Association within twin pairs for a dichotomous trait

We propose an odds-ratio measure of twin association for a dichotomous trait. This odds ratio can be estimated without arbitrarily specifying an index twin and without estimating additional nuisance parameters. Tests of association and confidence intervals may be computed easily, in contrast to those proposed previously [Donner et al. (1995) Genet Epidemiol 12:267-277] for a correlation measure of association. For testing homogeneity of association in two samples of twins, monozygotic and dizygotic, we propose a large-sample test and an exact test, both based on the odds-ratio parameterization. Large-sample tests of homogeneity are slightly anticonservative when some cell counts are small, and the exact test may be preferred in these situations. We also propose a long-linear parameterization useful for modeling more complex data sets.