Measures of association between disease and genotype

This paper is concerned with the statistical aspects of the phenomenon of disease occurring more frequently in individuals with some genotypes than in individuals with others. A correlation coefficient is defined to quantify association between disease and genotype. A distinction is made between the concepts of independence of allele and disease and independence of genotype and disease. This distinction is used to define two components of association which describe separate aspects of association of disease with genotype. One component is a measure of the association of disease with allele; the other a measure of the effect of allele interaction on association of disease and genotype. One aspect of the usefulness of the partition into components which is discussed is in expressing the recurrence risk of disease for a relative of an affected individual. A chi-squared analysis is provided to test hypotheses about the components of association and other hypotheses of genetic interest. This analysis is illustrated using a study done to determine the effect of the sex-linked dwarfing gene in male chickens on resistance to E. coli infection. This analysis shows a significant allele interaction effect on resistance to disease but no association of disease with alleles. In conclusion, some extensions and limitations of the proposed concepts and procedures are discussed.