Generalized dose-response function

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Question

Generalized dose-response function (GDR) describes general properties of the shape of the relationship between the dose of a chemical and a particular response in mammals. Often the focus is on the probability of a particular level of response. This is called generalised dose--response-probability function (GDRP). The primary source of information is pharmacology, toxicology, and epidemiology. This knowledge is then transformed into a mathematical form.

Rationale

Causality

Causally upstream variables have not been defined.

Data

There are several issues that may affect the shape of the dose-response function of a particular chemical. However, the GDR should be described in such a flexible and detailed way that it reflects any of the shapes determined by these factors.

• Mode of action
  • Mutagenicity
  • Enzyme induction
  • Depletion of an essential chemical in the body
  • Disruption of homeostasis
  • Block of a metabolic pathway
• Time course of the effect

This is a preliminary list of issues that are known (or suspected) about dose-response-probabilities.

• Usually there is a background risk >0 (probability of observing the response in absence of the chemical).
• The response is usually monotonically increasing. However, there are two important exceptions:
  • At large doses, other (toxic) mechanisms might activate and overrule the mechanism that is causing the response of interest.
  • At low doses, some defence mechanisms may activate thus preventing the (adverse) effect or even reversing it. When this occurs, the impact of this hormesis effect is typically ca. 10 % of the maximum response at high doses. How this reflects into the response probabilities needs to be discussed.
• The DRP curves are usually rather smooth. However, there might be threshold mechanisms working, resulting in no impact until the threshold is exceeded, and then there may be a rapid increase in response. Although this may be true in the individual level, usually interindividual variation about the threshold smooths the population-level observations. It is rare to have two different thresholds working in the same individual in such a way that it would be of biological interest. Therefore, a single threshold assumption is enough. (Should this be discussed?)

Formula

The multistage model is used as the first placeholder for a generalised DRP.

P(Response|Dose)= background +(1-background)*(1-exp(-q1*Dose -q2*Dose^2 -q3*Dose^3...))

Unit

• GDR: depends on the response
• GDRP: probability of the response