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

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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. © 1992 Wiley‐Liss, Inc. Copyright © 1992 Wiley‐Liss, Inc., A Wiley Company

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