Data collection and variables generation

Data were collected from medical and obstetrical records or by interviews, face-to-face or self-administered questionnaires and clinical examinations. Biological samples, anthropometric, and clinical parameters measurements were collected during clinical examinations at birth, 1, 3, and 5 years. In all children, weight and height from birth to early adolescence were obtained during these visits or from health records. Children had a mean of 10 weight and height measurements (interquartile range 6–14 and 5–13, respectively) from birth to 13 years. Maternal smoking status during pregnancy (yes/no); parental characteristics such as maternal age (years), maternal and paternal educational level and parental anthropometric measurements were collected during pregnancy. Newborn characteristics as well as sex, gestational age, and birth weight were taken at birth [26]. Preterm birth (yes/no) was defined as babies born before 37 weeks of gestation. Birth weight customized z-scores were calculated according to Gardosi references taking into account physiological fetal (sex and gestational age) and maternal factors (weight, height, parity, origin) [27]. Newborns were classified, according to this customized approach, into three classes: small for gestational age (SGA, ≤10th percentile), appropriate for gestational age (AGA, >10th percentile to ≤90^th percentile), and LGA (>90^th percentile).

Maternal and paternal education level was considered as the number of years of study. Parental weight and height were collected by interview at inclusion. Parental anthropometric measurements were collected at inclusion were used to calculate parental BMI by dividing the weight (kilograms) by the square of height (meters). Gestational weight gain (kilograms) was collected from obstetric records.

DNA samples were extracted from cord-blood at birth. Genotyping for 27 single-nucleotide polymorphisms (SNPs) was performed by the Epidemiology Unit of the Medical Research Council of Cambridge (iPLEX platform; Sequenom) [28]. Genotyping quality-control criteria (call rate, >95%; Hardy Weinberg balance, p > 0.01) were satisfactory for all variants. In the present study, we considered 27 of 32 SNPs associated with BMI in adults [21], of which also the 16 associated with childhood BMI in a meta-analysis of Elks et al. [23].

For each child, combined obesity risk‐allele scores across the 27 SNP loci were calculated as the sum of risk alleles (0, 1, or 2 at each locus) associated with increased BMI. The score indicating genetic predisposition to obesity ranged from 11 to 32. Combined obesity risk‐allele scores were available for 1322 children of the EDEN cohort and their mothers (N = 1678) and fathers (N = 1241) [29].

A weighted obesity risk-allele score was also computed by multiplying each risk-allele by the effect estimate on adult BMI as assessed in the genome-wide association study [21], for sensitivity analyses.

Age at AR is defined as the last minimum (nadir) BMI before the continuous increase in BMI over time [1].

We calculated BMI from weight and height measurements. We excluded children with fewer than three BMI measurements from age 18 months to 13 years. Included children had 10 BMI values on average (interquartile range 6–14) from age 18 months to 13 years. Individual growth curves were obtained by using mixed-effects cubic models separately for girls and boys. The methods for growth modeling of age at AR were inspired by the model of Sovio et al. [30]. To this previously described model, we added random effects for the quadratic and cubic terms for age with unstructured covariance matrix, which provided the best fit of individual predicted curves. The model was then fitted for log-transformed BMI, separately for boys and girls, as follows:

where BMI is expressed in kilograms per square meter and age in days; β₀, β_1, β₂, β₃, and β₄ are the fixed-effects terms; μ_0, μ_1, μ₂, and μ₃ are the individual-level random effects; and ɛ is the residual.

For each participant, we estimated age at AR by the first and second derivatives of individual BMI functions. Results of this modeling process are illustrated for a random sample of ten participants in Supplementary Fig. S1.