Test di permutazione multidimensionali in problemi d’inferenza isotonica: un’applicazione alla genetica

In this paper we present a permutation solution to an isotonic inference problem very usual in association case-control studies in genetic epidemiology. In similar studies, the data may be represented as: X = ....... where responses are ordered categorical such as (AA, aA, aa) or the like, where ordering is generally induced by the nature of the problem at hand. The hypotheses we are interested in are: .............. where at least one inequality is strong. This particular system of hypotheses arises when the variables are such that, under the alternative, both X11 and X12 stochastically non-increase or both stochastically non-decrease. The permutation solution presented is based on the nonparametric combination of dependent test (Pesarin, 1992, 1999).