The attributable risk in a multifactorial situation--evaluation of different methods of partitioning

Different approaches to partition the attributable risk into exposure-specific components are methodologically evaluated.

Two methods of partitioning the attributable risk in a multifactorial situation have been suggested. One is based on a solution adopted from game theory, the Shapley value, whereas the other recently suggested approach uses a heuristically motivated proportional weighting scheme. These two concepts are reviewed and compared in a situation with three exposure factors. A hypothetical numerical example is discussed illustrating differences in the case of complex interaction structures.

The two methods are found to differ in two critical features that affect the outcome of partitioning: i) including or ignoring the full interaction structure between exposure factors involved in the partitioning, ii) using an equal or proportional weighting scheme for the marginal excess risks of the exposures. As a result, not only the individual partial attributable risks for the exposure factors may be quantitatively different between the methods, but also their ranking depends on the partitioning approach.

The epidemiologic properties of the partitioning procedure based on the Shapley value are known and fit to the needs of epidemiologic applications. The alternative approach recently suggested can lead to considerably different results. As long as its epidemiologic properties are not fully understood, the traditional partitioning method should be given preference in practical applications.