Linear spline multilevel models for summarising childhood growth trajectories: A guide to their application using examples from five birth cohorts

Life Course Trajectories of Cardiovascular Risk Factors in Women With and Without Hypertensive Disorders in First Pregnancy: The HUNT Study in Norway

Background Women with hypertensive pregnancy disorders have adverse levels of cardiovascular risk factors. It is unclear how this adverse risk factor profile evolves during adult life. We compared life course trajectories of cardiovascular risk factors in women with preeclampsia or gestational hypertension in their first pregnancy to normotensive women. Methods and Results We linked information on cardiovascular risk factors from the population-based HUNT (Nord-Trøndelag Health Study) surveys with pregnancy information from the Medical Birth Registry of Norway. Trajectories of cardiovascular risk factors were constructed for 22 308 women with a normotensive first pregnancy; 1092 with preeclampsia, and 478 with gestational hypertension in first pregnancy. Already before first pregnancy, women with preeclampsia in their first pregnancy had higher measures of adiposity, blood pressure, heart rate, and serum lipids and glucose compared with women with a normotensive first pregnancy. After first pregnancy, there was a parallel development in cardiovascular risk factor levels, but women with a normotensive first pregnancy had a time lag of >10 years compared with the preeclampsia group. There were no clear differences in risk factor trajectories between women with gestational hypertension and women with preeclampsia. Conclusions Women with hypertensive pregnancy disorders in their first pregnancy had an adverse cardiovascular risk factor profile before pregnancy compared with normotensive women, and the differences persisted beyond 50 years of age. Hypertensive disorders in pregnancy signal long-term increases in modifiable cardiovascular risk factors, and may be used to identify women who would benefit from early prevention strategies.

How Is Adolescent Bone Mass and Density Influenced by Early Life Body Size and Growth? The Tromsø Study: Fit Futures-A Longitudinal Cohort Study From Norway

The effect of birth weight and childhood body mass index (BMI) on adolescents’ bone parameters is not established. The aim of this longitudinal, population‐based study was to investigate the association of birth weight, childhood BMI, and growth, with adolescent bone mass and bone density in a sample of 633 adolescents (48% girls) from The Tromsø Study: Fit Futures. This population‐based cohort study was conducted in 2010–2011 and 2012–2013 in Tromsø, Norway. Bone mineral content (BMC) and areal BMD (aBMD) were measured at total hip (TH) and total body (TB) by dual‐energy X‐ray absorptiometry (DXA) and converted to internal Z‐scores. Birth weight and childhood anthropometric measurements were retrospectively obtained from the Medical Birth Registry of Norway and childhood health records. Associations between birth weight, BMI, and growth were evaluated by fitting linear mixed models with repeated measures of BMC and aBMD at ages 15 to 17 and 18 to 20 years as the outcome. In crude analysis, a significant positive association (p < 0.05) with TB BMC was observed per 1 SD score increase in birth weight, observed in both sexes. Higher rate of length growth, conditioned on earlier size, from birth to age 2.5 years, and higher rate of weight gain from ages 6.0 to 16.5 years, conditioned on earlier size and concurrent height growth, revealed stronger associations with bone accrual at ages 15 to 20 years compared with other ages. Compared with being normal weight, overweight/obesity at age 16.5 years was associated with higher aBMD Z‐scores: β coefficient (95% confidence interval [CI]) of 0.78 (0.53, 1.03) and 1.08 (0.85, 1.31) in girls, 0.63 (0.42, 0.85) and 0.74 (0.54, 0.95) in boys at TH and TB, respectively. Similar associations were found for BMC. Being underweight was consistently negatively associated with bone parameters in adolescence. In conclusion, birth weight influences adolescent bone mass but less than later growth and BMI in childhood and adolescence. © 2018 The Authors. JBMR Plus Published by Wiley Periodicals, Inc. on behalf of the American Society for Bone and Mineral Research

Growth Trajectories, Breast Size, and Breast-Tissue Composition in a British Prebirth Cohort of Young Women

Mammographic percent density, the proportion of fibroglandular tissue in the breast, is a strong risk factor for breast cancer, but its determinants in young women are unknown. We examined associations of magnetic resonance imaging (MRI) breast-tissue composition at age 21 years with prospectively collected measurements of body size and composition from birth to early adulthood and markers of puberty (all standardized) in a sample of 500 nulliparous women from a prebirth cohort of children born in Avon, United Kingdom, in 1991-1992 and followed up to 2011-2014. Linear models were fitted to estimate relative change in MRI percent water, which is equivalent to mammographic percent density, associated with a 1-standard-deviation increase in the exposure of interest. In mutually adjusted analyses, MRI percent water was positively associated with birth weight (relative change (RC) = 1.03, 95% confidence interval (CI): 1.00, 1.06) and pubertal height growth (RC = 1.07, 95% CI: 1.02, 1.13) but inversely associated with pubertal weight growth (RC = 0.86, 95% CI: 0.84, 0.89) and changes in dual-energy x-ray absorptiometry percent body fat mass (e.g., for change between ages 11 years and 13.5 years, RC = 0.96, 95% CI: 0.93, 0.99). Ages at thelarche and menarche were positively associated with MRI percent water, but these associations did not persist upon adjustment for height and weight growth. These findings support the hypothesis that growth trajectories influence breast-tissue composition in young women, whereas puberty plays no independent role.

Associations of Y chromosomal haplogroups with cardiometabolic risk factors and subclinical vascular measures in males during childhood and adolescence

Background and aims

Males have greater cardiometabolic risk than females, though the reasons for this are poorly understood. The aim of this study was to examine the association between common Y chromosomal haplogroups and cardiometabolic risk during early life.

Methods

In a British birth cohort, we examined the association of Y chromosomal haplogroups with trajectories of cardiometabolic risk factors from birth to 18 years and with carotid-femoral pulse wave velocity, carotid intima media thickness and left ventricular mass index at age 18. Haplogroups were grouped according to their phylogenetic relatedness into categories of R, I, E, J, G and all other haplogroups combined (T, Q, H, L, C, N and O). Risk factors included BMI, fat and lean mass, systolic blood pressure (SBP), diastolic blood pressure, pulse rate, triglycerides, high density lipoprotein cholesterol (HDL-c), non-HDL-c and c-reactive protein. Analyses were performed using multilevel models and linear regression, as appropriate.

Results

Y chromosomal haplogroups were not associated with any cardiometabolic risk factors from birth to 18 years. For example, at age 18, the difference in SBP comparing each haplogroup with haplogroup R was −0.39 mmHg (95% Confidence Interval (CI): −0.75, 1.54) for haplogroup I, 2.56 mmHg (95% CI: −0.76, 5.89) for haplogroup E, −0.02 mmHg (95% CI: −2.87, 2.83) for haplogroup J, 1.28 mmHg (95% CI: −4.70, 2.13) for haplogroup G and −2.75 mmHg (95% CI: −6.38, 0.88) for all other haplogroups combined.

Conclusions

Common Y chromosomal haplogroups are not associated with cardiometabolic risk factors during childhood and adolescence or with subclinical cardiovascular measures at age 18.

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Common Y chromosomal haplogroups are not associated with cardiometabolic risk factors from birth to age 18.

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Common Y chromosomal haplogroups are not associated with cardiovascular structure and function at age 18.

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Common Y chromosomal haplogroups are not associated with cardiometabolic risk in males during early life.

The epigenetic clock and physical development during childhood and adolescence: longitudinal analysis from a UK birth cohort

Background: Statistical models that use an individual’s DNA methylation levels to estimate their age (known as epigenetic clocks) have recently been developed, with 96% correlation found between epigenetic and chronological age. We postulate that differences between estimated and actual age [age acceleration (AA)] can be used as a measure of developmental age in early life.

Methods: We obtained DNA methylation measures at three time points (birth, age 7 years and age 17 years) in 1018 children from the Avon Longitudinal Study of Parents and Children (ALSPAC). Using an online calculator, we estimated epigenetic age, and thus AA, for each child at each time point. We then investigated whether AA was prospectively associated with repeated measures of height, weight, body mass index (BMI), bone mineral density, bone mass, fat mass, lean mass and Tanner stage.

Results: Positive AA at birth was associated with higher average fat mass [1321 g per year of AA, 95% confidence interval (CI) 386, 2256 g] from birth to adolescence (i.e. from age 0–17 years) and AA at age 7 was associated with higher average height (0.23 cm per year of AA, 95% CI 0.04, 0.41 cm). Conflicting evidence for the role of AA (at birth and in childhood) on changes during development was also found, with higher AA being positively associated with changes in weight, BMI and Tanner stage, but negatively with changes in height and fat mass.

Conclusions: We found evidence that being ahead of one’s epigenetic age acceleration is related to developmental characteristics during childhood and adolescence. This demonstrates the potential for using AA as a measure of development in future research.

Breastfeeding duration, maternal body mass index, and birth weight are associated with differences in body mass index growth trajectories in early childhood

Background

Accelerated postnatal growth is an important predictor for obesity risk. It is unknown whether early-life obesity-related risk factors affect body mass index (BMI) growth rates during distinct growth periods from early infancy through preschool years.

Objective

We examined whether breastfeeding duration, maternal BMI, and birth weight are associated with growth trajectories of age- and sex-standardized WHO BMI z scores (zBMIs) in young children.

Design

Children (n = 5905) in The Applied Research Group for Kids (TARGet Kids!) prospective cohort study underwent repeated measures of weight and length or height from birth to 10 y of age. Piecewise linear mixed models were used to determine whether zBMI growth rates differ for each risk factor during periods of growth between birth and 1, 3, 18, 36, and 72 mo of age.

Results

Children who were breastfed <6 mo compared with ≥6 mo showed a higher growth rate between 1-3 and 3-18 mo, resulting in higher standardized BMIs (zBMIs) of +0.24, +0.12, and +0.19 at 18, 36, and 72 mo, respectively. Maternal BMI (in kg/m2) ≥30 compared with <30 resulted in higher growth rates between 1-3 and 36-72 mo and higher zBMIs of +0.22, +0.14, +0.18, and +0.41 at 3, 18, 36, and 72 mo, respectively. Infants weighing <2.5 kg at birth (compared with 2.5-4 kg) experienced higher growth rates between 1-3 and 3-18 mo but had lower zBMIs at all time points (zBMI: -1.45 to -0.21). Infants weighing ≥4 kg at birth (compared with 2.5-4 kg) had significantly lower growth rates in the first 3 mo but higher zBMIs at all time points (zBMI: +1.16 to +0.27).

Conclusion

Differences in zBMI growth rates by breastfeeding duration, maternal BMI, and birth weight are seen in early infancy and contribute to differences in zBMI, which persist into midchildhood. This trial was registered at www.clinicaltrials.gov as NCT01869530.

Socioeconomic differences in childhood BMI trajectories in Belarus

Objective

To examine associations of parental socioeconomic position with early-life offspring body mass index (BMI) trajectories in a middle-income country.

Subjects

Overall, 12,385 Belarusian children born 1996–97 and enrolled in a randomised breastfeeding promotion trial at birth, with 3–14 measurements of BMI from birth to 7 years.

Methods

Cohort analysis in which exposures were parental education (common secondary or less; advanced secondary or partial university; completed university) and occupation (manual; non-manual) at birth, and the outcome was BMI z-score trajectories estimated using multilevel linear spline models, controlling for trial arm, location, parental BMI, maternal smoking status and number of older siblings.

Results

Infants born to university-educated mothers were heavier at birth than those born to secondary school-educated mothers [by 0.13 BMI z-score units (95% confidence interval, CI: 0.07, 0.19) for girls and 0.11 (95% CI: 0.05, 0.17) for boys; equivalent for an infant of average birth length to 43 and 38 g, respectively]. Between the ages of 3–7 years children of the most educated mothers had larger BMI increases than children of the least educated mothers. At age 7 years, after controlling for trial arm and location,  children of university-educated mothers had higher BMIs than those born to secondary school-educated mothers by 0.11 z-score (95% CI: 0.03, 0.19) among girls and 0.18 (95% CI: 0.1, 0.27) among boys, equivalent to differences in BMI for a child of average height of 0.19 and 0.26 kg/m², respectively. After further controlling for parental BMI, these differences attenuated to 0.08 z-score (95% CI: 0, 0.16) and 0.16 z-score (95% CI: 0.07, 0.24), respectively, but changed very little after additional adjustment for number of older siblings and mother’s smoking status. Associations were similar when based on paternal educational attainment and highest household occupation.

Conclusions

In Belarus, consistent with some middle-income countries, higher socioeconomic position was associated with greater BMI trajectories from age 3 onwards.

Novel metrics for growth model selection

BACKGROUND

Literature surrounding the statistical modeling of childhood growth data involves a diverse set of potential models from which investigators can choose. However, the lack of a comprehensive framework for comparing non-nested models leads to difficulty in assessing model performance. This paper proposes a framework for comparing non-nested growth models using novel metrics of predictive accuracy based on modifications of the mean squared error criteria.

METHODS

Three metrics were created: normalized, age-adjusted, and weighted mean squared error (MSE). Predictive performance metrics were used to compare linear mixed effects models and functional regression models. Prediction accuracy was assessed by partitioning the observed data into training and test datasets. This partitioning was constructed to assess prediction accuracy for backward (i.e., early growth), forward (i.e., late growth), in-range, and on new-individuals. Analyses were done with height measurements from 215 Peruvian children with data spanning from near birth to 2 years of age.

RESULTS

Functional models outperformed linear mixed effects models in all scenarios tested. In particular, prediction errors for functional concurrent regression (FCR) and functional principal component analysis models were approximately 6% lower when compared to linear mixed effects models. When we weighted subject-specific MSEs according to subject-specific growth rates during infancy, we found that FCR was the best performer in all scenarios.

CONCLUSION

With this novel approach, we can quantitatively compare non-nested models and weight subgroups of interest to select the best performing growth model for a particular application or problem at hand.

The impact of parity on life course blood pressure trajectories: the HUNT study in Norway

The drop in blood pressure during pregnancy may persist postpartum, but the impact of pregnancy on blood pressure across the life course is not known. In this study we examined blood pressure trajectories for women in the years preceding and following pregnancy and compared life course trajectories of blood pressure for parous and nulliparous women. We linked information on all women who participated in the population-based, longitudinal HUNT Study, Norway with pregnancy information from the Medical Birth Registry of Norway. A total of 23,438 women were included with up to 3 blood pressure measurements per woman. Blood pressure trajectories were compared using a mixed effects linear spline model. Before first pregnancy, women who later gave birth had similar mean blood pressure to women who never gave birth. Women who delivered experienced a drop after their first birth of − 3.32 mmHg (95% CI, − 3.93, − 2.71) and − 1.98 mmHg (95% CI, − 2.43, − 1.53) in systolic and diastolic blood pressure, respectively. Subsequent pregnancies were associated with smaller reductions. These pregnancy-related reductions in blood pressure led to persistent differences in mean blood pressure, and at age 50, parous women still had lower systolic (− 1.93 mmHg; 95% CI, − 3.33, − 0.53) and diastolic (− 1.36 mmHg; 95% CI, − 2.26, − 0.46) blood pressure compared to nulliparous women. The findings suggest that the first pregnancy and, to a lesser extent, successive pregnancies are associated with lasting and clinically relevant reductions in systolic and diastolic blood pressure.

Relationship between growth and illness, enteropathogens and dietary intakes in the first 2 years of life: findings from the MAL-ED birth cohort study

BACKGROUND

Dietary and illness factors affect risk of growth faltering; the role of enteropathogens is less clear. As part of the Etiology, Risk Factors and Interactions of Enteric Infections and Malnutrition and the Consequences for Child Health and Development (MAL-ED) study, we quantify the effects of enteropathogen infection, diarrhoea and diet on child growth.

METHODS

Newborns were enrolled and followed until 24 months. Length and weight were assessed monthly. Illnesses and breastfeeding practices were documented biweekly; from 9 to 24 months, non-breast milk intakes were quantified monthly. Routinely collected non-diarrhoeal stools were analysed for a broad array of enteropathogens. A linear piecewise spline model was used to quantify associations of each factor with growth velocity in seven of eight MAL-ED sites; cumulative effects on attained size at 24 months were estimated for mean, low (10th percentile) and high (90th percentile) exposure levels. Additionally, the six most prevalent enteropathogens were evaluated for their effects on growth.

RESULTS

Diarrhoea did not have a statistically significant effect on growth. Children with high enteropathogen exposure were estimated to be 1.21±0.33 cm (p<0.001; 0.39 length for age (LAZ)) shorter and 0.08±0.15 kg (p=0.60; 0.08 weight-for-age (WAZ)) lighter at 24 months, on average, than children with low exposure. Campylobacter and enteroaggregativeEscherichia coli detections were associated with deficits of 0.83±0.33 and 0.85±0.31 cm in length (p=0.011 and 0.001) and 0.22±0.15 and 0.09±0.14 kg in weight (p=0.14 and 0.52), respectively. Children with low energy intakes and protein density were estimated to be 1.39±0.33 cm (p<0.001; 0.42 LAZ) shorter and 0.81±0.15 kg (p<0.001; 0.65 WAZ) lighter at 24 months than those with high intakes.

CONCLUSIONS

Reducing enteropathogen burden and improving energy and protein density of complementary foods could reduce stunting.

Practical Application of Linear Growth Measurements in Clinical Research in Low- and Middle-Income Countries

BACKGROUND/AIMS

Childhood stunting is a prevalent problem in low- and middle-income countries and is associated with long-term adverse neurodevelopment and health outcomes. In this review, we define indicators of growth, discuss key challenges in their analysis and application, and offer suggestions for indicator selection in clinical research contexts.

METHODS

Critical review of the literature.

RESULTS

Linear growth is commonly expressed as length-for-age or height-for-age z-score (HAZ) in comparison to normative growth standards. Conditional HAZ corrects for regression to the mean where growth changes relate to previous status. In longitudinal studies, growth can be expressed as ΔHAZ at 2 time points. Multilevel modeling is preferable when more measurements per individual child are available over time. Height velocity z-score reference standards are available for children under the age of 2 years. Adjusting for covariates or confounders (e.g., birth weight, gestational age, sex, parental height, maternal education, socioeconomic status) is recommended in growth analyses.

CONCLUSION

The most suitable indicator(s) for linear growth can be selected based on the number of available measurements per child and the child's age. By following a step-by-step algorithm, growth analyses can be precisely and accurately performed to allow for improved comparability within and between studies.

Effects of Promoting Long-term, Exclusive Breastfeeding on Adolescent Adiposity, Blood Pressure, and Growth Trajectories: A Secondary Analysis of a Randomized Clinical Trial

IMPORTANCE

Evidence that breastfeeding reduces child obesity risk and lowers blood pressure (BP) is based on potentially confounded observational studies.

OBJECTIVE

To investigate the effects of a breastfeeding promotion intervention on adiposity and BP at age 16 years and on longitudinal growth trajectories from birth.

DESIGN, SETTING, AND PARTICIPANTS

Cluster-randomized Promotion of Breastfeeding Intervention Trial. Belarusian maternity hospitals and affiliated polyclinics (the clusters) were allocated into intervention (n = 16) or control arms (n = 15) in 1996 and 1997. The trial participants were 17 046 breastfeeding mother-infant pairs; of these, 13 557 children (79.5%) were followed up at 16 years of age between September 2012 and July 2015.

INTERVENTIONS

Breastfeeding promotion, modeled on the Baby-Friendly Hospital Initiative.

MAIN OUTCOMES AND MEASURES

Body mass index (BMI, calculated as weight in kilograms divided by height in meters squared); fat and fat-free mass indices and percentage of body fat from bioimpedance; waist circumference; overweight and obesity; height; BP; and longitudinal growth trajectories. The primary analysis was modified intention-to-treat (without imputation for losses to follow-up) accounting for within-clinic clustering.

RESULTS

We examined 13 557 children at a median age of 16.2 years (48.5% were girls). The intervention substantially increased breastfeeding duration and exclusivity compared with the control arm (exclusively breastfed: 45% vs 6% at 3 months, respectively). Mean differences at 16 years between intervention and control groups were 0.21 (95% CI, 0.06-0.36) for BMI; 0.21 kg/m2 (95% CI, -0.03 to 0.44) for fat mass index; 0.00 kg/m2 (95% CI, -0.21 to 0.22) for fat-free mass index; 0.71% (95% CI, -0.32 to 1.74) for percentage body fat; -0.73 cm (-2.48 to 1.02) for waist circumference; 0.05 cm (95% CI, -0.85 to 0.94) for height; -0.54 mm Hg (95% CI, -2.40 to 1.31) for systolic BP; and 0.71 mm Hg (95% CI, -0.68 to 2.10) for diastolic BP. The odds ratio for overweight/obesity (BMI ≥85th percentile vs <85th percentile) was 1.14 (95% CI, 1.02-1.28) and the odds ratio for obesity (BMI ≥95th percentile vs <95th percentile) was 1.09 (95% CI, 0.92-1.29). The intervention resulted in a more rapid rate of gain in postinfancy height (1 to 2.8 years), weight (2.8 to 14.5 years), and BMI (2.8 to 8.5 years) compared with the control arm. The intervention had little effect on BMI z score changes after 8.5 years.

CONCLUSIONS AND RELEVANCE

A randomized intervention that increased the duration and exclusivity of breastfeeding was not associated with lowered adolescent obesity risk or BP. On the contrary, the prevalence of overweight/obesity was higher in the intervention arm. All mothers initiated breastfeeding, so findings may not apply to comparisons of the effects of breastfeeding vs formula feeding.

TRIAL REGISTRATION

isrctn.org: ISRCTN37687716; and clinicaltrials.gov: NCT01561612.

Longitudinal study of the associations between change in sedentary behavior and change in adiposity during childhood and adolescence: Gateshead Millennium Study

BACKGROUND

Sedentary time (ST) has been reported to have a range of negative health effects in adults, however, the evidence for such effects among children and adolescents is sparse. The primary aim of the study was to examine associations between changes in sedentary behavior (time and fragmentation) and changes in adiposity across childhood and adolescence.

METHODS

Participants were recruited as part of the Gateshead Millennium Study. Measures were taken at age 7 (n=502), 9 (n=506), 12 (n=420) and 15 years (n=306). Participants wore an ActiGraph GT1M and accelerometer epochs were 'sedentary' when recorded counts were ⩽25 counts per 15 s. ST was calculated and fragmentation (SF) was assessed by calculating the number of sedentary bouts per sedentary hour. Associations of changes in ST and SF with changes in adiposity (body mass index (BMI), and fat mass index (FMI)) were examined using bivariate linear spline models.

RESULTS

Increasing ST by 1% per year was associated with an increase in BMI of 0.08 kg m-2 per year (95% CI: 0.06-0.10; P<0.001) and FMI of 0.15  kg m-2 per year (0.11-0.19; P<0.001). Change in SF was associated with BMI and FMI (P<0.001). An increase of 1 bout per sedentary hour per year (that is, sedentary time becoming more fragmented) was associated with an increase in BMI of 0.07  kg m-2 per year (0.06-0.09; P<0.001) and an increase in FMI of 0.14  kg m-2 per year (0.10-0.18; P<0.001) over the 8 years period. However, an increase in SF between 9-12 years was associated with a 0.09  kg m-2 per year decrease in BMI (-0.18-0.00; P=0.046) and 0.11  kg m-2 per year decrease in FMI (-0.22-0.00; P=0.049).

CONCLUSIONS

Increased ST and increased SF from 7-15 years were associated with increased adiposity. This is the first study to show age-specific associations between change in objectively measured sedentary behavior and adiposity after adjustment of moderate-to-vigorous-intensity physical activity in children and adolescents. The study suggests that, targeting sedentary behavior for obesity prevention may be most effective during periods in which we see large increases in ST.

Bayesian hierarchical piecewise regression models: a tool to detect trajectory divergence between groups in long-term observational studies

Background

Bayesian hierarchical piecewise regression (BHPR) modeling has not been previously formulated to detect and characterise the mechanism of trajectory divergence between groups of participants that have longitudinal responses with distinct developmental phases. These models are useful when participants in a prospective cohort study are grouped according to a distal dichotomous health outcome. Indeed, a refined understanding of how deleterious risk factor profiles develop across the life-course may help inform early-life interventions. Previous techniques to determine between-group differences in risk factors at each age may result in biased estimate of the age at divergence.

Methods

We demonstrate the use of Bayesian hierarchical piecewise regression (BHPR) to generate a point estimate and credible interval for the age at which trajectories diverge between groups for continuous outcome measures that exhibit non-linear within-person response profiles over time. We illustrate our approach by modeling the divergence in childhood-to-adulthood body mass index (BMI) trajectories between two groups of adults with/without type 2 diabetes mellitus (T2DM) in the Cardiovascular Risk in Young Finns Study (YFS).

Results

Using the proposed BHPR approach, we estimated the BMI profiles of participants with T2DM diverged from healthy participants at age 16 years for males (95% credible interval (CI):13.5–18 years) and 21 years for females (95% CI: 19.5–23 years). These data suggest that a critical window for weight management intervention in preventing T2DM might exist before the age when BMI growth rate is naturally expected to decrease. Simulation showed that when using pairwise comparison of least-square means from categorical mixed models, smaller sample sizes tended to conclude a later age of divergence. In contrast, the point estimate of the divergence time is not biased by sample size when using the proposed BHPR method.

Conclusions

BHPR is a powerful analytic tool to model long-term non-linear longitudinal outcomes, enabling the identification of the age at which risk factor trajectories diverge between groups of participants. The method is suitable for the analysis of unbalanced longitudinal data, with only a limited number of repeated measures per participants and where the time-related outcome is typically marked by transitional changes or by distinct phases of change over time.

Electronic supplementary material

The online version of this article (doi:10.1186/s12874-017-0358-9) contains supplementary material, which is available to authorized users.

Conditional random slope: A new approach for estimating individual child growth velocity in epidemiological research

Objectives

Conditioning child growth measures on baseline accounts for regression to the mean (RTM). Here, we present the “conditional random slope” (CRS) model, based on a linear‐mixed effects model that incorporates a baseline‐time interaction term that can accommodate multiple data points for a child while also directly accounting for RTM.

METHODS

In two birth cohorts, we applied five approaches to estimate child growth velocities from 0 to 12 months to assess the effect of increasing data density (number of measures per child) on the magnitude of RTM of unconditional estimates, and the correlation and concordance between the CRS and four alternative metrics. Further, we demonstrated the differential effect of the choice of velocity metric on the magnitude of the association between infant growth and stunting at 2 years.

RESULTS

RTM was minimally attenuated by increasing data density for unconditional growth modeling approaches. CRS and classical conditional models gave nearly identical estimates with two measures per child. Compared to the CRS estimates, unconditional metrics had moderate correlation (r = 0.65–0.91), but poor agreement in the classification of infants with relatively slow growth (kappa = 0.38–0.78). Estimates of the velocity‐stunting association were the same for CRS and classical conditional models but differed substantially between conditional versus unconditional metrics.

CONCLUSION

The CRS can leverage the flexibility of linear mixed models while addressing RTM in longitudinal analyses.

Body mass index trajectories from 2 to 18 years - exploring differences between European cohorts

BACKGROUND

In recent decades, there has been an increase in the prevalence of childhood overweight in most high-income countries. Within northern Europe, prevalence tends to be higher in the UK compared with the Scandinavian countries. We aimed to study differences in body mass index (BMI) trajectories between large cohorts of children from UK and Scandinavian populations.

METHODS

We compared BMI trajectories in participants from the English Avon Longitudinal Study of Parents and Children born in 1991-1993 (ALSPAC) (N = 6517), the Northern Finland Birth Cohorts born in 1966 (NFBC1966) (N = 3321) and 1986 (NFBC1986) (N = 4764), and the Danish Aarhus Birth Cohort born in 1990-1992 (ABC) (N = 1920). We used multilevel models to estimate BMI trajectories from 2 to 18 years. We explored whether cohort differences were explained by maternal BMI, height, education or smoking during pregnancy and whether differences were attributable to changes in the degree of skew in the BMI distribution.

RESULTS

Differences in mean BMI between the cohorts were small but emerged early and persisted in most cases across childhood. Girls in ALSPAC had a higher BMI than all other cohorts throughout childhood, e.g. compared with the NFBC1986 BMI was 2.2-3.5% higher. For boys, the difference emerging over time (comparing the two NFBC's) exceeded the differences across populations (comparing NFBC1986, ABC and ALSPAC). BMI distribution demonstrated increasing right skew with age.

CONCLUSION

Population-level differences between cohorts were small, tended to emerge very early, persisted across childhood, and demonstrated an increase in the right-hand tail of the BMI distribution.

Exploring diurnal variation using piecewise linear splines: an example using blood pressure

Background

There are many examples of physiological processes that follow a circadian cycle and researchers are interested in alternative methods to illustrate and quantify this diurnal variation. Circadian blood pressure (BP) deserves additional attention given uncertainty relating to the prognostic significance of BP variability in relation to cardiovascular disease. However, the majority of studies exploring variability in ambulatory blood pressure monitoring (ABPM) collapse the data into single readings ignoring the temporal nature of the data. Advanced statistical techniques are required to explore complete variation over 24 h.

Methods

We use piecewise linear splines in a mixed-effects model with a constraint to ensure periodicity as a novel application for modelling daily blood pressure. Data from the Mitchelstown Study, a cross-sectional study of Irish adults aged 47–73 years (n = 2047) was utilized. A subsample (1207) underwent 24-h ABPM. We compared patterns between those with and without evidence of subclinical target organ damage (microalbuminuria).

Results

We were able to quantify the steepest rise and fall in SBP, which occurred just after waking (2.23 mmHg/30 min) and immediately after falling asleep (−1.93 mmHg/30 min) respectively. The variation about an individual’s trajectory over 24 h was 12.3 mmHg (standard deviation). On average those with microalbuminuria were found to have significantly higher SBP (7.6 mmHg, 95% CI 5.0–10.1) after adjustment for age, sex and BMI. Including an interaction term between each linear spline and microalbuminuria did not improve model fit.

Conclusion

We have introduced a practical method for the analysis of ABPM where we can determine the rate of increase or decrease for different periods of the day. This may be particularly useful in examining chronotherapy effects of antihypertensive medication. It offers new measures of short-term BP variability as we can quantify the variation about an individual’s trajectory but also allows examination of the variation in slopes between individuals (random-effects).

Electronic supplementary material

The online version of this article (doi:10.1186/s12982-017-0055-5) contains supplementary material, which is available to authorized users.

Childhood body mass index growth trajectories and endometrial cancer risk

Previously, we found that excess weight already in childhood has positive associations with endometrial cancer; however, associations with changes in body mass index (BMI) during childhood are not well understood. Therefore, we examined whether growth in childhood BMI is associated with endometrial cancer and its sub‐types. A cohort of 155,505 girls from the Copenhagen School Health Records Register with measured weights and heights at the ages of 6–14 years and born 1930–1989 formed the analytical population. BMI was transformed to age‐specific z scores. Using linear spline multilevel models, each girl's BMI growth trajectory was estimated as the deviance from the average trajectory for three different growth periods (6.25–7.99, 8.0–10.99, 11.0–14.0 years). Via a link to health registers, 1,020 endometrial cancer cases were identified, and Cox regressions were performed. A greater gain in BMI during childhood was positively associated with endometrial cancer but no differences between the different growth periods were detected in models adjusted for baseline BMI. The hazard ratios for the associations with overall growth during childhood per 0.1 z score increase were 1.15 (95% confidence interval [CI]: 1.07–1.24) for all endometrial cancers, 1.12 (95% CI: 1.04–1.21) for estrogen‐dependent cancers, 1.16 (95% CI: 1.06–1.26) for endometrioid adenocarcinomas and 1.46 (95% CI: 1.16–1.84) for non‐estrogen‐dependent cancers. Growth in BMI in early life is positively linked to later endometrial cancer risk. We did not identify any sensitive childhood growth period, which suggests that excess gain in BMI during the entire childhood period should be avoided.

What's new?

High body mass index (BMI) early in life is linked to an increased risk of endometrial cancer in adulthood. Potentially influencing that association are the amount by which BMI increases in childhood, as well as the timing of BMI increase. Here, analyses of data from the Copenhagen School Health Records Register for girls ages 6 to 14 shows that endometrial cancer risk is increased by greater BMI gain across ages, while the specific age at which BMI increases occurs has little impact. Excess BMI gain at any time during childhood could set the stage for endometrial carcinogenesis.

Development of sedentary behavior across childhood and adolescence: longitudinal analysis of the Gateshead Millennium Study

Background

In many parts of the world policy and research interventions to modify sedentary behavior of children and adolescents are now being developed. However, the evidence to inform these interventions (e.g. how sedentary behavior changes across childhood and adolescence) is limited. This study aimed to assess longitudinal changes in sedentary behavior, and examine the degree of tracking of sedentary behavior from age 7y to 15y.

Methods

Participants were part of the Gateshead Millennium Study cohort. Measures were made at age 7y (n = 507), 9y (n = 510), 12y (n = 425) and 15y (n = 310). Participants were asked to wear an ActiGraph GT1M and accelerometer epochs were defined as sedentary when recorded counts were ≤25 counts/15 s. Differences in sedentary time and sedentary fragmentation were examined using the Friedman test. Tracking was examined using Spearman’s correlation coefficients and trajectories over time were assessed using multilevel linear spline modelling.

Results

Median daily sedentary time increased from 51.3 % of waking hours at 7y to 74.2 % at 15y. Sedentary fragmentation decreased from 7y to 15y. The median number of breaks/hour decreased from 8.6 to 4.1 breaks/hour and the median bout duration at 50 % of the cumulative sedentary time increased from 2.4 min to 6.4 min from 7y to 15y. Tracking of sedentary time and sedentary fragmentation was moderate from 7y to 15y however, the rate of change differed with the steepest increases/decreases seen between 9y and 12y.

Conclusion

In this study, sedentary time was high and increased to almost 75 % of waking hours at 15y. Sedentary behavior became substantially less fragmented as children grew older. The largest changes in sedentary time and sedentary fragmentation occurred between 9y to 12y, a period which spans the transition to secondary school. These results can be used to inform future interventions aiming to change sedentary behavior.

Joint modelling compared with two stage methods for analysing longitudinal data and prospective outcomes: A simulation study of childhood growth and BP

There is a growing debate with regards to the appropriate methods of analysis of growth trajectories and their association with prospective dependent outcomes. Using the example of childhood growth and adult BP, we conducted an extensive simulation study to explore four two-stage and two joint modelling methods, and compared their bias and coverage in estimation of the (unconditional) association between birth length and later BP, and the association between growth rate and later BP (conditional on birth length). We show that the two-stage method of using multilevel models to estimate growth parameters and relating these to outcome gives unbiased estimates of the conditional associations between growth and outcome. Using simulations, we demonstrate that the simple methods resulted in bias in the presence of measurement error, as did the two-stage multilevel method when looking at the total (unconditional) association of birth length with outcome. The two joint modelling methods gave unbiased results, but using the re-inflated residuals led to undercoverage of the confidence intervals. We conclude that either joint modelling or the simpler two-stage multilevel approach can be used to estimate conditional associations between growth and later outcomes, but that only joint modelling is unbiased with nominal coverage for unconditional associations.

Cord blood leptin levels in relation to child growth trajectories

OBJECTIVE

Leptin represents a potential modulator of developmental programming of childhood obesity. We investigated the association of cord blood leptin with growth trajectories from birth to early childhood.

MATERIALS/METHODS

We used data from the prospective mother-child cohort "Rhea", Crete, Greece. Cord blood samples from 642 neonates were collected. 578 (90%) children had complete follow up data from birth to 4years. We measured child weight, height, waist circumference, skinfold thicknesses, blood pressure, and serum lipids, leptin, adiponectin and C-reactive protein in early childhood (median 4.2years). We estimated growth trajectories from 3months up to 4years using random-effects linear-spline models. Multivariable logistic and linear regression models were used adjusting for confounders.

RESULTS

Mean cord blood leptin levels were 7.3ng/mL (standard deviation: 6.3). Children with high cord blood leptin (>90th percentile) exhibited lower weight, height and body mass index from 6months to early childhood. Each SD increase in cord blood leptin was associated with lower weight at the age of 4 by 242g (95% CI: -416, -69). In a stratified analysis, the reverse association was observed in children born small for gestational age (p for interaction=0.001), and in those exhibiting rapid infant growth during the first 3months of life (p for interaction=0.002). Cord blood leptin levels were not associated with cardiometabolic risk factors at 4years.

CONCLUSIONS

Long term programming effects of in utero exposure to leptin extends beyond infancy into early childhood. Further studies are needed to explore potential effect modification by intrauterine and early infancy growth patterns.

Modelling subject-specific childhood growth using linear mixed-effect models with cubic regression splines

Background

Childhood growth is a cornerstone of pediatric research. Statistical models need to consider individual trajectories to adequately describe growth outcomes. Specifically, well-defined longitudinal models are essential to characterize both population and subject-specific growth. Linear mixed-effect models with cubic regression splines can account for the nonlinearity of growth curves and provide reasonable estimators of population and subject-specific growth, velocity and acceleration.

Methods

We provide a stepwise approach that builds from simple to complex models, and account for the intrinsic complexity of the data. We start with standard cubic splines regression models and build up to a model that includes subject-specific random intercepts and slopes and residual autocorrelation. We then compared cubic regression splines vis-à-vis linear piecewise splines, and with varying number of knots and positions. Statistical code is provided to ensure reproducibility and improve dissemination of methods. Models are applied to longitudinal height measurements in a cohort of 215 Peruvian children followed from birth until their fourth year of life.

Results

Unexplained variability, as measured by the variance of the regression model, was reduced from 7.34 when using ordinary least squares to 0.81 (p < 0.001) when using a linear mixed-effect models with random slopes and a first order continuous autoregressive error term. There was substantial heterogeneity in both the intercept (p < 0.001) and slopes (p < 0.001) of the individual growth trajectories. We also identified important serial correlation within the structure of the data (ρ = 0.66; 95 % CI 0.64 to 0.68; p < 0.001), which we modeled with a first order continuous autoregressive error term as evidenced by the variogram of the residuals and by a lack of association among residuals. The final model provides a parametric linear regression equation for both estimation and prediction of population- and individual-level growth in height. We show that cubic regression splines are superior to linear regression splines for the case of a small number of knots in both estimation and prediction with the full linear mixed effect model (AIC 19,352 vs. 19,598, respectively). While the regression parameters are more complex to interpret in the former, we argue that inference for any problem depends more on the estimated curve or differences in curves rather than the coefficients. Moreover, use of cubic regression splines provides biological meaningful growth velocity and acceleration curves despite increased complexity in coefficient interpretation.

Conclusions

Through this stepwise approach, we provide a set of tools to model longitudinal childhood data for non-statisticians using linear mixed-effect models.

Electronic supplementary material

The online version of this article (doi:10.1186/s12982-015-0038-3) contains supplementary material, which is available to authorized users.

Rapid increases in infant adiposity and overweight/obesity in childhood are associated with higher central and brachial blood pressure in early adulthood

Background:

Small size at birth and greater BMI in childhood are associated with greater brachial blood pressure (BP) in later life. Aortic (central) BP differs from brachial BP and is more predictive of organ damage and cardiovascular events; the relationship between BMI in childhood and central BP is not known.

Methods:

Using data from 3154 people from the Avon Longitudinal Study of Parents and Children, we assessed associations between repeated measures of BMI from birth to age 10 with central and brachial BP at age 17.

Results:

Lower BMI at birth (thinness) was associated with greater central and brachial BP. No associations were seen between BMI in early childhood (<7 years) and later BP, but greater BMI from 7 to 10 years was associated with higher BP. Associations were similar for central and brachial SBP and for DBP, and were stronger in males compared with females. The highest BP was seen in participants who were low-birth-weight and overweight or obese at both the end of infancy (age 2) and at the time of BP assessment (age 17); mean central SBP was 104.2 mmHg (SD = 11.0) compared with 100.7 (SD = 10.5) in participants who were normal-birth-weight and overweight or obese at 2 and 17 years.

Conclusion:

Small size at birth followed by rapid adiposity gain in infancy and continued overweight/obesity are associated with greater BP in young adulthood. These findings emphasize the importance of maintenance of normal weight in childhood for the prevention of high BP.

Associations between early body mass index trajectories and later metabolic risk factors in European children: the IDEFICS study

Faster growth seems to be a common factor in several hypotheses relating early life exposures to subsequent health. This study aims to investigate the association between body mass index (BMI) trajectories during infancy/childhood and later metabolic risk in order to identify sensitive periods of growth affecting health. In a first step, BMI trajectories of 3301 European children that participated in the multi-centre Identification and Prevention of Dietary and Lifestyle-induced Health Effects in Children and Infants (IDEFICS) study were modelled using linear-spline mixed-effects models. The estimated random coefficients indicating initial subject-specific BMI and rates of change in BMI over time were used as exposure variables in a second step and related to a metabolic syndrome (MetS) score and its single components based on conditional regression models (mean age at outcome assessment: 8.5 years). All exposures under investigation, i.e. BMI at birth, rates of BMI change during infancy (0 to <9 months), early childhood (9 months to <6 years) and later childhood (≥6 years) as well as current BMI z-score were significantly associated with the later MetS score. Associations were strongest for the rate of BMI change in early childhood (1.78 [1.66; 1.90]; β estimate and 99 % confidence interval) and current BMI z-score (1.16 [0.96; 1.38]) and less pronounced for BMI at birth (0.62 [0.47; 0.78]). Results slightly differed with regard to the single metabolic factors. Starting from birth rapid BMI growth, especially in the time window of 9 months to <6 years, is significantly related to later metabolic risk in children. Much of the associations of early BMI growth may further be mediated through the effects on subsequent BMI growth.

Developmental trajectories of adiposity from birth until early adulthood and association with cardiometabolic risk factors

OBJECTIVE

To identify developmental trajectories of adiposity from birth until early adulthood, and to investigate how they relate with cardiometabolic risk factors at 21 years of age.

METHODS

Participants' weight and height measurements were obtained using the EPITeen cohort protocol at 13, 17 and 21 years of age, and extracted from child health books as recorded during health routine evaluations since birth. Blood pressure, triglycerides, cholesterol and insulin resistance (HOMA-IR) were assessed at 21 years. Trajectories were defined using 719 participants contributing 11 459 measurements. The individual growth curves were modelled using mixed-effects fractional polynomial, and the trajectories were estimated using normal mixture modelling for model-based clustering. Differences in cardiometabolic risk factors at 21 years according to adiposity trajectories were estimated through analysis of covariance (ANCOVA), and adjusted means are presented.

RESULTS

Two trajectories-'Average body mass index (BMI) growth' (80.7%) and 'Higher BMI growth' (19.3%)-were identified. Compared with those in 'Average BMI growth', 'Higher BMI growth' participants were more frequently delivered by caesarean section, mothers were younger and had higher BMI, and parental education was lower; and at 21 years showed higher adjusted mean systolic (111.6 vs 108.3 mm Hg, P<0.001) and diastolic blood pressure (71.9 vs 68.4 mm Hg, P<0.001), and lower high-density lipoprotein cholesterol (53.3 vs 57.0 mg dl(-1), P=0.001). As there was a significant interaction between trajectories and sex, triglycerides and HOMA-IR were stratified by sex and we found significantly higher triglycerides, in males, and higher HOMA-IR in both sexes in 'Higher BMI growth' trajectory. All the differences were attenuated after adjustment for BMI at 21 years.

CONCLUSIONS

In this long-term follow-up, we were able to identify two adiposity trajectories, statistically related to the BMI and cardiometabolic profile in adulthood. Our results also suggest that the impact of the adiposity trajectory on cardiometabolic profile is mediated by current BMI.

A longitudinal model for disease progression was developed and applied to multiple sclerosis

Objectives

To develop a model of disease progression using multiple sclerosis (MS) as an exemplar.

Study Design and Settings

Two observational cohorts, the University of Wales MS (UoWMS), UK (1976), and British Columbia MS (BCMS) database, Canada (1980), with longitudinal disability data [the Expanded Disability Status Scale (EDSS)] were used; individuals potentially eligible for MS disease-modifying drugs treatments, but who were unexposed, were selected. Multilevel modeling was used to estimate the EDSS trajectory over time in one data set and validated in the other; challenges addressed included the choice and function of time axis, complex observation-level variation, adjustments for MS relapses, and autocorrelation.

Results

The best-fitting model for the UoWMS cohort (404 individuals, and 2,290 EDSS observations) included a nonlinear function of time since onset. Measurement error decreased over time and ad hoc methods reduced autocorrelation and the effect of relapse. Replication within the BCMS cohort (978 individuals and 7,335 EDSS observations) led to a model with similar time (years) coefficients, time [0.22 (95% confidence interval {CI}: 0.19, 0.26), 0.16 (95% CI: 0.10, 0.22)] and log time [−0.13 (95% CI: −0.39, 0.14), −0.15 (95% CI: −0.70, 0.40)] for BCMS and UoWMS, respectively.

Conclusion

It is possible to develop robust models of disability progression for chronic disease. However, explicit validation is important given the complex methodological challenges faced.

Biological embedding of early-life exposures and disease risk in humans: a role for DNA methylation

BACKGROUND

Following wider acceptance of 'the thrifty phenotype' hypothesis and the convincing evidence that early-life exposures can influence adult health even decades after the exposure, much interest has been placed on the mechanisms through which early-life exposures become biologically embedded.

MATERIALS AND METHODS

In this review, we summarize the current literature regarding biological embedding of early-life experiences. To this end, we conducted a literature search to identify studies investigating early-life exposures in relation to DNA methylation changes. In addition, we summarize the challenges faced in investigations of epigenetic effects, stemming from the peculiarities of this emergent and complex field. A proper systematic review and meta-analyses were not feasible given the nature of the evidence.

RESULTS

We identified seven studies on early-life socio-economic circumstances, 10 studies on childhood obesity and six studies on early-life nutrition all relating to DNA methylation changes that met the stipulated inclusion criteria. The pool of evidence gathered, albeit small, favours a role of epigenetics and DNA methylation in biological embedding, but replication of findings, multiple comparison corrections, publication bias and causality are concerns remaining to be addressed in future investigations.

CONCLUSIONS

Based on these results, we hypothesize that epigenetics, in particular DNA methylation, is a plausible mechanism through which early-life exposures are biologically embedded. This review describes the current status of the field and acts as a stepping stone for future, better designed investigations on how early-life exposures might become biologically embedded through epigenetic effects.

Sleep-disordered breathing, sleep duration, and childhood overweight: a longitudinal cohort study

OBJECTIVES

To examine independent associations between sleep-disordered breathing (SDB), sleep duration from birth through 6.75 years, and body mass index (BMI) through 15 years of age in a population-based cohort.

STUDY DESIGN

The Avon Longitudinal Study of Parents and Children collected parent questionnaire data on child sleep duration and SDB symptoms from birth through 6.75 years and child BMI from the Avon Longitudinal Study of Parents and Children research clinics (n = 1899). For SDB, logistic regression models-minimal, confounder, and confounder + sleep duration adjusted-examined associations with BMI at 7, 10, and 15 years of age. For short sleep duration (≤10th percentile), comparable SDB-adjusted models examined associations with BMI at 15 years of age.

RESULTS

Children with the worst SDB symptoms vs asymptomatic children, had increased odds of overweight at 7 (OR = 2.08, 95% CI = 1.04-4.17), 10 (OR = 1.79, 95% CI = 1.02-3.16), and 15 years of age (OR = 2.25, 95% CI = 1.27-3.97) in models adjusted for sleep duration. Similarly, short sleep duration at ≈5-6 years was associated with overweight at 15 years, independent of SDB. Children with short sleep duration at 4.75 years were more likely to be overweight at 15 years in minimally (OR = 2.21, 95% CI = 1.52-3.20), confounder (OR = 1.99, 95% CI = 1.34-2.96), and SDB-adjusted (OR = 2.04, 95% CI = 1.36-3.04) models.

CONCLUSIONS

Both SDB and short sleep duration significantly and independently increase children's odds of becoming overweight. Findings underscore the potential importance of early identification and remediation of SDB, along with insufficient sleep, as strategies for reducing childhood obesity.

Influence of childhood growth on asthma and lung function in adolescence

Background

Low birth weight and rapid infant growth in early infancy are associated with increased risk of childhood asthma, but little is known about the role of postinfancy growth in asthmatic children.

Objectives

We sought to examine the associations of children's growth patterns with asthma, bronchial responsiveness, and lung function until adolescence.

Methods

Individual growth trajectories from birth until 10 years of age were estimated by using linear spline multilevel models for 9723 children participating in a population-based prospective cohort study. Current asthma at 8, 14, and 17 years of age was based on questionnaires. Lung function and bronchial responsiveness or reversibility were measured during clinic visits at 8 and 15 years of age.

Results

Rapid weight growth between 0 and 3 months of age was most consistently associated with increased risks of current asthma at the ages of 8 and 17 years, bronchial responsiveness at age 8 years, and bronchial reversibility at age 15 years. Rapid weight growth was associated with lung function values, with the strongest associations for weight gain between 3 and 7 years of age and higher forced vital capacity (FVC) and FEV₁ values at age 15 years (0.12 [95% CI, 0.08 to 0.17] and 0.11 [95% CI, 0.07 to 0.15], z score per SD, respectively) and weight growth between 0 and 3 months of age and lower FEV₁/FVC ratios at age 8 and 15 years (−0.13 [95% CI, −0.16 to −0.10] and −0.04 [95% CI, −0.07 to −0.01], z score per SD, respectively). Rapid length growth was associated with lower FVC and FVC₁ values at age 15 years.

Conclusion

Faster weight growth in early childhood is associated with asthma and bronchial hyperresponsiveness, and faster weight growth across childhood is associated with higher FVC and FEV₁ values.

Analytical strategies in human growth research

Human growth research requires knowledge of longitudinal statistical methods that can be analytically challenging. Even the assessment of growth between two ages is not as simple as subtracting the first measurement from the second, for example. This article provides an overview of the key analytical strategies available to human biologists in increasing order of complexity, starting with a review on how to express cross-sectional measurements of size, before covering growth (conditional regression models, regression with conditional growth measures), growth curves (individual growth curves, mixed effects growth curves, latent growth curves), and patterns of growth (growth mixture modeling). The article is not a statistical treatise and has been written by a human biologist for human biologists; as such, it should be accessible to anyone with training in at least basic statistics. A summary table linking each analytical strategy to its applications is provided to help investigators match their hypotheses and measurement schedules to an analysis plan. In addition, worked examples using data on non-Hispanic white participants in the Fels Longitudinal Study are used to illustrate how the analytical strategies might be applied to gain novel insight into human growth and its determinants and consequences. All too often, serial measurements are treated as cross-sectional in analyses that do not harness the power of longitudinal data. The broad goal of this article is to encourage the rigorous application of longitudinal statistical methods to human growth research.

Modelling childhood growth using fractional polynomials and linear splines

BACKGROUND

There is increasing emphasis in medical research on modelling growth across the life course and identifying factors associated with growth. Here, we demonstrate multilevel models for childhood growth either as a smooth function (using fractional polynomials) or a set of connected linear phases (using linear splines).

METHODS

We related parental social class to height from birth to 10 years of age in 5,588 girls from the Avon Longitudinal Study of Parents and Children (ALSPAC). Multilevel fractional polynomial modelling identified the best-fitting model as being of degree 2 with powers of the square root of age, and the square root of age multiplied by the log of age. The multilevel linear spline model identified knot points at 3, 12 and 36 months of age.

RESULTS

Both the fractional polynomial and linear spline models show an initially fast rate of growth, which slowed over time. Both models also showed that there was a disparity in length between manual and non-manual social class infants at birth, which decreased in magnitude until approximately 1 year of age and then increased.

CONCLUSIONS

Multilevel fractional polynomials give a more realistic smooth function, and linear spline models are easily interpretable. Each can be used to summarise individual growth trajectories and their relationships with individual-level exposures.

Socioeconomic differences in childhood length/height trajectories in a middle-income country: a cohort study

BACKGROUND

Socioeconomic disadvantage is associated with shorter adult stature. Few studies have examined socioeconomic differences in stature from birth to childhood and the mechanisms involved, particularly in middle-income former Soviet settings.

METHODS

The sample included 12,463 Belarusian children (73% of the original cohort) born in 1996-1997, with up to 14 stature measurements from birth to 7 years. Linear spline multi-level models with 3 knots at 3, 12 and 34 months were used to analyse birth length and growth velocity during four age-periods by parental educational achievement (up to secondary school, advanced secondary/partial university, completed university) and occupation (manual, non-manual).

RESULTS

Girls born to the most (versus least) educated mothers were 0.43 cm (95% confidence interval (CI): 0.28, 0.58) longer at birth; for boys, the corresponding difference was 0.30 cm (95% CI: 0.15, 0.46). Similarly, children of the most educated mothers grew faster from birth-3 months and 12-34 months (p-values for trend ≤ 0.08), such that, by age 7 years, girls with the most (versus least) educated mothers were 1.92 cm (95% CI: 1.47, 2.36) taller; after controlling for urban/rural and East/West area of residence, this difference remained at 1.86 cm (95% CI: 1.42, 2.31), but after additionally controlling for mid-parental height, attenuated to 1.10 cm (95% CI: 0.69, 1.52). Among boys, these differences were 1.95 cm (95% CI: 1.53, 2.37), 1.89 cm (95% CI: 1.47, 2.31) and 1.16 cm (95% CI: 0.77, 1.55), respectively. Additionally controlling for breastfeeding, maternal smoking and older siblings did not substantively alter these findings. There was no evidence that the association of maternal educational attainment with growth differed in girls compared to boys (p for interaction = 0.45). Results were similar for those born to the most (versus least) educated fathers, or who had a parent with a non-manual (versus manual) occupation.

CONCLUSIONS

In Belarus, a middle-income former Soviet country, socioeconomic differences in offspring growth commence in the pre-natal period and generate up to approximately 2 cm difference in height at age 7 years. These associations are partly explained by genetic or other factors influencing parental stature.

TRIAL REGISTRATION

Current Controlled Trials: NCT01352247 assigned 9 Sept 2005; ClinicalTrials.gov. Identifier: NCT01561612 received 20 Mar 2012.

Weight trajectories through infancy and childhood and risk of non-alcoholic fatty liver disease in adolescence: the ALSPAC study

BACKGROUND & AIMS

Adiposity is a key risk factor for NAFLD. Few studies have examined prospective associations of infant and childhood adiposity with subsequent NAFLD risk. We examined associations of weight-for-height trajectories from birth to age 10 with liver outcomes in adolescence, and assessed the extent to which associations are mediated through fat mass at the time of outcome assessment.

METHODS

Individual trajectories of weight and height were estimated for participants in the Avon Longitudinal Study of Parents and Children using random-effects linear-spline models. Associations of birthweight (adjusted for birth length) and weight change (adjusted for length/height change) from 0-3 months, 3 months-1 y, 1-3 y, 3-7 y, and 7-10 y with ultrasound scan (USS) determined liver fat and stiffness, and serum alanine aminotransferase (ALT), aspartate aminotransferase (AST), and gamma-glutamyl transferase (GGT) at mean age 17.8 y were assessed with linear and logistic regressions. Mediation by concurrent fat mass was assessed with adjustment for fat mass at mean age 17.8 y.

RESULTS

Birth weight was positively associated with liver stiffness and negatively with ALT and AST. Weight change from birth to 1 y was not associated with outcomes. Weight change from 1-3 y, 3-7 y, and 7-10 y was consistently positively associated with USS and blood-based liver outcomes. Adjusting for fat mass at mean age 17.8 y attenuated associations toward the null, suggesting associations are largely mediated by concurrent body fatness.

CONCLUSIONS

Greater rates of weight-for-height change between 1 y and 10 y are consistently associated with adverse liver outcomes in adolescence. These associations are largely mediated through concurrent fatness.