Elementary methods for the analysis of dichotomous outcomes in unselected samples of twins

This paper presents an elementary statistical method for analyzing dichotomous outcomes in unselected samples of twin pairs using stratified estimators of the odds ratio. The methodology begins by first randomly designating one member of each twin pair as an "index" twin and the other member as the "co-twin." Stratifying on zygosity, odds ratios are used to measure the association between disease in the index twin and disease in the co-twin. From these zygosity-specific tables we calculate the Woolf-Haldane estimator of the common odds ratio (psi F, the weighted average of the zygosity-specific odds ratios), the Mantel-Haenszel test statistic (chi 2M-H) for the common odds ratio, and a test (chi 2G) for the difference in the zygosity-specific odds ratios. In this application, psi F provides an estimate of the familial association for disease and the accompanying chi 2M-H provides a test of the null hypothesis, psi F = 1 (i.e., there is no evidence for a familial influence on disease). The chi 2G is a test of the null hypothesis that psi MZ = psi DZ; a significant value for chi 2G suggests a genetic influence on disease (assuming that the observed odds ratios follow a pattern where psi MZ greater than psi DZ). A new test statistic (chi 2c) is proposed that incorporates the expectation that psi MZ = psi 2DZ under a purely additive genetic model with no common environmental effects. A significant value of chi c2 indicates that the different odds ratios across zygosity are partly due to common environmental influences. Conversely, a nonsignificant value of chi 2c is an indication that the zygosity-specific odds ratios are due solely to additive genetic effects and not to common environment. This basic approach is extended to examine the effects of measured indicators of the specific environment and the assessment of certain forms of gene by environment interaction. All of the methods are easily understood, highly flexible, readily computed using a hand calculator, and incorporate the inherent genetic information contained within twin samples.