Incorporation of twins in the regressive logistic model for pedigree disease data

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.