# Multistage model

From Opasnet

The **multistage model** is a dose-response model that attempts to reflect the biological process of carcinogenesis.

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

A more simple formula for (excess) risk is:

P(dose) = 1 - exp [-alfa_{o}_{} +alfa1*dose1 +...alfa_{k}_{}*dosek]

(alfa=dose-response)

At risk levels (<10-2) the following linear formula can be used for the upper bound (95%) risk

Risk = exposure (mg/kg/day) * q1 (risk per mg/kg/day)

q1=cancer slope factor, upper 95% confidence limit,

calculated from 10% point of departure (POD)

See e.g. Casarett & Doull's Toxicology , 6th ed. 2001, p. 95-97.