Regressive logistic models for familial diseases: a formulation assuming an underlying liability model.
Statistical models have been developed to delineate the major-gene and non-major-gene factors accounting for the familial aggregation of complex diseases. The mixed model assumes an underlying liability to the disease, to which a major gene, a multifactorial component, and random environment contribute independently. Affection is defined by a threshold on the liability scale. The regressive logistic models assume that the logarithm of the odds of being affected is a linear function of major genotype, phenotypes of antecedents and other covariates. An equivalence between these two approaches cannot be derived analytically. I propose a formulation of the regressive logistic models on the supposition of an underlying liability model of disease. Relatives are assumed to have correlated liabilities to the disease; affected persons have liabilities exceeding an estimable threshold. Under the assumption that the correlation structure of the relatives' liabilities follows a regressive model, the regression coefficients on antecedents are expressed in terms of the relevant familial correlations. A parsimonious parameterization is a consequence of the assumed liability model, and a one-to-one correspondence with the parameters of the mixed model can be established. The logits, derived under the class A regressive model and under the class D regressive model, can be extended to include a large variety of patterns of family dependence, as well as gene-environment interactions.
Demenais
F M
FM
Division of Biostatistics and Epidemiology, Howard University Cancer Center, Washington, DC 20060.
D004777:Environment; D005799:Genes, Dominant / Q000235:genetics; D030342:Genetic Diseases, Inborn / Q000453:epidemiology* / Q000235:genetics; D005838:Genotype; D016015:Logistic Models; D008433:Mathematics; D009679:Nuclear Family; D010641:Phenotype; D012044:Regression Analysis