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 (+F, the weighted average of the zygosity-specific odds ratios), the Mantel-Haenszel test statistic ( x $ -~) for the common odds ratio, and a test (&) for the difference in the zygosity-specific odds ratios. In this application, Jlp provides an estimate of the familial association for disease and the accompanying x&-" provides a test of the null hypothesis, +F = 1 (i.e., there is no evidence for a familial influence on disease).
The x : is a test of the null hypothesis that JIMZ = +Dz; a significant value for x'& suggests a genetic influence on disease (assuming that the observed odds ratios follow a pattern where +MZ>+DZ). A new test statistic (x:) is proposed that incorporates the expectation that JIMZ = +& under a purely additive genetic model