An example of individual parameter and covariate model

Introduction
In the previous example, when only iiv was under consideration, all the individuals share the same distribution, and thus be linked on the same typical value. If we consider male and female for example, they would not share the same typical value. Indeed, as the men are bigger to women, their volumes are bigger too. The goal is to then study a population while keeping the inter individual variability.

Inter individual variability and covariate on the volume
In that case, we define a dependency of the volume on the weight of the individual. For that, we suppose that

$V=V_{pop}\left(\frac{w}{w_{pop}}\right)^{\beta}$

In our case, we define the weight as normally distributed with a typical value $w_{pop} = 70$ , and a standard deviation $\textrm{omega}_{w}=12$ . $\beta$ is set to 1. The model is implemented in the file mlxt_iiv_covariate.txt as the following. The only difference from the previous example is the addition of a covariate section and the addition of a covariate dependence in the volume distribution.
In Mlxtran, it writes

[INDIVIDUAL]
input = {V_pop, omega_V, w, w_pop, beta}

EQUATION:
lw = log(w/w_pop)

DEFINITION:
V = {distribution = lognormal, typical = V_pop, covariate = lw, coefficient=beta, sd = omega_V}

[COVARIATE]
input = {w_pop, omega_w}

DEFINITION:
w = {distribution = normal, typical = w_pop, sd = omega_w}