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Segregation and twin disease concordance analyses have assumed a theoretical underlying liability following a multivariate normal distribution. For reasons of computation, of incorporation of measured explanatory variables, and of testing of fit and assumptions, newer analytical methods are being developed. The regressive logistic model (RLM) relies on expressing the pedigree likelihood as a product of conditional probabilities, one for each individual. In addition to logistic regression modelling of measured epidemiological variables on disease prevalence, there is modelling of vertical transmission, of transmission of unmeasured genotypes and of sibship environment. This paper discusses methods for the analysis of binary traits in twins and in pedigrees. Some extensions to the RLM for pedigrees which include twins are proposed. These enable exploration of twin concordance in the context of the twins' common parenthood, the sibship similarities within the family, and the twins' similarity in age, sex, genes and environment.
Advances in computer technology have made possible a greater sophistication in the statistical analysis of pedigree data, however this is not necessarily manifest by fitting more comprehensive causative models. Planned twin and family studies measure numerous explanatory variables, including perhaps genetic and DNA marker information status on all pedigree members, and the cohabitation of all pairs of individuals. A statistical analysis should examine the contribution of these measured factors on individual means, and in explaining the variation and covariation between individuals, concurrently with the postulated effect of unmeasured factors such as polygenes. We present two models that meet this requirement: the Multivariate Normal Model for Pedigree Analysis for quantitative traits, and a Log-Linear Model for Binary Pedigree Data. For both models, important issues are examination of fit, detection of outlier pedigrees and outlier individuals, and critical examination of the model assumptions. Procedures for fulfilling these needs and examples of modelling are discussed.
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