Statistical Analyses of Monozygotic and Dizygotic Twinning Rates

Abstract

The French mathematician Bertillon reasoned that the number of dizygotic (DZ) pairs would equal twice the number of twin pairs of unlike sexes. The remaining twin pairs in a sample would presumably be monozygotic (MZ). Weinberg restated this idea and the calculation has come to be known as Weinberg's differential rule (WDR). The keystone of WDR is that DZ twin pairs should be equally likely to be of the same or the opposite sex. Although the probability of a male birth is greater than .5, the reliability of WDR's assumptions has never been conclusively verified or rejected. Let the probability for an opposite-sex (OS) twin maternity be p O , for a same-sex (SS) twin maternity p S and, consequently, the probability for other maternities 1 − p S − p O . The parameter estimatesp O andp S are relative frequencies. Applying WDR, the MZ rate is m = p S − p O and the DZ rate is d = 2 p O , but the estimatesm andd are not relative frequencies. The maximum likelihood estimatorsp S andp O are unbiased, efficient, and asymptotically normal. The linear transformationsm =p S −p O andd = 2p O are efficient and asymptotically normal. If WDR holds they are also unbiased. For the tests of a set of m and d rates, contingency tables cannot be used. Alternative tests are presented and the models are applied on published data.

Neonatal outcomes among twins following assisted reproductive technology: an Australian population-based retrospective cohort study

“…Due to high proportion of missing data BMI and smoking during pregnancy, a sensitivity analysis was conducted by excluding smoking or BMI in the adjustment. Weinberg’s differential rule was used to estimate monozygotic twin rate [ 12 ]. Data were analysed using Statistical Package for Social Sciences (SPSS) software, version 22 (SPSS, Inc., Chicago, IL, USA).…”

Seasonality in Multiple Maternities

“…Hence, the variance formulae given for observed rates are incorrect for these estimated rates. Following a different route, Fellman (2013) later found similar results and presented exact alternative formulae for the SD s of the MZR and DZR. Elster and Bleyl (1991) noted seasonality in the number of triplet births and that its pattern differed markedly from the seasonality of the births of the entire U.S. population (cf.…”

Twinning Rates in Isolates

“…In our statistical analyses, we paid special attention to: (a) the robustness of the variance formula of the TWR, and (b) the most precise confidence intervals for the TWRs. Eriksson (2004, 2006) and Fellman (2013) have considered these aspects of the statistical analyses of the TWRs more thoroughly. These statistical methods are crucial when the extreme TWRs within often small subpopulations are compared with the TWRs within the general population.…”

“…Fellman and Eriksson (2004, 2006) and Fellman (2013) have considered these aspects of the statistical analyses of the TWRs more thoroughly. These statistical methods are crucial when the extreme TWRs within often small subpopulations are compared with the TWRs within the general population.…”