SuperImposition By Translation And Rotation Model Research Articles

5174 A longitudinal retrospective cohort study on the application of the Superimposition by translation and rotation (SITAR) model to estimate body composition growth trajectory in Korean children and adolescents during puberty

Abstract Disclosure: S. Kim: None. S. Kim: None. J. Suh: None. Introduction: In addition to adulthood, pediatricians have noted a growing emphasis on research concerning sarcopenic obesity. Studies in this field have expanded beyond basic BMI-related inquiries, actively delving into investigations based on body fat mass (BFM) and fat-free mass (FFM). However, limited research has systematically analyzed the acquisition of body composition during children and adolescence based on longitudinal data. Objective: This study aims to assess the acquisition of weight, FFM, and BFM during the pubertal growth of Korean children and adolescents. Methods: This study utilized mixed longitudinal body measurement and body composition data, employing bioelectrical impedance analysis, from 4,641 height measurements (2,204 for boys and 2,437 for girls) obtained from 361 individuals (170 boys and 191 girls) among Korean children and adolescents aged 7 to 18. The SITAR (the Superimposition by Translation and Rotation) model, a shape-invariant growth curve model, was used to estimate a reference height velocity curve during pubertal growth. Results: The SITAR methodology allowed us to investigate the timing, magnitude, and intensity of adolescent weight, FFM, and BFM gain. The results revealed significant differences in growth trajectories between boys and girls, with boys exhibiting a persistent elevation in FFM and a pattern of ascent followed by a decline in BFM, while girls show an increase in BFM and a deceleration in FFM growth. In Korean boys, the peak weight velocity (PWV) occurred at a mean age of 12.41 years, with a rate of 8.19 kg/year. Peak fat-free mass velocity (PFV) was observed at a mean age of 9.69 years, with a rate of 7.60 kg/year, and peak body fat mass velocity (PBV) at a mean age of 12.70 years, with a rate of 2.67 kg/year. In Korean girls, the mean age of PWV was 11.28 years, with a velocity of 6.33 kg/year. PFV occurred at a mean age of 12.33 years, with a rate of 4.86 kg/year, and PBV at a mean age of 11.13 years, with a rate of 2.72 kg/year. The ages of peak velocities of height (PHV), PWV, PFV, and PBW positively correlated. Conclusions: This study is the first to apply the SITAR model to examine the acquisition of body composition in Korean children and adolescents. Future research should delve into exploring the connections between various disease groups during childhood and adolescence and the patterns of change in body composition. Presentation: 6/1/2024

The estimation of pubertal growth spurt parameters using the superimposition by translation and rotation model in Korean children and adolescents: a longitudinal cohort study.

Understanding the characteristics of the pubertal growth spurt in Korean children and adolescents can serve as crucial foundational data for researching puberty and growth-related disorders. This study aims to estimate the key parameters of pubertal growth, specifically the age and magnitude of the pubertal growth spurt, utilizing longitudinal data from a cohort of Korean children and adolescents. This study used mixed longitudinal height data from a cohort of Korean elementary, middle, and high school students aged 7-18 years. The Superimposition by Translation and Rotation (SITAR) model, a shape-invariant growth curve model, was utilized to estimate a reference height velocity curve for the entire dataset and individual curves via random effects to evaluate pubertal growth parameters. Altogether, 3,339 height measurements (1,519 for boys and 1,820 for girls) from 270 individuals (123 boys and 147 girls) were analyzed. The average age of growth spurt onset in Korean boys was 10.17 ± 0.61 years (mean ± SE), with peak height velocity occurring at 12.46 ± 0.69 years of age (9.61 ± 1.26 cm/year). Korean girls, contrarily, experience their growth spurt at an earlier age (8.57 ± 0.68 years), with peak height velocity occurring at 10.99 ± 0.74 years of age (8.32 ± 1.09 cm/year). An earlier onset of puberty in both sexes is associated with a shorter growth spurt duration (0.63 years for boys and 0.58 years for girls) and a higher peak height velocity (1.82 cm/year for boys and 1.39 cm/year for girls). These associations were statistically significant for both sexes (all p < 0.0001). This study is the first to use the height velocity curve from the SITAR model to examine the pubertal growth spurt of Korean children and adolescents. The estimated timing and magnitude of the pubertal growth spurt, and their relationships can be useful data for clinicians and researchers.

Analyzing longitudinal growth data in orthodontics

Longitudinal growth data with repeated measurements of distances and angles on radiographs are usually collected to study skeletal and dental changes throughout childhood and adolescence. The analysis of longitudinal data usually requires sophisticated statistical methods and modeling techniques because repeated measurements made on the same subject violate the assumption of independence underlying classical statistical tests. Advanced methods, such as multilevel modeling, must be used to account for the correlations between repeated measurements. In this article, we describe four statistical models for the analysis of growth data: linear multilevel model, curvilinear multilevel model, multilevel Preece-Baines model, and super imposition by translation and rotation (SITAR) model. We use data of 42 children on the mandibular length obtained from the archives at the AAOF Craniofacial Growth Legacy Collection for demonstration. Our analyses showed that although the multilevel curvilinear model appears to fit the data well from a statistical perspective, the Preece-Baines model and the SITAR model provide additional insights into mandibular growth. The SITAR model suggests two growth peaks which is consistent with the current understanding of mandibular growth and deserves more attention from orthodontic researchers.

Skeletal maturation in male elite youth athletes from the Middle East.

To examine the timing and intensity of skeletal maturation of the radius-ulna-short (RUS) bones in elite youth Arab athletes. We compared SuperImposition by Translation And Rotation (SITAR) models with different spline degrees of freedom and transformation expressions to summarize 492 longitudinal measurements for individual RUS bones scores assessed from 99 male academy student-athletes (chronological age range, 11.4 to 18 years; annual screening range, four to seven visits). The SITAR model with 5 degrees of freedom and untransformed chronological age was superior to the other models. The mean growth curve increased with age and showed a mid-pubertal double-kink at a RUS score of ~600 bone score units (au). The SITAR model revealed a first peak in the skeletal maturation velocity curve of ~206 au·year-1 occurred at ~13.5 years. The mean age at the second and largest peak occurred at 15.1 years (95% confidence interval [CI], 14.9 to 15.3 years), with the respective estimated peak skeletal ossification rate of 334 au·year-1 (95% CI, 290 to 377 au·year-1 ). The mean age at peak height velocity was 13.5 years (95% CI, 13.3 to 13.7 years), with peak height velocity of 10 cm·year-1 (95% CI, 9.6 to 10.4 cm·year-1 ). Application of the SITAR method confirmed two peaks in the skeletal maturation velocity curve, with the second and largest rate of ossification occurring at a relatively later timing of ~1.5 yearsthan the height growth spurt. Knowledge of the RUS bonestiming and intensity can be important to advance strategies for athlete performance development purposes.

Changes in the growth of very preterm infants in England 2006–2018

ObjectiveTo compare weight gain from birth to term equivalent age in very preterm infants in England born during two eras (2006–2011 and 2014–2018); to assess demographic and care factors influencing...

Using linear and natural cubic splines, SITAR, and latent trajectory models to characterise nonlinear longitudinal growth trajectories in cohort studies

BackgroundLongitudinal data analysis can improve our understanding of the influences on health trajectories across the life-course. There are a variety of statistical models which can be used, and their fitting and interpretation can be complex, particularly where there is a nonlinear trajectory. Our aim was to provide an accessible guide along with applied examples to using four sophisticated modelling procedures for describing nonlinear growth trajectories.MethodsThis expository paper provides an illustrative guide to summarising nonlinear growth trajectories for repeatedly measured continuous outcomes using (i) linear spline and (ii) natural cubic spline linear mixed-effects (LME) models, (iii) Super Imposition by Translation and Rotation (SITAR) nonlinear mixed effects models, and (iv) latent trajectory models. The underlying model for each approach, their similarities and differences, and their advantages and disadvantages are described. Their application and correct interpretation of their results is illustrated by analysing repeated bone mass measures to characterise bone growth patterns and their sex differences in three cohort studies from the UK, USA, and Canada comprising 8500 individuals and 37,000 measurements from ages 5–40 years. Recommendations for choosing a modelling approach are provided along with a discussion and signposting on further modelling extensions for analysing trajectory exposures and outcomes, and multiple cohorts.ResultsLinear and natural cubic spline LME models and SITAR provided similar summary of the mean bone growth trajectory and growth velocity, and the sex differences in growth patterns. Growth velocity (in grams/year) peaked during adolescence, and peaked earlier in females than males e.g., mean age at peak bone mineral content accrual from multicohort SITAR models was 12.2 years in females and 13.9 years in males. Latent trajectory models (with trajectory shapes estimated using a natural cubic spline) identified up to four subgroups of individuals with distinct trajectories throughout adolescence.ConclusionsLME models with linear and natural cubic splines, SITAR, and latent trajectory models are useful for describing nonlinear growth trajectories, and these methods can be adapted for other complex traits. Choice of method depends on the research aims, complexity of the trajectory, and available data. Scripts and synthetic datasets are provided for readers to replicate trajectory modelling and visualisation using the R statistical computing software.

Bayesian Shape Invariant Model for Latent Growth Curve with Time-Invariant Covariates

In the attention-deficit hyperactivity disorder (ADHD) study, children are prescribed different stimulant medications. The height measurements are recorded longitudinally along with the medication time. Differences among the patients are captured by the parameters suggested the Superimposition by Translation and Rotation (SITAR) model using three subject-specific parameters to estimate their deviation from the mean growth curve. In this paper, we generalize the SITAR model in a Bayesian way with time-invariant covariates. The time-invariant model allows us to predict latent growth factors. Since patients suffer from a common disease, they usually exhibit a similar pattern, and it is natural to build a nonlinear model that is shaped invariant. The model is semi-parametric, where the population time curve is modeled with a natural cubic spline. The original shape invariant growth curve model, motivated by epidemiological research on the evolution of pubertal heights over time, fits the underlying shape function for height over age and estimates subject-specific deviations from this curve in terms of size, tempo, and velocity using maximum likelihood. The usefulness of the model is illustrated in the attention deficit hyperactivity disorder (ADHD) study. Further, we demonstrated the effect of stimulant medications on pubertal growth by gender.

Pubertal growth in height, sitting height and leg length in achondroplasia

Background: Children with achondroplasia (ACH) appear to lack a pubertal growth spurt in height. Aim To explore the growth spurt in height and its segments sitting height and leg length, in a large sample of ACH cases using growth curve modelling. Subjects and methods: Height and sitting height were measured longitudinally in ACH children, and the data were analysed using the SITAR (SuperImposition by Translation and Rotation) growth model, which estimates a mean growth curve and random effects for individuals defining differences in size, pubertal timing and intensity. Results: Out of 402 ACH children, 85 boys and 75 girls aged 7–20 years had respectively 529 and 454 measurements of height and sitting height, with leg length calculated by difference. SITAR analysis identified peaks in mean height velocity at 13.3 and 11.3 years in boys and girls, with peak velocities of 4.3 and 4.4 cm/year. Mean peak velocity for sitting height was 3.0 cm/year, but leg length showed no peak. The SITAR models explained 92% to 99% of the cross-sectional variance. Conclusion: ACH children do experience a growth spurt in puberty, but only half that of control children. The spurt is due entirely to sitting height, with no leg length spurt.

Developmental trajectories of infants born at less than 30 weeks’ gestation on the Bayley-III Scales

ObjectiveTo describe the cognitive, language and motor developmental trajectories of children born very preterm and to identify perinatal factors that predict the trajectories.DesignData from a cohort of 1142 infants born...

Using the SITAR Method to Estimate Age at Peak Height Velocity of Children in Rural South Africa: Ellisras Longitudinal Study.

Various studies have been conducted on children using the Ellisras Longitudinal Study Survey in South Africa, but none of these has addressed growth variations of children in this rural location. The aim of this paper is to assess the age at peak height velocity using the superimposition by translation and rotation (SITAR) method for both boys and girls in rural South Africa. The study is part of the on-going Ellisras Longitudinal Study, and has employed secondary data during the period from November 1996 to November 2003. The data was collected biannually in May and November each year. The Ellisras study initially followed a cluster sampling method. All participating children underwent a series of anthropometric measurements of height and weight according to the standard procedures recommended by the International Society for the Advancement of Kinanthropometry. The analysis was done using the SITAR model. Age at peak height velocity for Ellisras rural children was at 14.45 years for boys at 11.82 years for girls. Ellisras rural girls had their age at peak height velocity way earlier than Ellisras rural boys did by an estimated 2.63 years. Ellisras rural children and their growth variations were comparable to other studies.

Tanner’s tempo of growth in adolescence: recent SITAR insights with the Harpenden Growth Study and ALSPAC

Background: James Tanner emphasised the “tempo” of growth, i.e. the adolescent spurt as summarised by its timing (age at peak velocity or APV) and intensity (peak velocity, PV).Aim: The paper applies the SITAR growth curve model to pubertal growth data with the aim of clarifying the growth pattern across multiple measurements and the spectrum of APV and PV.Subjects and methods: Data for 7–20 years on ten anthropometric measurements in 619 children from the Harpenden Growth Study, and on height in 10410 children from the ALSPAC study, were analysed using SITAR (SuperImposition by Translation And Rotation). SITAR models pubertal growth as a mean curve with APV and PV fitted as subject-specific random effects, and a random measurement intercept.Results: Mean APV for Harpenden girls and boys averaged 12.0 and 13.9 years across the ten measurements. PV expressed as percent per year lay in the narrow range 4–8%. Splitting the ALSPAC subjects into 9 by 5 APV and PV groups and fitting separate SITAR models to each group confirmed SITAR’s good fit while highlighting the spectrum of growth patterns.Conclusion: SITAR works well to summarise pubertal growth. The disappointment is that Tanner did not live to see it in action.

Life course associations of height, weight, fatness, grip strength, and all-cause mortality for high socioeconomic status Guatemalans.

ObjectivesThe objective of this study was to investigate the association between physical growth in preadult life with five outcomes at ages 64 to 76: weight, body mass index (BMI), estimated body fat percentage, hand grip strength, and mortality.MethodsSuper‐imposition by translation and rotation (SITAR) growth curves of 40 484 Guatemalan individuals aged 3 to 19 years were modeled for the parameters of size, timing and intensity (peak growth velocity, eg, cm/year) of height, weight, BMI, and grip strength. Associations between the SITAR parameters and old age outcomes were tested using linear and binary logistic regression for a follow‐up sample of high socioeconomic status (SES) Guatemalans, of whom 50 were aged 64 to 76 years at re‐measurement and 45 died prior to the year 2017.ResultsSITAR models explained 69% to 98% of the variance in each outcome, with height the most precise. Individuals in the follow‐up sample who had a higher BMI before the age of 20 years had higher estimated body fat (B = 1.4 CI −0.02‐2.8) and BMI (B = 1.2, CI 0.2‐2.2) at the ages of 64 to 76 years. Those who grew slower in height but faster in weight and BMI before the age of 20 years had higher BMI and body fat later in life.ConclusionsThese findings highlight the importance of a life course perspective on health and mortality risk. Childhood exposures leading to variation in preadult growth may be key to better understanding health and mortality risks in old age.

Association of Height Growth in Puberty with Lung Function. A Longitudinal Study.

Rationale: Puberty may influence lung function, but the precise role of pubertal height growth in lung development is unclear.Objectives: To examine associations of timing of puberty and peak velocity of pubertal height growth with lung function in adolescence and early adulthood.Methods: Longitudinal analyses of repeat height measurements from age 5 to 20 years for a British birth cohort with 4,772 males and 4,849 females were conducted to characterize height growth trajectories and to derive pubertal age and peak height velocity using the validated SITAR (SuperImposition by Translation and Rotation) model. Association of these estimates with prebronchodilator and post-bronchodilator spirometry measures: FEV1; FVC; FEV1/FVC; FEF25-75% at age 15 and 24 years were investigated using multivariable regression models adjusted for lung function at age 8 years, height and age at time of outcome measurements, and potential confounders.Measurements and Main Results: Later pubertal age and greater peak velocity were associated with higher FEV1 and FVC at 24 years in both sexes. A 1-year increase in pubertal age was associated with a 263-ml higher FVC (95% confidence interval [CI], 167-360 ml) for males (n = 567) and 100-ml (95% CI, 50-150 ml) higher FVC for females (n = 990). A 1-cm/yr increase in peak velocity was associated with 145-ml (95% CI, 56-234 ml) and 50-ml (95% CI, 2-99 ml) increases in FVC for males and females, respectively. No associations were found with FEV1/FVC.Conclusions: Later onset and greater peak velocity of height growth in puberty are associated with increased FEV1 and FVC in young adults but there was no evidence of dysanapsis of pubertal lung growth.

Optimal design for longitudinal studies to estimate pubertal height growth in individuals

Background: The SITAR model expresses individual pubertal height growth in terms of mean size, peak height velocity (PHV) and age at PHV.Aim: To use SITAR to identify the optimal time interval between measurements to summarise individual pubertal height growth.Subjects and methods: Heights in 3172 boys aged 9–19 years from Christ’s Hospital School measured on 128 679 occasions (a median of 42 heights per boy) were analysed using the SITAR (SuperImposition by Translation And Rotation) mixed effects growth curve model, which estimates a mean curve and three subject-specific random effects. Separate models were fitted to sub-sets of the data with measurement intervals of 2, 3, 4, 6, 12 and 24 months, and the different models were compared.Results: The models for intervals 2–12 months gave effectively identical results for the residual standard deviation (0.8 cm), mean spline curve (6 degrees of freedom) and random effects (correlations >0.9), showing there is no benefit in measuring height more often than annually. The model for 2-year intervals fitted slightly less well, but needed just four-to-five measurements per individual.Conclusions: Height during puberty needs to be measured only annually and, with slightly lower precision, just four biennial measurements can be sufficient.

Modelling height in adolescence: a comparison of methods for estimating the age at peak height velocity

Background: Controlling for maturational status and timing is crucial in lifecourse epidemiology. One popular non-invasive measure of maturity is the age at peak height velocity (PHV). There are several ways to estimate age at PHV, but it is unclear which of these to use in practice.Aim: To find the optimal approach for estimating age at PHV.Subjects and methods: Methods included the Preece & Baines non-linear growth model, multi-level models with fractional polynomials, SuperImposition by Translation And Rotation (SITAR) and functional data analysis. These were compared through a simulation study and using data from a large cohort of adolescent boys from the Christ’s Hospital School.Results: The SITAR model gave close to unbiased estimates of age at PHV, but convergence issues arose when measurement error was large. Preece & Baines achieved close to unbiased estimates, but shares similarity with the data generation model for our simulation study and was also computationally inefficient, taking 24 hours to fit the data from Christ’s Hospital School. Functional data analysis consistently converged, but had higher mean bias than SITAR. Almost all methods demonstrated strong correlations (r > 0.9) between true and estimated age at PHV.Conclusions: Both SITAR or the PBGM are useful models for adolescent growth and provide unbiased estimates of age at peak height velocity. Care should be taken as substantial bias and variance can occur with large measurement error.

Classifying Gestational Weight Gain Trajectories Using the SITAR Growth Model.

Gestational weight gain is often characterized by the total amount of weight gained during pregnancy, however, the pattern of gain may be an important determinant of health outcomes. The SITAR (Super Imposition by Translation And Rotation) model has been used to describe childhood growth trajectories and has appeal because of the biological interpretability of its parameters. The objective of this study was to determine the feasibility of applying this model to gestational weight gain trajectories. The study cohort included 3470 normal-weight, overweight, and obese women delivering at Magee-Womens Hospital in Pittsburgh, Pennsylvania, 1998 to 2010. We applied the SITAR model, a non-linear mixed effects model, to serial prenatal weight gain measurements in each pre-pregnancy body mass index (BMI) category. We fit models of varying complexity, and chose the best-fitting model to describe the pattern of weight gain (by its absolute amount, timing, and acceleration) for each BMI group. The most complex SITAR models failed to converge, but reduced models could successfully be fit by specifying fewer random effects and simplifying the modelling of gestational age. Best-fitting models for each BMI group explained between 95% and 97% of the variation in weight gain trajectories. Peak rates of weight gain were reached between the 20th and 22nd weeks, and were higher for normal and overweight women (0.59 kg/week and 0.57 kg/week, respectively) than obese women (0.46 kg/week). Following some modifications, the SITAR model can be used to characterize pregnancy weight gain patterns.

A multivariate Bayesian model for embryonic growth.

Most longitudinal growth curve models evaluate the evolution of each of the anthropometric measurements separately. When applied to a 'reference population', this exercise leads to univariate reference curves against which new individuals can be evaluated. However, growth should be evaluated in totality, that is, by evaluating all body characteristics jointly. Recently, Cole et al. suggested the Superimposition by Translation and Rotation (SITAR) model, which expresses individual growth curves by three subject-specific parameters indicating their deviation from a flexible overall growth curve. This model allows the characterization of normal growth in a flexible though compact manner. In this paper, we generalize the SITAR model in a Bayesian way to multiple dimensions. The multivariate SITAR model allows us to create multivariate reference regions, which is advantageous for prediction. The usefulness of the model is illustrated on longitudinal measurements of embryonic growth obtained in the first semester of pregnancy, collected in the ongoing Rotterdam Predict study. Further, we demonstrate how the model can be used to find determinants of embryonic growth.

The relationship between Insulin-like Growth Factor 1, sex steroids and timing of the pubertal growth spurt.

SummaryObjectiveProgress through puberty involves a complex hormonal cascade, but the individual contributions of hormones, particularly IGF‐1, are unknown. We reanalysed Chard growth study data to explore the tempo of puberty based on changes in both height and hormone levels, using a novel method of growth curve analysis.Design and SubjectsSchoolboys (n = 54) and girls (n = 70) from Chard, Somerset, England, recruited in 1981 at age 8/9 and followed to age 16.MeasurementsEvery 6 months, height and Tanner stages (genitalia, breast, pubic hair) were recorded, and in a subsample (24 boys, 27 girls), blood samples were taken. Serum IGF‐1, testosterone (boys) and oestradiol (girls) were measured by radioimmunoassay. Individual growth curves for each outcome were analysed using variants of the super‐imposition by translation and rotation (SITAR) method, which estimates a mean curve and subject‐specific random effects corresponding to size, and age and magnitude of peak velocity.ResultsThe SITAR models fitted the data well, explaining 99%, 65%, 86% and 47% of variance for height, IGF‐1, testosterone and oestradiol, respectively, and 69–88% for the Tanner stages. During puberty, the variables all increased steeply in value in individuals, the ages at peak velocity for the different variables being highly correlated, particularly for IGF‐1 vs height (r = 0·74 for girls, 0·92 for boys).Conclusions IGF‐1, like height, the sex steroids and Tanner stages, rises steeply in individuals during puberty, with the timings of the rises tightly synchronized within individuals. This suggests that IGF‐1 may play an important role in determining the timing of puberty.

Early life growth trajectories and future risk for overweight

Objective:Standard approaches have found that rapid growth during the first 2 years of life is a risk factor for overweight in later childhood. Our objective was to test whether growth velocity, independent of concurrent size, was associated with overweight using a nonlinear random-effects model that allows for enhanced specifications and estimations.Methods:Longitudinal data from a birth cohort in Mexico (n=586) were used to estimate growth trajectories over 0–24 months for body mass index (BMI), length and weight using the SuperImposition by Translation and Rotation (SITAR) models. The SITAR models use a nonlinear random-effects model to estimate an average growth curve for BMI, length and weight and each participant's deviation from this curve on three dimensions—size, velocity and timing of peak velocity. We used logistic regression to estimate the association between overweight status at 7–9 years and size, velocity and timing of BMI, length and weight trajectories during 0–24 months. We tested whether any association between velocity and overweight varied by relative size during 0–24 months or birth weight.Results:SITAR models explained the majority of the variance in BMI (73%), height (86%) and weight (85%) between 0–24 months. When analyzed individually, relative BMI/length/weight (size) and BMI/length/weight velocity during 0–24 months were each associated with increased odds of overweight in late childhood. Associations for timing of peak velocity varied by anthropometric measure. However, in the mutually adjusted models, only relative BMI/length/weight (size) remained statistically significant. We found no evidence that any association between velocity and overweight varied by size during 0–24 months or birth weight.Conclusions:After mutual adjustment, size during 0–24 months of life (as opposed to birth size), but not velocity or timing of peak velocity, was most consistently associated with overweight in later childhood.

SITAR—a useful instrument for growth curve analysis

Background Growth curve analysis is a statistical issue in life course epidemiology. Height in puberty involves a growth spurt, the timing and intensity of which varies between individuals. Such data can be summarized with individual Preece–Baines (PB) curves, and their five parameters then related to earlier exposures or later outcomes. But it involves fitting many curves.Methods We present an alternative SuperImposition by Translation And Rotation (SITAR) model, a shape invariant model with a single fitted curve. Curves for individuals are matched to the mean curve by shifting their curve up–down (representing differences in mean size) and left–right (for differences in growth tempo), and the age scale is also shrunk or stretched to indicate how fast time passes in the individual (i.e. velocity). These three parameters per individual are estimated as random effects while fitting the curve. The outcome is a mean curve plus triplets of parameters per individual (size, tempo and velocity) that summarize the individual growth patterns. The data are heights for Christ’s Hospital School (CHS) boys aged 9–19 years (N = 3245, n = 129 508), and girls with Turner syndrome (TS) aged 9–18 years from the UK Turner Study (N = 105, n = 1321).Results The SITAR model explained 99% of the variance in both datasets [residual standard deviation (RSD) 6–7 mm], matching the fit of individually-fitted PB curves. In CHS, growth tempo was associated with insulin-like growth factor-1 measured 50 years later (P = 0.01, N = 1009). For the girls with TS randomized to receive oxandrolone from 9 years, velocity was substantially increased compared with placebo (P = 10−8).Conclusions The SITAR growth curve model is a useful epidemiological instrument for the analysis of height in puberty.