Partitioning methods for multifactorial risk attribution

Abstract

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.

Generalized approaches to partitioning the attributable risk of interacting risk factors can remedy existing pitfalls

“…Land et al [10] explained this weighting on the basis of the sufficient cause model by Rothman [15]: if we observe more cases as expected from an additive model when two factors are simultaneously present, then these additional cases probably emerge from a different disease mechanism, which is only initiated when both factors are present. Hence, as long as no additional knowledge about the details of this causal mechanism is available, for these cases both factors have to be considered equally important and the additional amount should be split into equal parts.…”

“…A clear advantage of the equal distribution rule is that it is not restricted to situations where the relative risks in all strata are at least 1, as is the proportional value. Table 3 Allocation of the joint excess risk of three exposure factors to its components for the situation presented in Table 2 Method Table 4 Partial attributable risks derived from different methods for the situation given in Table 2 Method Land et al [9,10] and Gefeller et al [8] discussed the analogy between game theory and risk allocation and found arguments for the application of the Shapley value in an epidemiologic environment. Although some properties of the Shapley value can be directly adopted from game theory to the PAR like symmetry (independence of the ordering of factors), the dummy property (i.e., the PAR of an irrelevant factor is zero), and efficiency (the sum of all PARs adds to the combined attributable risk), the game-theoretical axiom of additivity has to be reformulated, as it has no meaningful counterpart in an epidemiological context.…”

A Scaled Sample Space Cube Used to Illustrate Attributable Fractions

“…Attributable fractions in various forms are being applied to an increasing extent in medical research, especially in epidemiology (Benichou et al, 1998;Eide and Heuch, 2001;Uter and Pfahlberg, 2001;Gefeller, 2001;Land et al, 2001). Magnus and Beaglehole (2001) recently showed how proper use of these concepts should change the longstanding professional opinion about one of the world's great public health challenges, coronary heart disease.…”

The one-year non-life insurance risk

“…If it is preferred to calculate a global risk margin for the total technical provisions of the company, the risk margin in this paper could be thought of as being derived by some special method for allocating the diversification effect to the LoB, such as the Shapley method, see e.g. Land et al (2001).…”