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:

    \[f(C_c) = \frac {E_{max} \cdot C_c } { EC_{50} + C_c }\]

  • Sigmoidal:

    \[f(C_c) = \frac{E_{max} \cdot C_c^n}{EC_{50}^n+C^n}\]
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)
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