Multivariate analysis of HLA-disease associations

A multivariate procedure is presented for the analysis of HLA-disease associations. This formulation explicitly accounts for the inner correlations of the HLA complex itself, both within loci (arising from the fact that multinomial allelic frequencies must sum to unity) and between loci (arising from a failure of independent assortment). The analysis yields a single test criterion for association of the HLA complex, as a whole, with the disease in question: this criterion has an approximately chi square distribution. The overall test may conveniently be partitioned into a variety of interesting and independent subtests, so a decomposition of the problem is possible. The analysis is illustrated with data derived from a study of guttate psoriasis by Williams et al. (1976, British Journal of Dermatology 95, 163-167). Extensions to related problems are indicated.