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Twin concordance for a binary trait: III. A bivariate analysis of hay fever and asthma

Self‐reported histories of hay fever and asthma were obtained from 3,808 pairs of adult twins 18 years and over registered with the Australian National Health Medical Research Council Twin Registry (1232 MZF, 567 MZM, 751 DZF, 352 DZM, 906 DZO). The prevalence of hay fever and asthma was 0.32 and 0.13, respectively, with little variation with zygosity, sex, and age. The associations between twin pairs for these two traits were analysed, under the assumption of constant prevalences, as a special case of a log‐linear model for binary traits in pedigrees using the statistical package GLIM. The model assumption that there are no secondor higher‐order interactions was tested in the 2 × 2 × 2 × 2 table of twin by disease outcomes without revealing strong evidence of departure, even in this large data set. The log‐linear modelling showed that only three first‐order interactions, namely 1) between hay fever in a twin pair, 2) asthma in a twin pair, and 3) hay fever and asthma in the same twin, were necessary to describe the data. The first two interaction terms were significantly larger in identical pairs; the third was independent of zygosity. Under this parsimonious model, there was a significant difference between identical and fraternal pairs in marginal correlation, both in asthma and hay fever, and in the cross‐correlation between hay fever in one twin and asthma in the other. This suggests that genetic factors are implicated in both hay fever and asthma and that some of these genetic factors are common (at least among a subgroup of individuals) to both traits.