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# [LONGITUDINAL]

## Description

The [LONGITUDINAL] section is used to describe the structural model and the observation model discrete and time-to-event data. In Simulx it is also used to define the error model for continuous observations.

## Scope

The [LONGITUDINAL] section is mandatory for all Mlxtran models for Monolix and Simulx.

## Inputs

In Monolix, the input = { } list of the [LONGITUDINAL] section declares the individual parameters and the regressors. In Simulx, the error model parameters also also declared in the input (while this is done automatically via the GUI in Monolix). The inputs can have been defined in the [INDIVIDUAL] section, or be global variables defined via the Monolix or Simulx GUI.

For regressors, the regressor status must be specified using the following syntax, for instance for a regressor called regvar. 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).

regvar = {use=regressor}

The inputs of [LONGITUDINAL] specified as regressors will be recognized as such and appear in the regressor element in Simulx GUI. Inputs of [LONGITUDINAL] which have been defined in the DEFINITION block of the [INDIVIDUAL] section will be recognized as individual parameters. All others (in particular error model parameters) will be recognized as population parameters in Simulx.

Example for Monolix:

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.

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

Example for Simulx:

In this example, in addition to the individual parameters ka, V, Cl, Emax and EC50 and the regressor E0, population error model parameters a and b are also defined.

[LONGITUDINAL]
input = {ka, V, Cl, E0, Emax, EC50, a, b}
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.

In Simulx, variables listed in table={} or output={} will have an output element generated automatically. It is also possible to request any model variable as output in Simulx, no matter if it has been declared in the OUTPUT section or not.

Note that from the 2020R1 version, the OUTPUT: section is mandatory.

Example:

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

## Usage

The [LONGITUDINAL] section can contain three different blocks. The PK: block permits to define PK models using macros, and to link the administration information of the data set with the model. The EQUATION: block is for mathematical equations including ODEs and DDEs. The DEFINITION: block is used to define a random variable and its probability distribution.

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.

#### PK: block

In the PK: block, macros can be used to define compartmental models using base building blocks.

#### EQUATION: block

In the EQUATION: block, ODEs and DDEs can be defined.

#### DEFINITION: block

The DEFINITION: block is used to define random variable, which represent observations. The observations can be continuous, count, categorical or time-to-event. In Monolix, only count, categorical and time-to-event observation models are defined in the structural model file, while the continuous error models are defined in the GUI. In Simulx, they are all defined in the model file.

## Library of models and examples

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

• 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
• TTE: time-to-event models
• Count: models for count data
• TGI: tumor growth and tumor growth inhibition models

For common models which are not (yet) in the libraries, we provide an example page.