The Danish Civil Registration System (CRS) [17
], which includes continuously updated information on vital status, was established in 1968, when all residents of Denmark were assigned a unique identifier (CRS number). All Danish national registries are based on this identifier, enabling accurate linkage between them. We linked the individual information recorded in the CRS to that of the Danish Medical Birth Registry [18
] which includes the birth record of all live births in Denmark since 1973. Due to secular changes in recording, we restricted our analysis to children born between 1979 and 2002, the most recent year with fully updated information at the time this study was initiated. Because of digit preference primarily to the nearest 100 grams, we rounded birth weight to the nearest 100 grams interval. Gestational age is based on the date of last menstrual period, but often corrected by ultrasound measurements, especially in the most recent period. Gestational age was recorded in completed weeks between 1978 and 1996, and in days from 1997 onward.
During the study period, there were 1,476,753 live births to Danish residents, all of which are included in the Medical Birth Registry. We excluded 51,372 (3.5%) births due to missing information on birth weight or gestational age.
Inconsistencies in gestational age
Gestational age is often estimated with error [19
], with an excess of unlikely large birth weights among infants with a low gestational age. To assess the consistency between birth weight and gestational age among preterm births, we applied a strategy similar to the mixture of two Normal distributions used previously [20
]. Maximum likelihood estimates of the mixture model parameters were obtained using the Newton-Rapson Method [25
]. We stratified the data by sex and gestational age (Table ). Among very preterm births (22–33 weeks), we observed a bimodal distribution and thus considered the data as inconsistent if the observed birth weight was greater than three times the standard deviation of the major Gaussian component of the distribution. Overall, 629 (2.7%) of the 23,425 very preterm births were considered inconsistent (see Table ). We also applied the mixture model to gestational ages beyond 33 weeks. Like Tentoni et al [20
], we found that the two model components overlapped almost completely, thus making the correction unnecessary.
Parameters of the major and secondary components in the mixture of two Normal distributions of birth weight among preterm births (22–33 weeks) stratified by gestational age and sex
Identification of sibships
Using data on family members recorded in the CRS [17
], we identified all sibships in Denmark consisting of first- and second-born singletons born alive between 1979 and 2002 (481,526 sibships). The pair of siblings had the same mother, but not necessarily the same father. We restricted the analyses to sibships with available and credible information on birth weight and gestational age of both babies, and to instances in which both live-born babies had a gestational age of at least 28 completed weeks (411,957 sibships). The included sibships constitute 86% (= 411,957/481,526) of the total number of sibships where the first and second baby were both born in Denmark during the study period.
Prediction of birth weight in second-born babies
We first calculated the predicted birth weight of second-born babies using the strategy described by Skjaerven et al [12
], based on the younger sibling's sex and gestational age and on the older sibling's birth weight. Since this approach did not take into consideration either the first-born's sex or gestational age, we explored whether including these factors improved the prediction. Since the variance of birth weight increases with increasing gestational age, the model used to predict the birth weight of the second-born needs to allow for this heterogeneity. Therefore, we used a variance component model [26
] to predict the second-born's birth weight, using the first birth weight as a linear term for each stratum of gestational age of first- and second-born babies, with a common sex correction. The birth weights of the second-born babies were assumed to be independent and normally distributed with a variance depending on their gestational age only. The model used to predict the absolute birth weight of the second-born baby was analogous to using a separate linear normal regressions for each stratum of gestational age of first- and second-born babies, except that we used a common sex correction independent of the gestational age of either baby and we constrained the variance of the second-born babies birth weights to be the same across all first-born's gestational ages.
We thus used the following equation to predict the birth weight of the second-born baby:
Pred(W2) = I(g1, g2) + β(g1, g2) * w1 + γ(s1, s2),
Pred(W2): predicted birth weight of the second-born child,
I(g1, g2): estimated intercept among sibs where the first-born had a gestational age of g1 and the second-born had a gestational age of g2.
β(g1, g2): estimated slope among sibs where the first-born had a gestational age of g1 and the second-born had a gestational age of g2
w1: first-born baby's observed birth weight
γ(s1, s2): estimated sex correction depending of the first-borns sex (s1) and the second-borns sex (s2)
Note: All parameters were estimates simultaneously using a variance component model.
In these analyses, first-borns' gestational age (g1) was categorized as 28–33, 34–35, 36–37, 38–39, 40–41, and >= 42 completed weeks, and second-borns' gestational age (g2) was categorized as 28–29, 30–31, 32–33, 34, 35, 36, 37, 38, 39, 40, 41, and >= 42 weeks. Since we expected gestational age of the second-born babies to be more important for predicting their own birth weight than gestational age of their older sibling, we decided a priori to use a more detailed categorization of gestational age for the second-born. For each gestational age of the first- and second-born, the parameters of intercept I(g1, g2) and slope β(g1, g2) are presented in Table . At the foot of the Table, the estimated common sex correction γ(s1, s2) is shown for each of the four combinations (female – female, female – male, male – female, male – male).
Parameters of intercept (I) and slope (β) for predicting the birth weights of second-born children based on gestational age and sex * of first- and second-born children.
Initially, we investigated the assumption that the variance of the second-born babies birth weights were the same across all first-born's gestational ages. Though, significant variation was observed, the estimated variance seemed to vary at no meaningful pattern, and we thus decided not to included this term in the model.
Estimating the relative risk of neonatal death
Second-born babies were followed from birth to the 27th
day of life, death, or emigration from Denmark, whichever came first. Neonatal death was defined as death occurring within 27 days after birth. We estimated the relative risk of neonatal death as a function of the deviation from the predicted birth weight, expressed by the birth weight ratio [(observed birth weight)/(predicted birth weight) × 100]. The relative risk of death was estimated by log-linear Poisson regression treating the number of person-years as an offset variable [27
]. All estimated relative risks were adjusted for year of birth, sex, and gestational age of the second baby. Though, we acknowledge that the reported relative risks are in principle incidence rate ratios, we prefer to refer to these as relative risks as most readers are familiar with this term.