Weinberg's differential rule reconsidered

A central problem in research on twins is the estimation of the rates of monozygotic and dizygotic twin maternities. The estimation usually follows Weinberg's differential rule. According to this rule, the rate of dizygotic twinning is twice the rate of twin maternities in which the twins are of opposite sex. The monozygotic twinning rate is the difference between the rates of same-sex and opposite-sex twin sets. Weinberg's differential rule is implicitly based on the assumptions that the probability of a male equals the probability of a female and that the sexes in a dizygotic twin set are independent. Although Weinberg's differential rule has been the target of continuing discussions, the reliability of these assumptions has never been conclusively verified or rejected. In this study we present new variance formulas for the monozygotic and dizygotic twinning rates obtained using Weinberg's differential rule and stress that these new formulas have to be used. We analyze the accuracy of Weinberg's differential rule by considering alternative attempts. Especially, we build a general likelihood function and show that the maximum-likelihood estimates differ only slightly from the rates obtained using Weinberg's differential rule. In addition, our methods are applied to twinning data from Finland and Sweden. We compare our results with findings in the literature. In conclusion, our findings indicate that Weinberg's differential rule is rather robust and that despite its simplicity, it gives reliable results when official birth registers are analyzed.