Insight on the structural model

Prerequisite

The examples below require the package campismod.

library(campsismod)

Equation

Equations are described by 3 fields:

• lhs: the left-hand side string, which corresponds to the variable name
• rhs: the right-hand side string, which corresponds to the formula
• comment: a possible comment

Example:

equation <- Equation("KA", "THETA_KA * exp(ETA_KA)", comment="This is my KA parameter")

The equivalent text form is:

equation

## KA=THETA_KA * exp(ETA_KA) # This is my KA parameter

Ordinary differential equation (ODE)

Similarly, Ordinary differential equations (ODE’s) are described by 3 fields as well:

• lhs: the left-hand side string, which corresponds to the variable name, must start with ‘A_’
• rhs: the right-hand side string, which corresponds to the derivative formula
• comment: a possible comment

Example:

ode <- Ode("A_DEPOT", "-KA * A_DEPOT", comment="This is my depot compartment")

The equivalent text form is:

ode

## d/dt(A_DEPOT)=-KA * A_DEPOT # This is my depot compartment

Line break

Line breaks can be added to a model to add clear separations between blocks of equations. It does not have any field.

Example:

linebreak <- LineBreak()

The equivalent text form is obviously a separation line.

Comment

Comments can be specified at any place in the model. They have a unique field:

• x: the comment you’d like to add

Example:

comment <- Comment("This is my first comment")

The equivalent text form is:

comment

## # This is my first comment

If-statement

If-statements allow a variable to take different values according to different specified conditions.

• condition: the given condition
• equation: an equation (see definition above)
• comment: a possible comment

Example:

ifStatement <- IfStatement("COV==1", Equation("COV_EFFECT", "0.2"), comment="This is an if statement")

The equivalent text form is:

ifStatement

## if (COV==1) COV_EFFECT=0.2 # This is an if statement

A common use of the if-statements is to add covariate effects into the model. Here is an example:

main <- MainRecord()
main <- main %>%
  add(Equation("COV_EFFECT", "0")) %>% # Initialisation
  add(IfStatement("COV==1", Equation("COV_EFFECT", "0.1"))) %>%  # Covariate value is 1 in dataset
  add(IfStatement("COV==2", Equation("COV_EFFECT", "0.2"))) %>%  # Covariate value is 2 in dataset
  add(IfStatement("COV==3", Equation("COV_EFFECT", "0.3")))      # Covariate value is 3 in dataset

The equivalent text would then be:

main

## [MAIN]
## COV_EFFECT=0
## if (COV==1) COV_EFFECT=0.1
## if (COV==2) COV_EFFECT=0.2
## if (COV==3) COV_EFFECT=0.3

Please note that mrgsolve require all extra variables (like COV_EFFECT in the previous example) to be initialised to a predefined value, which makes a lot of sense in general.

Additional remarks

Package campsismod does not check the equations from a grammar point of view. This work is delegated to the simulation engine (RxODE or mrgsolve) and C compiler.

In general, respecting the few rules listed below will give you a successful compatibility with both engines:

• All formula’s and if-statement conditions must be written in C code
• Functions included in the Math library of C are compatible (e.g. cos, sin, etc)
• Use the pow function for writing exponents (^ is accepted in RxODE, not in mrgsolve)
• Scientific notation for numbers is accepted (e.g. 2.51e-01)
• Initialise all extra variables (see example in the section above)