Detection of HLA haplotype associations with disease

In a recent paper, Thomson & Bodmer (1979) explored several conceptual and analytic issues involved in studying the association of HLA haplotypes with disease. One key problem they emphasized was the assessment of the statistical significance of the third order linkage disequilibrium between two HLA genes and a disease susceptibility gene. We have formulated an approach to this problem and illustrate this approach by deriving such statistical tests of true haplotype associations for two models of disease susceptibility previously studied by Terasaki & Mickey (1975) and by Thomson & Bodmer (1977). A numerical example using actual phenotypic data is then presented to demonstrate the practicality of the methods.