The objective of this application is to give an introduction to population PK modelling. Here are the steps you should follow:

### Data & Model

Click on ** Project** to select the datafile and define the model.

- Use the tab
`dataset`

to select one of the 3 following PK examples- phenobarbital
- theophylline
- warfarin

- Use the tab
`model`

to define the model

Select one of the following structural models (all these models are one compartment PK models)

- (ka, V, Cl) first order absorption with linear elimination (model for oral administration)
- (Tk0, V, Cl) zero order absorption with linear elimination (model for oral administration)
- (Tlag, ka, V, Cl) lag, first order absorption with linear elimination (model for oral administration)
- (Tlag, Tk0, V, Cl) lag, zero order absorption with linear elimination (model for oral administration)
- (V, Cl) linear elimination (model for intravenous administration)

Select one of the 3 following residual error models (more information about residual error models can be found here. )

- constant: \(y = f + a \, e\)
- proportional: \(y = f + b \, f \, e\)
- combined: \(y = f + (a + b \, f) \, e\)

- Select which individual PK parameters vary within the population and which ones are fixed. Here, all the PK parameters are log-normally distributed.

- Select which individual PK parameters are function of the weight. Here weight is the only covariate used in the model for explaining part of the inter individual variability of the parameters. Since the individual parameters are log-normally distributed, we use the following model for parameter \(\psi_i\): \[\log(\psi_i) = \log(\psi_{\rm pop}) + \beta \log(w_i/w_{\rm pop}) + \eta_i\] where \(w_i\) is the weight of patient \(i\) and \(w_{\rm pop}\) a typical weight in the population (the median weight is used here).

### Tasks

Once the model is defined, you can run a reduced version of Monolix for

estimating the population parameters, the Fisher information matrix, the individual parameters and some information criteria,

performing statistical tests for the covariate model.

Estimation of the population parameters using the SAEM requires to provide some initial values and some settings. Use the tabs `initial values`

and `settings`

if you want to see and/or modify the default values.

See Section `Tasks and Methods`

for more details about the methods and the algorithms used in this application.

**Remark:** the project defined in this application (data, model, initial values, settings) is automatically converted into a Mlxtran script file (use the tab `mlxtran`

to display this model file). Monolix then uses this project file to run the sequence of predifined tasks.

### Results

At the end of the run, you can either display some tables with numerical results or some diagnostic plots.

This Shiny application has been developed by Marc Lavielle,

Inria Saclay & Ecole Polytechnique, Xpop team

September 25th, 2016