Longitudinal growth modeling and derivation of early growth traits
AA Alexessander Couto Alves NS N. Maneka G. De Silva VK Ville Karhunen US Ulla Sovio SD Shikta Das HT H. Rob Taal NW Nicole M. Warrington AL Alexandra M. Lewin MK Marika Kaakinen DC Diana L. Cousminer ET Elisabeth Thiering NT Nicholas J. Timpson TB Tom A. Bond EL Estelle Lowry CB Christopher D. Brown XE Xavier Estivill VL Virpi Lindi JB Jonathan P. Bradfield FG Frank Geller DS Doug Speed LC Lachlan J. M. Coin ML Marie Loh SB Sheila J. Barton LB Lawrence J. Beilin HB Hans Bisgaard KB Klaus Bønnelykke RA Rohia Alili IH Ida J. Hatoum KS Katharina Schramm RC Rufus Cartwright MC Marie-Aline Charles VS Vincenzo Salerno KC Karine Clément AC Annique A. J. Claringbould CD Cornelia M. van Duijn EM Elena Moltchanova JE Johan G. Eriksson CE Cathy Elks BF Bjarke Feenstra CF Claudia Flexeder SF Stephen Franks TF Timothy M. Frayling RF Rachel M. Freathy PE Paul Elliott EW Elisabeth Widén HH Hakon Hakonarson AH Andrew T. Hattersley AR Alina Rodriguez MB Marco Banterle JH Joachim Heinrich BH Barbara Heude JH John W. Holloway AH Albert Hofman EH Elina Hyppönen HI Hazel Inskip LK Lee M. Kaplan AH Asa K. Hedman EL Esa Läärä HP Holger Prokisch HG Harald Grallert TL Timo A. Lakka DL Debbie A. Lawlor MM Mads Melbye TA Tarunveer S. Ahluwalia MM Marcella Marinelli IM Iona Y. Millwood LP Lyle J. Palmer CP Craig E. Pennell JP John R. Perry SR Susan M. Ring MS Markku J. Savolainen FR Fernando Rivadeneira MS Marie Standl JS Jordi Sunyer CT Carla M. T. Tiesler AU Andre G. Uitterlinden WS William Schierding JO Justin M. O’Sullivan IP Inga Prokopenko KH Karl-Heinz Herzig GS George Davey Smith PO Paul O'Reilly JF Janine F. Felix JB Jessica L. Buxton AB Alexandra I. F. Blakemore KO Ken K. Ong VJ Vincent W. V. Jaddoe SG Struan F. A. Grant  SS Sylvain Sebert  MM Mark I. McCarthy  MJ Marjo-Riitta Järvelin

Early growth traits were derived from sex-specific individual growth curves using mixed-effects models of height, weight, and BMI measurements from birth to 13 years (fig. S1). All height and weight data were collected prospectively via either self-reported data or clinical measurements (tables S1 and S2). These traits were derived separately in each cohort (note S2).

Derivation of PHV and PWV. The methods for growth modeling and derivation of growth parameters from the fitted curves are described in detail in a previous publication (38). Parametric Reed1 growth model was fitted in sex-stratified nonlinear random-effect model as described previously (39). Term-born singletons (defined as ≥37 completed weeks of gestation) with at least three height or weight measurements from birth to 24 months of age were included in the Reed1 model fitting. Maximum-likelihood method for best fitting curves for each individual was used to estimate the growth parameter, PHV (in centimeters per month), and PWV (in kilograms per month).

Derivation of Age-AP, Age-AR, BMI-AP, and BMI-AR. The methods used for growth modeling of age and BMI have been previously described in detail by Sovio et al. (26). Because of the specificity of longitudinal changes in BMI, i.e., succession of peak and nadir as described in fig. S1, the data were divided into two age windows for modeling: (i) growth in infancy using height and weight data from 2 weeks to 18 months of age and (ii) growth in childhood using growth and weight data from 18 months to 13 years of age. Each cohort contributed most data available within any of these two age windows. In studies where the data available consisted of both height and weight data within a given window, the data point nearest to the mid time points of that window was used as a proxy for the BMI measurement. Before model fitting, age was centered using the median age of the relevant age window. For example, in the infant growth model at 0 to 1.5 years, the median age was 0.75 years (which was close to the average Age-AP), and in the childhood growth model at >1.5 to 13 years, the median age was 7.25 years (on average shortly after AR). Linear mixed-effects models were then fitted for log-transformed BMI. We used sex and its interaction with age as covariates, with random effects for intercepts (i.e., baseline BMI) and linear slope (i.e., linear change in BMI) over time. In addition to linear age effect, quadratic and cubic terms for age were included in the fixed effects to account for nonlinearity of BMI change over time.

Growth in infancy. The following model was used to calculate the Age-AP and BMI-AP, and the analysis was restricted to singletons with BMI measures from 2 weeks to 18 months of age. The model is as follows

log(BMI) = β0 + β1 Age + β2 Age2 + β3 Age3 + β4 Sex + u0 + u1 (Age) + ε

where BMI is expressed in kilograms per square meter and age in years. β0, β1, β2, β3, and β4 are the fixed-effects terms, u0 and u1 are the individual-level random effects, and ε is the residual error. The Age-AP was calculated from the model as the age at maximum BMI between 0.25 and 1.25 years according to preliminary research (38).

Growth in childhood. The model used to measure the age and BMI-AR in childhood is as follows

log(BMI) = β0 + β1 Age + β2 Age2 + β3 Age3 + β4 Sex +β5 Age × Sex + β6 Age2 × Sex + u0 + u1 (Age) + ε

where BMI is expressed in kilograms per square meter and age in years. β0, β1, β2, β3, β4, β5, and β6 are the fixed-effects terms, u0 and u1 are the individual-level random effects, and ε is the residual error. Age-AR was calculated as the age at minimum BMI between 2.5 and 8.5 years according to preliminary research (38).

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