A game-theoretic approach to partitioning attributable risks in epidemiology

The concept of attributable risk has been developed to quantify that proportion of disease events in a population that can be ascribed to an exposure factor under study. Typically, several exposures have to be considered simultaneously in observational epidemiological studies when assessing their impact on the disease load. Whenever these exposures are subject of complex interactions the question arises, what contribution should be assigned to each of them. The paper points out that the epidemiological problem of finding "sensible" risk allocation methods can be formalized in a way that is equivalent to the game-theoretic description of several players that act together in a grand coalition and are faced with the problem of dividing their profit "fairly" among them. The transfer of game-theoretic results to epidemiology yields a unique method of allocating shares of the joint attributable risk, called partial attributable risks, to each exposure factor. Application and justification of the method are illustrated using data from the G.R.I.P.-study (Gottinger Risiko-, Inzidenz- und Pravalenzstudie).