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Background  The association between a slower physical growth and poorer neurodevelopment has been established in infants born preterm or small for gestational age. However, this association is inconsistent in term-born infants, and detailed investigations in infancy, when intervention is most beneficial for improving outcomes, are lacking. We therefore examined this association separately by sex during the first year of life in term-born infants.    Methods  Using data collected until children reached 12 months old in an ongoing prospective cohort of the Japan Environment and Children’s Study, we analyzed 44,264 boys and 42,541 girls with singleton term-birth. The exposure variables were conditional variables that disentangle linear growth from weight gain relative to linear growth, calculated from the length and weight at birth and 4, 7 and 10 months old. Neurodevelopmental delay was identified using the Japanese-translated version of Ages & Stages Questionnaires, third edition.    Results  A reduced risk of neurodevelopmental delay at 6 months old was observed in children with a higher birth weight (adjusted relative risks [aRRs]: 0.91 and 0.93, 95 % confidence intervals [95 % CIs]: 0.87–0.96 and 0.88–0.98 in boys and girls, respectively) and increased linear growth between 0 and 4 months old (aRRs: 0.85 and 0.87, 95 % CIs: 0.82–0.88 and 0.83–0.91 in boys and girls, respectively). A reduced risk at 12 months was found in children with an increased linear growth between 0 and 4 months (aRRs: 0.92 and 0.90, 95 % CIs: 0.87–0.98 and 0.84–0.96 in boys and girls, respectively), boys with an increased relative weight gain between 0 and 4 months (aRR: 0.90, 95 % CI: 0.84–0.97), and girls with a higher birth weight (aRR: 0.89, 95 % CI: 0.83–0.96).    Conclusions  These results suggest that a slow physical growth by four months old may be a predictor of neurodevelopmental delay during infancy.    Supplementary Information  The online version contains supplementary material available at 10.1186/s12887-021-02815-9.

Physical growth and neurodevelopment during the first year of life: a cohort study of the Japan Environment and Children’s Study