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We extend the usual logistic model between a dichotomous phenotype and an allele count in two ways: a polytomous phenotype with  K  > 2 levels, and modeling of allele counts at two unlinked marker loci. Inference is based on within-family information to guard against potential bias due to population genetic structure. Score tests of the model coefficients taking into account the correlation between relatives in entire pedigrees are derived as an extension of the Generalized Disequilibrium Test (GDT). Simulations confirm that the tests have the expected statistical properties, and that their power exceeds that of the GDT under a favorable scenario. The score tests are illustrated with candidate genetic markers, a major psychosis phenotype and a cognitive endophenotype in large kindreds from Eastern Quebec.

Extension of the generalized disequilibrium test to polytomous phenotypes and two-locus models