add_indirect_effect#

pharmpy.modeling.add_indirect_effect(model, expr, prod=True)[source]#

Add indirect (turnover) effect

The concentration $C_c$ has an impact on the production or degradation rate of the response R:

• Production:

  $$\frac{dR}{dt}=k_{in}\cdot (1+f(C_c))-k_{out}\cdot R$$

• Degradation:

  $$\frac{dR}{dt}=k_{in}-k_{out}\cdot (1+f(C_c))\cdot R$$

$k_{in}$ and $k_{out}$ can either be inhibited or stimulated. Baseline $B=R(0)=R_0=k_{in}/k_{out}$.

Models:

• Linear:

  $$f(C_c)=\text{slope}\cdot C_c$$

• Emax:

  $$f(C_c)=\frac{E_{max}\cdot C_c}{E{C}_{50}+C_c}$$

• Sigmoidal:

  $$f(C_c)=\frac{E_{max}\cdot C_c^n}{E{C}_{50}^n+C^n}$$

Parameters:

• model (Model) – Pharmpy model

• prod (bool) – Production (True) (default) or degradation (False)

• expr ({‘linear’, ‘emax’, ‘sigmoid’, ‘step’}) – Name of PD effect function.

Returns:

Model – Pharmpy model object

Examples

>>> from pharmpy.modeling import *
>>> model = load_example_model("pheno")
>>> model = add_indirect_effect(model, expr='linear', prod=True)