- Model with continuous covariates
- Model with categorical covariates
- Transforming categorical covariates

**Objectives:** learn how to implement a model for continuous and/or categorical covariates.

**Projects:** warfarin_covariate1_project, warfarin_covariate2_project, warfarin_covariate3_project, phenobarbital_project

**See also:** Complex parameter-covariate relationships and time-dependent covariates

## Model with continuous covariates

**warfarin_covariate1_project**(data = ‘warfarin_data.txt’, model = ‘lib:oral1_1cpt_TlagkaVCl.txt’)

The warfarin data contains 2 individual covariates: `weight` which is a continuous covariate and `sex` which is a categorical covariate with 2 categories (1=Male, 0=Female). We can ignore these columns if are sure not to use them, or declare them using respectively the reserved keywords `COV`

(for continuous covariate) and `CAT`

(for categorical covariate):

Even if these 2 covariates are now available, we can choose to define a model without any covariate:

Here, a 0 on the first row (weight) and the third column (V), for instance, means that there is no relationship between weight and volume in the model. A diagnostic plot `Covariates `

is generated which displays possible relationships between covariates and individual parameters (even if these covariates are not used in the model):

**warfarin_covariate2_project**(data = ‘warfarin_data.txt’, model = ‘lib:oral1_1cpt_TlagkaVCl.txt’)

We decide to use the weight in this project in order to explain part of the variability of and . We will implement the following model for these two parameters:

which means that population parameters of the PK parameters are defined for a typical individual of the population with weight=70kg.

**More details about the model**

The model for and can be equivalently written as follows:

The individual predicted values for and are therefore

and the statistical model describes how and are distributed around these predicted values:

Here, and are linear functions of : we then need to transform first the original covariate into by clicking on the button `Transform`

of the main GUI. We can then transform and rename the original covariates of the dataset:

We then define a new covariate model, where and are linear functions of the transformed weight :

Coefficients and are now estimated with their s.e. and the p-values of the Wald tests are derived to test if these coefficients are different from 0:

## Model with categorical covariates

**warfarin_covariate3_project**(data = ‘warfarin_data.txt’, model = ‘lib:oral1_1cpt_TlagkaVCl.txt’)

We use `sex` instead of `weight` in this project, assuming different population values of volume and clearance for males and females.

More precisely, we consider the following model for and :

where if individual is a female and 0 otherwise. Then, and are the population volume and clearance for males while and are the population volume and clearance for females. By clicking on the button `Transform`

, we can modify the name of the categories (click on the name of each category and enter a new name) and the reference category (Male is the reference category in this project):

Define then the covariate model in the main GUI:

We can furthermore assume different variances of the random effects for males and females by clicking on the button `Cat. Var.`

and selecting which variances depend on the categorical covariate:

Estimated population parameters, including the coefficients and and the 2 standard deviations and are displayed with the results:

Estimated population parameters are also computed and displayed per category:

We can display the probability distribution functions of the 4 PK parameters:

We can then distinguish the distributions for males and females by clicking on `Settings` and ticking the box `By group`:

## Transforming categorical covariates

**phenobarbital_project**(data = ‘phenobarbital_data.txt’, model = ‘lib:bolus_1cpt_Vk.txt’)

The phenobarbital data contains 2 covariates: the weight and the Apgar score which is considered as a categorical covariate:

Instead of using the 10 original levels of the Apgar score, we will transform this categorical covariate and create 3 categories: Low = {1,2,3}, Medium = {4, 5, 6, 7} and High={8,9,10}.

If we assume, for instance that the volume is related to the Apgar score, then and are estimated (assuming that `Medium` is the reference level).