Correlations Between Live and Stillbirth Outcomes in Twin Pairs

Abstract

A relationship has been proposed to exist between individual outcomes (live or stillbirth) of twins in the same set. Here, we analyze this association between live births and stillbirths among individuals in different twin pairs. When national birth registers are analyzed, individuals in opposite-sex twin sets can be identified and the correlation between individual outcomes estimated. However, full information about the individuals in same-sex twin sets is not, as a rule, available, and consequently, correlation coefficients cannot be estimated, but upper and lower limits of the correlation coefficients can be obtained. The methods introduced here were applied to data from Sweden (1869-1967), the Åland Islands (Finland) (1750-1949), the Kingdom of Saxony (1881-1900), and England and Wales (1940-2003). Comparisons between the correlation coefficients among opposite-sex twins and the lower bound (minimum) of correlation coefficients among same-sex twins indicate that in all populations studied a stronger association exists between twins in same-sex rather than opposite-sex twin sets or pairs. For opposite-sex twin sets no general association between the correlation coefficient and the stillbirth rate was identified.

KEY WORDS: BIRTH OUTCOME, STILLBIRTH RATE, OPPOSITE-SEX TWINS, SAME-SEX TWINS, CORRELATION COEFFICIENTS, ENGLAND, WALES, SAXONY, SWEDEN, ÅLAND ISLANDS (FINLAND).

(ProQuest: ... denotes formulae omitted.)

A clear dependence has been postulated in the state of health at birth of individual twins in the same set (Salihu et al. 2004; Fellman and Eriksson 2006). In this study we assume that the outcome of the child can be classified as a live birth or a stillbirth. We analyze the correlation between the outcomes of the subjects in a twin set. In the text we use the shorter expression "correlation between the twins."

In opposite-sex (OS) twin sets, the individuals, being of different sex, can be identified. Consequently, the correlation coefficient can be estimated. When national birth registers are analyzed, exact information about individuals in same-sex (SS) twin sets is not, as a rule, available, and thus correlation coefficients cannot be estimated. However, upper and lower bounds of these coefficients can be obtained. Fellman and Eriksson (2006b) also analyzed these data in a different way.

The stillbirth rate (SBR) is higher among SS twins than among OS (dizygotic) twins. Especially high is the SBR among monozygotic twins (Fellman and Eriksson 2007). We analyzed the association between the SBR and the correlation coefficient among OS twin sets.

Materials and Methods

We analyzed data from Sweden for the period 1869-1967. These data were also considered and presented in more detail by Fellman and Eriksson (2006a, 2006c) and Eriksson and Fellman (2006). We compared the Swedish data with data from the Aland Islands (Finland) (1750-1949), reported by Eriksson (1973), the Kingdom of Saxony (in present-day Germany) (1881-1900), reported by Lommatzsch (1902), and England and Wales (1940-2003), obtained from published registers and from the website http://www.statistics.gov.uk/. Summaries of the data sets are presented in Table 1.

The data set from England and Wales (1996-2003) is also classified according to maternal age and is presented in Table 2.

Opposite-Sex Twin Sets. Let the condition of the twins in a male-female (MF) twin set be characterized by the variables X for males and Y for females, such that

...

Consequently, all values of the variables are known, and the correlation coefficient can be estimated. Assume that the number of twin sets with two live-born twins is n^sub 11^, that the number of twin sets with one live-born male and one stillborn female is n^sub 10^, that the number of twin sets with one stillborn male and one live-born female is n^sub 01^, and that the number of twin sets with both twins stillborn is n^sub 00^. The total number of sets is

n = n^sub 11^ + n^sub 10^ + n^sub 01^ + n^sub 00^. (2)

The data for the MF twins are presented in Table 3.

The means of the variables X and Y are

..., (3)

that is, the live-birth rates for males and females, respectively. The correlation coefficient is

... (4)

After some tedious but straightforward calculations, one obtains the simplified formula

... (5)

Written in this form, we observe that the correlation coefficient is identical to the association coefficient V presented by Kendall and Stuart (1967, p. 539). In fact, this association measure has already been given and analyzed in detail by Yule (1900, 1912). Assuming that one considers such large samples that the observed frequencies can be used instead of their expectations, one obtains the variance formula (Kendall and Stuart 1967, p. 541)

... (6)

Kendall and Stuart (1967, p. 549) showed that χ^sup 2^ = nV^sup 2^ is asymptotically chisquare distributed with 1 degree of freedom. In fact, this chi-square value equals the classical chi-square value defined for 2 by 2 contingency tables (Kendall and Stuart 1967, p. 552). Fellman and Eriksson (2006b) applied it in the study of dependence in MF twin pairs.