Statistical Problems of Allelic Association

Abstract

This chapter introduces a new approach for testing for allelic association by means of nonparametric permutation tests. The genetic configuration our statistical problem can be formalized by considering bivariate responses: (X ₁, X ₂) where the observed subjects are partitioned into two groups (according to the typical case–control study), so that data may be represented as:

$$ X = \left\{{\left({X_{1ji},X_{2ji}} \right),\;i = 1, \ldots,n_{j},\;j = 1,2} \right\} $$

where responses are binary ordered categorical such as (AA, Aa, aa) or the like. An exact permutation test is then derived to efficiently solve this problem. Such novel approach is compared with competitors within parametric tests mostly used in genetics and in isotonic inference testing problems. Finally, an extension to the multivariate case is introduced and discussed.