MULTISTAGE MODEL
The multistage model is a family of dose-response models often used to describe quantal dose-response data in which the number of individuals developing the specified response during their lifetimes and the total number of individuals at risk are provided at several different dose levels.
The biological assumption underlying the multistage dose-response model is that an individual develops the specified response, say cancer, when a normal tissue or cell undergoes a certain number of irreversible transitions or mutations in a prescribed order(4). Under this assumption, the cumulative hazard rate which defines the multistage model is a multiple integral of the hazard rates for each of the transitions from stage to stage in the multistage process. If there are k transition rates and these transition rates are independent of age, then the cumulative hazard rate by a specified time T is proportional to the product of the k transition rates and Tk. If T is fixed at some specific value corresponding to a lifetime, then the cumulative hazard rate is simply proportional to the product of the transition rates. If the transition rates are assumed to be linear functions of dose, then the product of the transition rates and the cumulative hazard function are polynomials in dose. The multistage dose-response model is simply the general mathematical expression for the probability of a specified response by a specified time in which the cumulative hazard rate has been replaced by a polynomial in dose.
The multistage model and numerous other alternative dose-response models are documented in detail in GEN.T. |