A computationally simple test of homogeneity of odds ratios for twin data

It is of interest to compare measures of association of binary traits among samples of bivariate data. One example is the comparison of association within a sample of monozygotic (MZ) twins to that within a sample of dizygotic (DZ) twins. A larger association in the MZ twins suggests that the trait of interest may have a genetic component. The Bivariate data in this example are binary traits for the twins in each pair. Another example is the comparison of a measure of Hardy-Weinberg disequilibrium across several populations. The bivariate data in this example are the two alleles comprising the genotype of interest. We propose using derived logistic regression equations from the full exponential model for the bivariate outcomes to test for homogeneity. We adjust for correlation among outcomes via generalized estimating equations. This modeling approach allows for adjustment for individual-level and pair-level covariates and thereby allows for testing for gene x environment interactions. Further, we extend the model to allow for simultaneous analysis of two diseases, which allows for testing for a genetic component to the coaggregation of two diseases. In contrast to approaches proposed by previous authors, no special software is required; our approach can be easily implemented in standard software packages. We compare our results to those of other methods proposed in the literature for data from the Vietnam Era Twin Study. We apply our methods also to the Anqing Twin Study and data on major depression and generalized anxiety disorder from the Virginia Twin Register.