An aggregable family of multidimensional concentration indices is characterized, in order to be consistent with a property of exogenous risk factors, i.e. health risks for which agents are not responsible for. The family of concentration indices (or achievement indices by duality) lies in the class of polynomial functions. Necessary and sufficient conditions are stated in order to rank two health distributions thanks to the generalized concentration curves. It is shown that the properties of mirror and symmetry are compatible with a sub-family of concentration indices being polynomial functions. A dominance criterion exists for this sub-family of indices, provided that the decision maker is an inequality lover.