff <- mkinfit(SFO_SFO.ff, FOCUS_D, quiet = TRUE)
fit.ff.s <- summary(fit.ff)
print(fit.ff.s$par, 3)
print(fit.ff.s$bpar, 3)
initials <- c("f_parent_to_m1" = 0.5)
transformed <- transform_odeparms(initials, SFO_SFO.ff)
backtransform_odeparms(transformed, SFO_SFO.ff)

# And without sink
SFO_SFO.ff.2 <- mkinmod(
  parent = list(type = "SFO", to = "m1", sink = FALSE),
  m1 = list(type = "SFO"),
  use_of_ff = "max")


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$par, 3)
print(fit.ff.2.s$bpar, 3)
}