MATHEMATICAL MODELS FOR THE QUANTAL BIOLOGICAL EFFECTS OF SEVERAL TOXICANTS COMBINED

摘要

Quantal biological effects caused by the combined action of a number of toxic agents are modelled using the information available for each toxicant acating in isolation. Two basic models are being presented here(ⅰ) Independent action model and (ⅱ) Separable action model. Independent action model depends exclusively on data for the marginal risks and there is no overlap to be subtracted because imdependent action leads directly to the sum of hazardous functions. Any additional term in the exponent result in either synergism or antagonism. In the separable interaction model the/risk function can be separated into a product of factors, each describing the action of one toxic agent . There are no non linear cross-terms within these facators and in this the actions of the toxicants are independent. The model apply to quantal biological effects and provide a probability for the incidence of a disease, not for its severity. An exposure to two toxic agents requires close to nine dose combinations for an analysis and exposures to three or more agents need correspondingly more. The predictive power of these models is difficult to assess. Four out of the four cases of epidemiological data analyzed show compatibility with two models.