GXXI was established in 2005 in the Porto region of Portugal. All children born of women resident in the region and admitted to one of its five public hospitals for delivery, with a gestational age at birth greater than 24 weeks, were eligible to participate. Recruitment lasted from April 2005 to August 2006. Women were enrolled a few days before their due date and, the majority, completed baseline questionnaires between 24 and 72 hours after delivery. In total the baseline data consist of 8,311 singleton children. Children were actively followed-up through interviewer-administered questionnaires planned at 3, 6, 12–15 and 24 months of age. Due to logistic and financial constraints a restricted time window was allocated for each follow-up occasion and therefore it was not possible to interview every participant at each follow-up visit. The present analyses are based on the information collected at baseline and at the 2-years follow-up, which is available for 786 infants (9.5% of the original cohort). Maternal and birth characteristics of infants invited to participate in the 2-years follow-up were compared with the rest of the cohort. No systematic differences were found, suggesting that participants who were followed-up at 2 years of age are a representative sample of the whole cohort (Table S1); thus restriction of the analyses to this subgroup of subjects should not have biased the exposure-outcome estimates of interest. Further restrictions (subjects without follow-up weight measures (n = 3), subjects without gestational age data (n = 35) and subjects with missing data for the gender variable (n = 10)) were applied leading to 738 singleton babies included in the analyses. All growth data were retrieved prospectively from the child's health records by health professionals. These include anthropometric measures taken at birth and at about 1, 2, 4, 6, 9, 12, 15, 18 and 24 months of age, together with the actual dates of measurement. Up to 6 additional measurements and dates reported in the health records were also entered into the database. The median number of measurements per child is 10.

NINFEA is an on-going Italian web-based cohort study which started in 2005 and aims to recruit pregnant women via the Internet and follow up their children (more details in [31]–[32]). Enrollment is carried out at the study website (www.progettoninfea.it) where women complete the first questionnaire (Q1) at any time during their pregnancy. Active follow up is via online questionnaires administered at around 6 (Q2), 18 (Q3), 48 (Q4) months and 7 years (Q5) of age of the child. At Q2 women were asked to report the child's anthropometric measurements at birth, 3 and 6 months, while at Q3 they were asked to report the measures at 12 and 18 months. Revisions of these questionnaires, undertaken after approximately the first 1,500 mothers enrolled, led to inclusion of additional questions on the child's measures at the time of their completion. The analyses involve weight data from birth to around age 2, resulting in a median of 4 (range 1–7) measurements per child. These were obtained from the NINFEA database version 12.03 (downloaded in March 2012) and concern 2,925 singleton children with available data on gestational age at birth, whose mothers were born in Italy, and who, at the time of the data download, were eligible for at least the 6-months questionnaire (Q2). This implies that growth data up to about 6 months of age only are available for those infants who, at the time of the data download, were not eligible for the 18-months questionnaire (Q3). When comparing the distribution of baseline characteristics of infants with/without data from both Q2 and Q3 no systematic differences were observed (data not shown).

GOCS is an on-going Chilean cohort aiming to study the association of early growth with children's maturation, adiposity and associated metabolic complications (more details in [33]). The study was initiated in 2006 when all children aged 2.6–4 years attending public nursery schools in six counties of Santiago were invited to participate if they were singleton births with a gestational age at birth between 37 and 42 weeks, and birth weight between 2500 and 4500 grams. Among the 1,498 eligible children 1,195 (80%) accepted the invitation. The analyses include all 959 children with exact gestational age data. Weight and height measurements from birth up to 36 months of age were extracted from routinely-completed health records; from the time of recruitment onwards, children were measured yearly at their nursery by a dietician. For these analyses only growth data up to around age 2 years were used, yielding a median of 6 (range 1–8) measurements per child. These include measures taken at birth and at about 1, 2, 4, 6, 12, 18 and 24 months of age. When comparing the distribution of baseline characteristics of infants with/without complete growth data, differences were observed with respect to maternal pre-pregnancy BMI, smoking and age at birth of the child (data not shown). Since these variables are included in the growth models described below, results can still be generalized to the full cohort under the assumption of missingness at random (see Methods section).

The observed weight trajectories were modelled using a recently developed shape invariant random effects model. It was introduced by Cole [28] to study height trajectories in puberty, following the model proposed by Beath to analyse weight growth in infancy [23]. Let y_it be the weight of child i at age t, then SITAR is specified as:(1)where h(z) is a natural cubic spline of transformed age z, α_i, β_i and γ_i are subject-specific growth parameters, and ε_it is the residual error term assumed to have mean zero and constant variance. The three parameters correspond respectively to the size, tempo and velocity of growth specific to each child: α_i (size) represents the shift in the weight axis, while β_i (tempo) and γ_i (velocity) represent the change in location and scale to be applied to the age axis, respectively, in order for all children to share the same shape (mean spline curve h(z)). Size (α_i) is expressed in units of weight, tempo (β_i) in units of age, while velocity (γ_i) is a multiplier, and therefore is scale-free and reported as a percentage. Pizzi et al [34] discuss in detail how these parameters are to be interpreted given their close correlations. In brief they can be parameterized as follows: let α_i = α₀+α_1i, where α₀ is a fixed parameter, representing the size of a reference child, and α_1i a random, normally distributed variable with mean zero and constant variance, and let similar specifications for β_i and γ_i, then estimation can be carried out by maximum likelihood as for any (non-linear) mixed effects model [35]. Irregular observations can be handled under the assumption of missing at random (MAR) [36]. From a biological perspective α_1i (size) will be positive for heavier children, while β_1i (tempo) is related to the timing of maximum growth velocity and therefore will be negative for children whose growth is more advanced at earlier ages (earlier velocity peak), and γ_1i (velocity) will be positive for children with faster growth [28].

A covariate X with observed value x_i on subject i can be included in the model by specifying the three growth parameters as follow:(2)where δ_α, δ_β and δ_γ represent the contribution of the covariate to a child's size, tempo and velocity, respectively. Generalization of equation (2) to multiple covariates is straightforward. This is a slightly different parameterization from the one adopted by Beath [23].

Weight was log-transformed to aid meeting the distributional assumptions of the model. As a consequence δ_α is to be interpreted as percentage changes in size relative to the reference child [37]. Age was measured in months, hence δ_β is also expressed in months. The spline function h(z) was defined by placing the internal knots at quantiles of the age distribution, appropriate for each cohort because of varying richness and spread of the available weight measurements (four knots were used for analyses of GXXI and GOCS data and three for analyses of NINFEA). The complexity of the SITAR model relatively to the available data led to imposing constraints on its parameters, namely that the tempo of the standard child, β₀, was zero. Furthermore to be able to compare the three cohorts, δ_β, the contribution of each covariate on a child's tempo, was also constrained to be zero. These constraints were relaxed in analyses specific to GXXI as it had more weight growth measurements.

Models were initially fitted separately by study. We first included one explanatory variable at a time, with adjustment by gender and gestational age (we will refer to the latter results as “minimally-adjusted estimates”). We used all available data and also just the core datasets to allow comparisons between unadjusted and adjusted estimates for each of these variables. Fully-adjusted estimates were obtained by fitting two separate models to the core datasets: (i) the background explanatory variables were mutually adjusted, as well as adjusted for gestational age and gender; (ii) the intermediate explanatory variables were mutually adjusted, as well as adjusted for the background variables, gestational age and gender.

Models were also refitted on the pooled data from the three cohorts, including a fixed effect for the study indicators and assessing evidence of heterogeneity via significance tests of the interaction between each covariate and the study indicators (one covariate at a time, using the Wald test).

Table 2 presents the estimated minimally-adjusted and fully-adjusted covariate-specific parameters (i.e. the relevant δ_α and δ_γ), by cohort, obtained from models fitted to the core datasets. The minimally-adjusted estimates obtained when fitting the models to each whole cohort are reported in Table S2: they are generally close to the minimally-adjusted estimates in Table 2 indicating that the core datasets are likely to be representative of the corresponding whole cohorts. The minimally-adjusted and fully-adjusted estimates in Table 2 are very similar, indicating little reciprocal confounding among these variables. Despite some between-cohort differences, the findings overall are consistent with size (α_i) being positively associated with maternal height (NINFEA, fully-adjusted: δ_α = 0.4%; similarly in the other cohorts), pre-pregnancy overweight/obesity (NINFEA, fully-adjusted: δ_α = 2.1%; similarly in the other cohorts) and parity (GXXI, fully-adjusted: δ_α = 4.5%; similarly in NINFEA), but negatively associated with smoking during pregnancy (fully-adjusted: δ_α≈−3% in GXXI and NINFEA) and maternal pre-pregnancy underweight (fully-adjusted: δ_α≈−4% in each cohort). Post-natal growth velocity (γ_i) was positively associated with maternal smoking (GXXI, fully-adjusted: δ_γ = 13.2%; NINFEA, fully-adjusted: δ_γ = 6.5%), and possibly maternal underweight (NINFEA, fully-adjusted: δ_γ = 4.4%), but negatively associated with parity (GXXI, fully-adjusted: δ_γ = −6.1%; similarly in NINFEA). The results for education were heterogeneous: while in GXXI medium/highly educated women have bigger children who tend to have slower growth velocity, and in GOCS the children from less educated mothers have slower growth compared to those in the reference group, in NINFEA no association was found.

The model that examined pregnancy complications showed that, when fully adjusted for the other characteristics, gestational diabetes was not associated with infant weight growth (Table 3). In contrast, children from mothers with gestational hypertension were smaller and with a steeper growth curve (GXXI, fully-adjusted: δ_α = −6.4%, δ_γ = 12.8%; similarly in NINFEA), although this pattern was not present in GOCS.

Pooled analyses of the three cohorts show significant heterogeneity of effects for some covariates (smoking, gestational hypertension and gestational diabetes), with the differences arising from GOCS, unsurprisingly given the results of Tables 2–3, the retrospective collection of its prenatal data and its inclusion criteria. As there was no evidence of heterogeneity between GXXI and NINFEA, their data were pooled with results reported in Table 4 (only the fully adjusted estimates are reported). The estimated coefficients for pre-pregnancy BMI confirm that babies from underweight mothers are smaller but with a greater postnatal growth rate (i.e. velocity (γ_i)), while children from overweight/obese women have a bigger size (α_i) without evidence of decreased postnatal growth rate. Results for maternal education show that less educated mothers have smaller children that however have the same growth velocity (γ_i) as children of more educated mothers (Table 4).

In order to examine whether the observed heterogeneity across the cohorts was due to differences in entry criteria, we replicated cohort-specific analyses on the subset of GXXI and NINFEA children who were born at term and with a birth weight of 2500–4500 grams, using the same entry criteria as GOCS. The results pointed to much more similar effects across the cohorts.