Breast cancer risk factors in African-American women: the Howard University Tumor Registry experience.

This retrospective case-control study examines risk factors for breast cancer in African-American women, who recently have shown an increase in the incidence of this malignancy, especially in younger women. Our study involves 503 cases from the Howard University Hospital and 539 controls from the same hospital, seen from 1978 to 1987. Using information culled from medical charts, an analysis of various factors for their effect on breast cancer risk was made. The source of data necessarily meant that some known risk factors were missing. Increases in risk were found for known risk factors such as decreased age at menarche and a family history of breast cancer. No change in risk was observed with single marital status, nulliparity, premenopausal status, or lactation. An increased odds ratio was found for induced abortions, which was significant in women diagnosed after 50 years of age. Spontaneous abortions had a small but significant protective effect in the same subgroup of women. Birth control pill usage conferred a significantly increased risk. It is of note that abortions and oral contraceptive usage, not yet studied in African Americans, have been suggested as possibly contributing to the recent increase in breast cancer in young African-American women.

Numerical comparisons of two formulations of the logistic regressive models with the mixed model in segregation analysis of discrete traits.

Segregation analysis of discrete traits can be conducted by the classical mixed model and the recently introduced regressive models. The mixed model assumes an underlying liability to the disease, to which a major gene, a multifactorial component, and random environment contribute independently. Affected persons have a liability exceeding a threshold. The regressive logistic models assume that the logarithm of the odds of being affected is a linear function of major genotype effects, the phenotypes of older relatives, and other covariates. A formulation of the regressive models, based on an underlying liability model, has been recently proposed. The regression coefficients on antecedents are expressed in terms of the relevant familial correlations and a one-to-one correspondence with the parameters of the mixed model can thus be established. Computer simulations are conducted to evaluate the fit of the two formulations of the regressive models to the mixed model on nuclear families. The two forms of the class D regressive model provide a good fit to a generated mixed model, in terms of both hypothesis testing and parameter estimation. The simpler class A regressive model, which assumes that the outcomes of children depend solely on the outcomes of parents, is not robust against a sib-sib correlation exceeding that specified by the model, emphasizing testing class A against class D. The studies reported here show that if the true state of nature is that described by the mixed model, then a regressive model will do just as well. Moreover, the regressive models, allowing for more patterns of family dependence, provide a flexible framework to understand gene-environment interactions in complex diseases.

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.

Search for faster methods of fitting the regressive models to quantitative traits.

The regressive models describe familial patterns of dependence of quantitative measures by specifying regression relationships among a person's phenotype and genotype and the phenotypes and genotypes of antecedents. When the number of sibs in the pattern of dependence increases, as in the class D regressive model, computation of the likelihood becomes time consuming, since the Elston-Stewart algorithm cannot be used generally. On the other hand, the simpler class A regressive model, which imposes a restriction on the sib-sib correlation, may lead to inference of a spurious major gene, as already observed in some instances. A simulation study is performed to explore the robustness of class A model with respect to false inference of a major gene and to search for faster methods of computing the likelihood under class D model. The class A model is not robust against the presence of a sib-sib correlation exceeding that specified by the model, unless tests on transmission probabilities are performed carefully: false detection of a major gene is reduced from a number of 26-30 to between 0 and 4 data sets out of 30 replicates after testing both the Mendelian transmission and the absence of transmission of a major effect against the general transmission model. Among various approximations of the likelihood formulation of the class D model, approximations 6 and 8 are found to work appropriately in terms of both the estimation of all parameters and hypothesis testing, for each generating model. These approximations lessen the computer time by allowing use of the Elston-Stewart algorithm.

Equivalence of the mixed and regressive models for genetic analysis. I. Continuous traits.

The mixed model of segregation analysis specifies major gene effects and partitions the residual variance into polygenic and environmental components. The model explains familial correlations essentially in terms of genetic causation. The regressive model, on the other hand, is constructed by successively conditioning on ancestral phenotypes and major genes. Familial patterns of dependence are described in terms of correlations without necessarily introducing a particular scheme of causal relationship. These two approaches are compared both theoretically and numerically through computer simulations for the case of continuous traits on nuclear families. The class D regressive model, which is characterized by equal sib-sib correlations, is mathematically and numerically equivalent to the mixed model. The simpler class A regressive model, which is also characterized by equal sib-sib correlations determined in this case by the common parentage, provides good estimates of the mixed model parameters: major gene parameters and residual polygenic heritability, derived from the parent-offspring correlation. However, in the absence of a major gene, the restriction imposed by the class A model on the sibling correlation can affect the conclusions of segregation analysis: False inference of a major gene was observed in two out of ten replicates. Our simulations also indicate that the mixed model allowing for different heritabilities in adults and children leads to correct estimates of the major gene parameters and residual familial correlations (parent-offspring and sib-sib) as specified by the class A model. For all the models studied, major gene effects, when present, are correctly detected and estimated.

A general transmission probability model for pedigree data.

The three basic transmission probabilities of the two-allele autosomal genetic model proposed by Elston and Stewart in 1971 are made dependent on sex. It is shown that this more general model, comprising twelve transmission probabilities, subsumes the most important simple modes of genetically or environmentally determined transmission that may be responsible for the familial aggregation of traits. Although this does not necessarily solve the problem of testing alternative hypotheses, it provides a holistic parametrization of familial transmission.