Introduction: model structure for Monolix

Structural model

In Monolix, the model code defined in the “Structural model” tab (external .txt file loaded into Monolix or model selected from a library) contains only the structural part of the model in a single [LONGITUDINAL] section.

The [LONGITUDINAL] section is itself divided into blocks, which allows to define different types of variables in different ways. Here are the possible blocks and variable lists in that section:

DESCRIPTION: (optional): block to put comments on the model
input (mandatory): list of input parameters
PK: (optional): block were macros can be used and combined to define compartments and transfers between them
EQUATION: (optional): block were ODEs and DDES can be defined, as well as mathematical expressions (e.g parameter transformations)
DEFINITION: (optional): block to define random variables (discrete or continuous) which represent observations, via their probability distribution: error model, probability distribution for count/categorical output and hazard for time-to-event output
OUTPUT: (mandatory): block indicating the output of the model
output (mandatory): list of output parameters included in the OUTPUT block.

In all blocks, it is possible to use:

Reserved keywords of the Mlxtran language cannot be used as names for other parameters. Mlxtran is a declarative language, not an imperative language. Therefore equations are mathematical definitions rather than a series of instructions.

Inputs

In Monolix, the input = { } list of the [LONGITUDINAL] section declares the individual parameters and the regressors.

CODE

[LONGITUDINAL]
input = {ka, V, Cl}

For regressors, the regressor status must be specified using the following syntax, for instance for two regressors called regvar1 and regvar2. One line per regressor is necessary. As a reminder, in Monolix, the regressors are mapped to the regressor columns of the data set by declaration order (first column tagged as regressor mapped to the first regressor appearing in the input list).

CODE

[LONGITUDINAL]
input = {..., regvar1, regvar2}
regvar1 = {use=regressor}
regvar2 = {use=regressor}

Example:

In this example, ka, V, Cl, Emax and EC50 are individual parameters and E0 is declared as a regressor and will be read from the first data set column tagged as regressor.

CODE

[LONGITUDINAL]
input = {ka, V, Cl, E0, Emax, EC50}
E0 = {use = regressor}

Outputs

In Monolix, the OUTPUT: block declare the variables which will be mapped to the observations in the data set via the output={} list, and the additional variables recorded in the output tables via the table={} list. The outputs are mapped to the observation ids of the data set via the mapping panel in the Monolix GUI. The variables in the table={} statement are outputted in the result folder of Monolix.

Example:

CODE

OUTPUT:
output = {Conc, Effect}
table  = {Ap, T12}

Library of models and examples

The MonolixSuite contains libraries of pre-written structural models which can be directly selected via the GUI in Monolix:

PK: typical pharmacokinetics models with several types of administrations and 1 to 3 compartments
PK/PD: joint PK/PD model with direct effect, effect compartment or turnover
PK double absorption
TMDD: target mediated drug disposition models
Parent-Metabolite models
TTE: time-to-event models
Count: models for count data
TGI: tumor growth and tumor growth inhibition models

Examples of common models which are not (yet) in the libraries are also given here: Advanced models

Statistical model

In Monolix the statistical part of the model (covariate effects, parameter distributions and error model) is defined through the graphical user interface. Then when saving a Monolix project, the statistical part of the model is automatically written in the .mlxtran project file using mlxtran language, divided into three parts:

The observation (error) model: defined inside the DEFINITION: block below the [LONGITUDINAL] section.
The individual model: describes the distributions for the individual parameters, correlation structure and covariate effects, defined inside the [INDIVIDUAL] section.
The covariates defined in the project: described inside the [COVARIATE] section.

Example

Here is the description of the full model (structural and statistical) corresponding to the Monolix demo 1.1.libraries_of_models/theophylline_project.mlxtran, automatically saved by Monolix inside the <MODEL> part of the theophylline_project.mlxtran file:

CODE

<MODEL>

[COVARIATE]
input = {WEIGHT, SEX}

SEX = {type=categorical, categories={'F', 'M'}}

[INDIVIDUAL]
input = {ka_pop, omega_ka, V_pop, omega_V, Cl_pop, omega_Cl}

DEFINITION:
ka = {distribution=logNormal, typical=ka_pop, sd=omega_ka}
V = {distribution=logNormal, typical=V_pop, sd=omega_V}
Cl = {distribution=logNormal, typical=Cl_pop, sd=omega_Cl}

[LONGITUDINAL]
input = {a, b}

file = 'lib:oral1_1cpt_kaVCl.txt'

DEFINITION:
CONC = {distribution=normal, prediction=Cc, errorModel=combined1(a, b)}

Note that when exporting the model from Monolix to Simulx, this full model then appears in the interface of Simulx: