Three-locus haplotype interactions in the analysis of linkage disequilibrium

We have shown that the application of Piazza's formula for the estimation of the "three-locus interaction delta" should not be used for that purpose. In addition, the method of Porta & McHugh, for the demonstration of haplotype interaction in associations between HLA and disease, leads to completely erroneous conclusions. Other methods of calculation that have been used to analyse haplotype interactions also appear to be based on erroneous concepts. We suggest that nothing more than the estimation of heterogeneity in simple 2 X 2 contingency tables should be used for the analysis of linkage disequilibria. This principle is applied to the HLA-A, -B and -C haplotype frequency tables of Baur & Danilovs. For the greater part of the HLA-B alleles, three-locus haplotype frequencies can be explained from the A, B and the B, C disequilibria, without any further haplotype interactions. The predominant exceptions in that respect are haplotypes containing the B44 allele, which has been shown to contain two subgroups and therefore, we are not justified to conclude that this exceptional behaviour of haplotypes with B44 should be attributed to three-locus haplotype interactions.