| HLA antigens, determined by genes in the major histocompatibility region of the sixth human chromosome, have been shown in case-control studies to be associated with more than 100 different diseases. One possible mechanism for such associations is linkage disequilibrium between HLA genes and certain disease susceptibility genes, sometimes called immune response genes. For non-zero linkage disequilibrium to exist between two genes, it is sufficient that the genes occur together on a chromosome with frequency not equal to the product of the individual gene frequencies. Developed in this dissertation are estimable functions of 2-way linkage disequilibrium, between a single HLA gene and a disease susceptibility gene, and 3-way linkage disequilibrium, between a pair of HLA genes (termed a haplotype) and a disease susceptibility gene.; Because expressions for linkage disequilibrium involve gene frequencies, which are not directly observable from the usual HLA phenotype data, it is necessary to assume certain genetic models. Two models are considered here: the autosomal recessive model, and the rare autosomal dominant model. Under the autosomal recessive model, an individual with disease is assumed to be homozygous for a disease susceptibility gene; under the rare autosomal dominant model, diseased individuals are assumed to have one disease susceptibility gene and one normal gene.; Under both the autosomal recessive and the rare autosomal dominant models estimators of gene and haplotype frequencies are: (1) method of moments, (2) maximum likelihood, and (3) gene counting. Further, the models are treated for the simple case of single antigens or single haplotypes and for the more realistic case of multiple antigens or multiple haplotypes. The latter case is shown to give more efficient estimates than when antigens or haplotypes are considered singly.; Since linkage disequilibrium is shown to be proportional to a nonlinear function of gene frequencies (in the case of antigen associations), or to haplotype frequencies (in the case of haplotype associations), consistent estimators of relative linkage disequilibrium are presented as functions of the above estimators. Variances estimators are derived and confidence intervals and tests of significance presented. Finally, data is presented from the literature which demonstrates, for the first time, that there may in fact be true HLA haplotype associations with disease. |
