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The epidemiological problem of risk attribution in the framework of multiple exposures has been the subject of intensive research activities in the last decade. In particular, partitioning methods have been developed to define new multidimensional measures of attributable risk putting the task of quantifying a proportion of disease events in a population that can be ascribed to the adverse health effects of certain risk factors into a multifactorial perspective. The parameters generalize the concept of attributable risk to different multifactorial frameworks in which multiple exposures might be arranged in hierarchically ordered classes or in equally ranking groups. Partitioning methods are reviewed and differences between the multifactorial variants of attributable risk are illustrated by a component causes model. [PUBLICATION ABSTRACT]