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

Immediate drop of urine osmolality upon tolvaptan initiation predicts impact on renal prognosis in patients with ADPKD

BACKGROUND

Tolvaptan, a vasopressin V2 receptor antagonist, is used for treating autosomal dominant polycystic kidney disease (ADPKD). We focused on changes in urinary osmolality (U-Osm) after tolvaptan initiation to determine whether they were associated with the therapeutic response to tolvaptan.

METHODS

This was a single-centre, prospective, observational cohort study. Seventy-two patients with ADPKD who received tolvaptan were recruited. We analysed the relationship between changes in U-Osm and annual estimated glomerular filtration rate (eGFR) in terms of renal prognostic value using univariable and multivariable linear regression analyses.

RESULTS

The mean value of U-Osm immediately before tolvaptan initiation was 351.8 ± 142.2 mOsm/kg H2O, which decreased to 97.6 ± 23.8 mOsm/kg H2O in the evening. The decrease in U-Osm was maintained in the outpatient clinic 1 month later. However, the 1-month values of U-Osm showed higher variability (160.2 ± 83.8 mOsm/kg H2O) than did those in the first evening of tolvaptan administration. Multivariate analysis revealed that the baseline eGFR, baseline urinary protein and U-Osm change in the evening of the day of admission (initial U-Osm drop) were significantly correlated with the subsequent annual change in eGFR.

CONCLUSIONS

U-Osm can be measured easily and rapidly, and U-Osm change within a short time after tolvaptan initiation may be a useful index for the renal prognosis in actual clinical practice.

Exploring examinees' responses to constructed response items with a supervised topic model

Textual data are increasingly common in test data as many assessments include constructed response (CR) items as indicators of participants' understanding. The development of techniques based on natural language processing has made it possible for researchers to rapidly analyse large sets of textual data. One family of statistical techniques for this purpose are probabilistic topic models. Topic modelling is a technique for detecting the latent topic structure in a collection of documents and has been widely used to analyse texts in a variety of areas. The detected topics can reveal primary themes in the documents, and the relative use of topics can be useful in investigating the variability of the documents. Supervised latent Dirichlet allocation (SLDA) is a popular topic model in that family that jointly models textual data and paired responses such as could occur with participants' textual answers to CR items and their rubric-based scores. SLDA has an assumption of a homogeneous relationship between textual data and paired responses across all documents. This approach, while useful for some purposes, may not be satisfied for situations in which a population has subgroups that have different relationships. In this study, we introduce a new supervised topic model that incorporates finite-mixture modelling into the SLDA. This new model can detect latent groups of participants that have different relationships between their textual responses and associated scores. The model is illustrated with an example from an analysis of a set of textual responses and paired scores from a middle grades assessment of science inquiry knowledge. A simulation study is presented to investigate the performance of the proposed model under practical testing conditions.

Comparing statistical methods in assessing the prognostic effect of biomarker variability on time-to-event clinical outcomes

Background

In recent years there is increasing interest in modeling the effect of early longitudinal biomarker data on future time-to-event or other outcomes. Sometimes investigators are also interested in knowing whether the variability of biomarkers is independently predictive of clinical outcomes. This question in most applications is addressed via a two-stage approach where summary statistics such as variance are calculated in the first stage and then used in models as covariates to predict clinical outcome in the second stage. The objective of this study is to compare the relative performance of various methods in estimating the effect of biomarker variability.

Methods

A joint model and 4 different two-stage approaches (naïve, landmark analysis, time-dependent Cox model, and regression calibration) were illustrated using data from a large multi-center randomized phase III trial, the Ocular Hypertension Treatment Study (OHTS), regarding the association between the variability of intraocular pressure (IOP) and the development of primary open-angle glaucoma (POAG). The model performance was also evaluated in terms of bias using simulated data from the joint model of longitudinal IOP and time to POAG. The parameters for simulation were chosen after OHTS data, and the association between longitudinal and survival data was introduced via underlying, unobserved, and error-free parameters including subject-specific variance.

Results

In the OHTS data, joint modeling and two-stage methods reached consistent conclusion that IOP variability showed no significant association with the risk of POAG. In the simulated data with no association between IOP variability and time-to-POAG, all the two-stage methods (except the naïve approach) provided a reliable estimation. When a moderate effect of IOP variability on POAG was imposed, all the two-stage methods underestimated the true association as compared with the joint modeling while the model-based two-stage method (regression calibration) resulted in the least bias.

Conclusion

Regression calibration and joint modelling are the preferred methods in assessing the effect of biomarker variability. Two-stage methods with sample-based measures should be used with caution unless there exists a relatively long series of longitudinal measurements and/or strong effect size (NCT00000125).

Maternal blood pressure associates with placental DNA methylation both directly and through alterations in cell-type composition

BACKGROUND

Maternal blood pressure levels reflect cardiovascular adaptation to pregnancy and proper maternal-fetal exchanges through the placenta and are very sensitive to numerous environmental stressors. Maternal hypertension during pregnancy has been associated with impaired placental functions and with an increased risk for children to suffer from cardiovascular and respiratory diseases later on. Investigating changes in placental DNA methylation levels and cell-type composition in association with maternal blood pressure could help elucidate its relationships with placental and fetal development.

METHODS

Taking advantage of a large cohort of 666 participants, we investigated the association between epigenome-wide DNA methylation patterns in the placenta, measured using the Infinium HumanMethylation450 BeadChip, placental cell-type composition, estimated in silico, and repeated measurements of maternal steady and pulsatile blood pressure indicators during pregnancy.

RESULTS

At the site-specific level, no significant association was found between maternal blood pressure and DNA methylation levels after correction for multiple testing (false discovery rate < 0.05), but 5 out of 24 previously found CpG associations were replicated (p-value < 0.05). At the regional level, our analyses highlighted 64 differentially methylated regions significantly associated with at least one blood pressure component, including 35 regions associated with mean arterial pressure levels during late pregnancy. These regions were found enriched for genes implicated in lung development and diseases. Further mediation analyses show that a significant part of the association between steady blood pressure-but not pulsatile pressure-and placental methylation can be explained by alterations in placental cell-type composition. In particular, elevated blood pressure levels are associated with a decrease in the ratio between mesenchymal stromal cells and syncytiotrophoblasts, even in the absence of preeclampsia.

CONCLUSIONS

This study provides the first evidence that the association between maternal steady blood pressure during pregnancy and placental DNA methylation is both direct and partly explained by changes in cell-type composition. These results could hint at molecular mechanisms linking maternal hypertension to lung development and early origins of childhood respiratory problems and at the importance of controlling maternal blood pressure during pregnancy.

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

BACKGROUND

Longitudinal 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.

METHODS

This 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.

RESULTS

Linear 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.

CONCLUSIONS

LME 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.

Modelling of longitudinal data to predict cardiovascular disease risk: a methodological review

OBJECTIVE

The identification of methodology for modelling cardiovascular disease (CVD) risk using longitudinal data and risk factor trajectories.

METHODS

We screened MEDLINE-Ovid from inception until 3 June 2020. MeSH and text search terms covered three areas: data type, modelling type and disease area including search terms such as "longitudinal", "trajector*" and "cardiovasc*" respectively. Studies were filtered to meet the following inclusion criteria: longitudinal individual patient data in adult patients with ≥3 time-points and a CVD or mortality outcome. Studies were screened and analyzed by one author. Any queries were discussed with the other authors. Comparisons were made between the methods identified looking at assumptions, flexibility and software availability.

RESULTS

From the initial 2601 studies returned by the searches 80 studies were included. Four statistical approaches were identified for modelling the longitudinal data: 3 (4%) studies compared time points with simple statistical tests, 40 (50%) used single-stage approaches, such as including single time points or summary measures in survival models, 29 (36%) used two-stage approaches including an estimated longitudinal parameter in survival models, and 8 (10%) used joint models which modelled the longitudinal and survival data together. The proportion of CVD risk prediction models created using longitudinal data using two-stage and joint models increased over time.

CONCLUSIONS

Single stage models are still heavily utilized by many CVD risk prediction studies for modelling longitudinal data. Future studies should fully utilize available longitudinal data when analyzing CVD risk by employing two-stage and joint approaches which can often better utilize the available data.

Impact of Mode of Conception on Early Pregnancy Human Chorionic Gonadotropin Rise and Birthweight

Objective

To assess whether the mode of conception and embryo biopsy impact first-trimester human chorionic gonadotropin (hCG) dynamics and subsequent risk of small for gestational age (SGA) or large for gestational age (LGA).

Design

Retrospective cohort study.

Setting

University fertility center.

Patient(s)

Six hundred-two pregnant patients with singleton live births.

Intervention(s)

Serial serum hCG measurements were obtained between 10 and 28 days postconception to determine the within-woman rate of change in hCG (slope) by mode of conception (unassisted pregnancy, fresh embryo transfer (ET), frozen ET, and frozen ET following preimplantation genetic testing for aneuploidy (PGT-A).

Main Outcome Measure(s)

Primary outcomes included birth weight, SGA, and LGA.

Result(s)

Mode of conception is not independently associated with birth weight, SGA, or LGA. Mediation analysis revealed an expected one-day increase in log-transformed hCG varied by mode of conception: unassisted (0.41), fresh ET (0.39), frozen ET (0.42), PGT-A (0.44). Human chorionic gonadotropin rise has a positive effect on birth weight (55 g per SD increase in hCG slope) and is associated with SGA (odds ratio, 0.65), but not with LGA (odds ratio, 1.18).

Conclusion(s)

Human chorionic gonadotropin rise is an important mediator of the mode of conception/birth weight relationship. Preimplantation genetic testing for aneuploidy has the highest rate of hCG rise, followed by frozen ET, unassisted, and fresh ET. Faster rise is associated with higher birth weight and lower risk of SGA but does not impact LGA risk. Importantly, PGT-A does not increase the risk of extreme birth weight relative to other modes of conception evaluated.

Media use trajectories and risk of metabolic syndrome in European children and adolescents: the IDEFICS/I.Family cohort

Background

Media use may influence metabolic syndrome (MetS) in children. Yet, longitudinal studies are scarce. This study aims to evaluate the longitudinal association of childhood digital media (DM) use trajectories with MetS and its components.

Methods

Children from Belgium, Cyprus, Estonia, Germany, Hungary, Italy, Spain and Sweden participating in the IDEFICS/I.Family cohort were examined at baseline (W1: 2007/2008) and then followed-up at two examination waves (W2: 2009/2010 and W3: 2013/2014). DM use (hours/day) was calculated as sum of television viewing, computer/game console and internet use. MetS z-score was calculated as sum of age- and sex-specific z-scores of four components: waist circumference, blood pressure, dyslipidemia (mean of triglycerides and HDL-cholesterol⁻¹) and homeostasis model assessment for insulin resistance (HOMA-IR). Unfavorable monitoring levels of MetS and its components were identified (cut-off: ≥ 90^th percentile of each score). Children aged 2–16 years with ≥ 2 observations (W1/W2; W1/W3; W2/W3; W1/W2/W3) were eligible for the analysis. A two-step procedure was conducted: first, individual age-dependent DM trajectories were calculated using linear mixed regressions based on random intercept (hours/day) and linear slopes (hours/day/year) and used as exposure measures in association with MetS at a second step. Trajectories were further dichotomized if children increased their DM duration over time above or below the mean.

Results

10,359 children and adolescents (20,075 total observations, 50.3% females, mean age = 7.9, SD = 2.7) were included. DM exposure increased as children grew older (from 2.2 h/day at 2 years to 4.2 h/day at 16 years). Estonian children showed the steepest DM increase; Spanish children the lowest. The prevalence of MetS at last follow-up was 5.5%. Increasing media use trajectories were positively associated with z-scores of MetS (slope: β = 0.54, 95%CI = 0.20–0.88; intercept: β = 0.07, 95%CI = 0.02–0.13), and its components after adjustment for puberty, diet and other confounders. Children with increasing DM trajectories above mean had a 30% higher risk of developing MetS (slope: OR = 1.30, 95%CI = 1.04–1.62). Boys developed steeper DM use trajectories and higher risk for MetS compared to girls.

Conclusions

Digital media use appears to be a risk factor for the development of MetS in children and adolescents. These results are of utmost importance for pediatricians and the development of health policies to prevent cardio-metabolic disorders later in life.

Trial registration

ISRCTN, ISRCTN62310987. Registered 23 February 2018- retrospectively registered.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12966-021-01186-9.

Joint Modeling of Individual Trajectories, Within-Individual Variability, and a Later Outcome: Systolic Blood Pressure Through Childhood and Left Ventricular Mass in Early Adulthood

Within-individual variability of repeatedly measured exposures might predict later outcomes (e.g., blood pressure (BP) variability (BPV) is an independent cardiovascular risk factor above and beyond mean BP). Because 2-stage methods, known to introduce bias, are typically used to investigate such associations, we introduce a joint modeling approach, examining associations of mean BP and BPV across childhood with left ventricular mass (indexed to height; LVMI) in early adulthood with data (collected 1990-2011) from the UK Avon Longitudinal Study of Parents and Children cohort. Using multilevel models, we allowed BPV to vary between individuals (a "random effect") as well as to depend on covariates (allowing for heteroskedasticity). We further distinguished within-clinic variability ("measurement error") from visit-to-visit BPV. BPV was predicted to be greater at older ages, at higher body weights, and in female participants and was positively correlated with mean BP. BPV had a weak positive association with LVMI (10% increase in within-individual BP variance was predicted to increase LVMI by 0.21%, 95% credible interval: -0.23, 0.69), but this association became negative (-0.78%, 95% credible interval: -2.54, 0.22) once the effect of mean BP on LVMI was adjusted for. This joint modeling approach offers a flexible method of relating repeatedly measured exposures to later outcomes.

Lower Airway Dysbiosis Affects Lung Cancer Progression

In lung cancer, enrichment of the lower airway microbiota with oral commensals commonly occurs, and ex vivo models support that some of these bacteria can trigger host transcriptomic signatures associated with carcinogenesis. Here, we show that this lower airway dysbiotic signature was more prevalent in the stage IIIB-IV tumor-node-metastasis lung cancer group and is associated with poor prognosis, as shown by decreased survival among subjects with early-stage disease (I-IIIA) and worse tumor progression as measured by RECIST scores among subjects with stage IIIB-IV disease. In addition, this lower airway microbiota signature was associated with upregulation of the IL17, PI3K, MAPK, and ERK pathways in airway transcriptome, and we identified Veillonella parvula as the most abundant taxon driving this association. In a KP lung cancer model, lower airway dysbiosis with V. parvula led to decreased survival, increased tumor burden, IL17 inflammatory phenotype, and activation of checkpoint inhibitor markers. SIGNIFICANCE: Multiple lines of investigation have shown that the gut microbiota affects host immune response to immunotherapy in cancer. Here, we support that the local airway microbiota modulates the host immune tone in lung cancer, affecting tumor progression and prognosis.See related commentary by Zitvogel and Kroemer, p. 224.This article is highlighted in the In This Issue feature, p. 211.

A two-stage Generalized Method of Moments model for feedback with time-dependent covariates

Correlated observations in longitudinal studies are often due to repeated measures on the subjects. Additionally, correlation may be realized due to the association between responses at a particular time and the predictors at earlier times. There are also feedback effects (relation between responses in the present and the covariates at a later time), though these are not always relevant and are often ignored. All these cases of correlation must be accounted for as they can have different effects on the regression coefficients. Several authors have provided models that reflect the direct and delayed impact of covariates on the response, utilizing valid moment conditions to estimate the relevant regression coefficients. However, there are applications when one cannot ignore the effect of the responses on future covariates. A two-stage model to account for the feedback, modeling the direct as well as the delayed effects of the covariates on future responses and vice versa is presented. The use of the two-stage model is demonstrated by revisiting child morbidity and its impact on future values of body mass index using Philippines health data. Also, obesity status and its feedback effects on physical activity and depression levels using the Add Health dataset are analyzed.

Childhood growth prior to screen-detected celiac disease: prospective follow-up of an at-risk birth cohort

OBJECTIVES

To determine the association between childhood growth prior to the development of celiac disease (CD) and CD autoimmunity (CDA) identified by periodic serological screening.

STUDY DESIGN

The Diabetes Autoimmunity Study in the Young cohort includes 1979 genetically at-risk children from Denver, Colorado, with annual growth measurements from age nine months until ten years. Between 1993 and February 2019, 120 children developed CDA defined by persistent positive tissue transglutaminase autoantibodies (TGA); among these, 71 met our criteria for CD based on histopathological findings or high TGA levels. Age- and sex-specific z-scores of weight, body mass index (BMI), and height prior to seroconversion were derived using US reference charts as standards. Joint modeling of serial growth measurements was used to estimate adjusted hazard ratios (aHRs) accounting for celiac-associated human leukocyte antigens, early-life feeding practices, and socio-demographics.

RESULTS

In the first 10 years of life, there were no significant associations between the child's current weight, BMI and height and the risk of screening-detected CDA or CD, neither was the weight nor BMI velocity associated with CDA or CD as identified by screening (all aHRs approximated 1). Increased height velocity was associated with later CD, but not CDA, development (aHR per 0.01-z score/year, 1.28; 95% confidence interval [CI] 1.18-1.38 and 1.03; 0.97-1.09, respectively).

CONCLUSIONS

In the first 10 years of life, from prospectively collected serial growth measurements, we found no evidence of impaired childhood growth before CD and CDA development as identified through early and periodic screening.

Structural brain networks and functional motor outcome after stroke-a prospective cohort study

The time course of topological reorganization that occurs in the structural connectome after an ischaemic stroke is currently not well understood. We aimed to determine the evolution of structural brain networks in stroke patients with motor deficits and relate changes in their global topology to residual symptom burden and functional impairment. In this prospective cohort study, ischaemic stroke patients with supratentorial infarcts and motor symptoms were assessed longitudinally by advanced diffusion MRI and detailed clinical testing of upper extremity motor function at four time points from the acute to the chronic stage. For each time point, structural connectomes were reconstructed, and whole-hemisphere global network topology was quantified in terms of integration and segregation parameters. Using non-linear joint mixed-effects regression modelling, network evolution was related to lesion volume and clinical outcome. Thirty patients were included for analysis. Graph-theoretical analysis demonstrated that, over time, brain networks became less integrated and more segregated with decreasing global efficiency and increasing modularity. Changes occurred in both stroke and intact hemispheres and, in the latter, were positively associated with lesion volume. Greater change in topology was associated with larger residual symptom burden and greater motor impairment 1, 3 and 12 months after stroke. After ischaemic stroke, brain networks underwent characteristic changes in both ipsi- and contralesional hemispheres. Topological network changes reflect the severity of damage to the structural network and are associated with functional outcome beyond the impact of lesion volume.

Analysing trajectories of a longitudinal exposure: A causal perspective on common methods in lifecourse research

Longitudinal data is commonly analysed to inform prevention policies for diseases that may develop throughout life. Commonly methods interpret the longitudinal data as a series of discrete measurements or as continuous patterns. Some of the latter methods condition on the outcome, aiming to capture ‘average’ patterns within outcome groups, while others capture individual-level pattern features before relating these to the outcome. Conditioning on the outcome may prevent meaningful interpretation. Repeated measurements of a longitudinal exposure (weight) and later outcome (glycated haemoglobin levels) were simulated to match three scenarios: one with no causal relationship between growth rate and glycated haemoglobin; two with a positive causal effect of growth rate on glycated haemoglobin. Two methods that condition on the outcome and one that did not were applied to the data in 1000 simulations. The interpretation of the two-step method matched the simulation in all causal scenarios, but that of the methods conditioning on the outcome did not. Methods that condition on the outcome do not accurately represent a causal relationship between a longitudinal pattern and outcome. Researchers considering longitudinal data should carefully determine if they wish to analyse longitudinal data as a series of discrete time points or by extracting pattern features.

Association Between Age at Puberty and Bone Accrual From 10 to 25 Years of Age

Importance

Bone health in early life is thought to influence the risk of osteoporosis in later life.

Objective

To examine whether puberty timing is associated with bone mineral density accrual up to adulthood.

Design, Setting, and Participants

This cohort study used data from the Avon Longitudinal Study of Parents and Children, a prospective population-based birth cohort initiated in 1991 to 1992 in southwest England. The participants were 6389 healthy British people who underwent regular follow-up, including up to 6 repeated bone density scans from ages 10 to 25 years. Data analysis was performed from June 2018 to June 2019.

Exposures

Age at puberty from estimated age at peak height velocity (years).

Main Outcomes and Measures

Gains per year in whole-body bone mineral density (grams per square centimeter), assessed by dual-energy x-ray absorptiometry at ages 10, 12, 14, 16, 18, and 25 years and modeled using linear splines.

Results

A total of 6389 participants (3196 [50.0%] female) were included. The mean (SD) age at peak height velocity was 13.5 (0.9) years for male participants and 11.6 (0.8) years for female participants. Male participants gained bone mineral density at faster rates than did female participants, with the greatest gains in both male participants (0.139 g/cm2/y; 95% CI, 0.127-0.151 g/cm2/y) and female participants (0.106 g/cm2/y; 95% CI, 0.098-0.114 g/cm2/y) observed between the year before and 2 years after peak height velocity. When aligned by chronological age, per 1-year older age at puberty was associated with faster subsequent gains in bone mineral density; the magnitudes of faster gains were greatest between ages 14 and 16 years in both male participants (0.013 g/cm2/y; 95% CI, 0.011-0.015 g/cm2/y) and female participants (0.014 g/cm2/y; 95% CI, 0.014-0.015 g/cm2/y), were greater in male participants (0.011 g/cm2/y; 95% CI, 0.010-0.013 g/cm2/y) than in female participants (0.003 g/cm2/y; 95% CI, 0.003-0.004 g/cm2/y) between ages 16 and 18 years, and were least in both male participants (0.002 g/cm2/y; 95% CI, 0.001-0.003 g/cm2/y) and female participants (0.000 g/cm2/y; 95% CI, -0.001 to 0.000 g/cm2/y) between ages 18 and 25 years. Despite faster gains, older age at puberty was associated with persistently lower bone mineral density, changing from 0.050 g/cm2 (95% CI, -0.056 to -0.045 g/cm2) lower at age 14 years to 0.047 g/cm2 (95% CI, -0.051 to -0.043 g/cm2) lower at age 25 years in male participants and from 0.044 g/cm2 (95% CI, -0.046 to -0.041 g/cm2) to 0.034 g/cm2 (95% CI, -0.036 to -0.032 g/cm2) lower at the same ages in female participants.

Conclusions and Relevance

People with older pubertal age should be advised on how to maximize bone mineral density and minimize its decrease in later life to help prevent fracture and osteoporosis.

Association of accelerated body mass index gain with repeated measures of blood pressure in early childhood

Background/objectives

We examined the association for rates of age- and sex-standardized body mass index (zBMI) gain between 0–3, 3–18, and 18–36 months with BP in children at 36–72 months of age.

Methods

We collected repeated measures of zBMI and BP in 2502 children. zBMI was calculated using the World Health Organization standards. Each child’s zBMI at birth and rates of zBMI gain in each period from birth to 36 months were estimated using linear spline multilevel models. Generalized estimating equations were used to determine whether zBMI at birth and zBMI gain between 0–3, 3–18, and 18–36 months were each associated with repeated measures of BP at 36–72 months of age. We sequentially conditioned on zBMI at birth and zBMI gain in each period prior to each period tested, as covariates, and adjusted for important socio-demographic, familial, and study design covariates. We examined whether these associations were modified by birthweight or maternal obesity, by including interaction terms.

Results

After adjusting for all covariates and conditioning on prior zBMI gains, a 1 standard deviation unit faster rate of zBMI gain during 0–3 months, (β = 0.59 mmHg; 95% CI 0.31, 0.86) and 3–18 months (β = 0.74 mmHg; 95% CI 0.46, 1.03) were each associated with higher systolic BP at 36–72 months. No significant associations were observed, however, for zBMI at birth or zBMI gain in the 18–36 month growth period. zBMI gains from 0–3 and 3–18 months were also associated with diastolic BP. Birthweight significantly modified the relationship during the 3–18 month period (p = 0.02), with the low birthweight group exhibiting the strongest association for faster rate of zBMI gain with higher systolic BP (β = 1.31 mmHg; 95% CI 0.14, 2.48).

Conclusions

Given that long-term exposure to small elevations in BP are associated with subclinical cardiovascular disease, promoting interventions targeting healthy growth in infancy may be important.

A discussion of statistical methods to characterise early growth and its impact on bone mineral content later in childhood

BACKGROUND

Many statistical methods are available to model longitudinal growth data and relate derived summary measures to later outcomes.

AIM

To apply and compare commonly used methods to a realistic scenario including pre- and postnatal data, missing data, and confounders.

SUBJECTS AND METHODS

Data were collected from 753 offspring in the Southampton Women's Survey with measurements of bone mineral content (BMC) at age 6 years. Ultrasound measures included crown-rump length (11 weeks' gestation) and femur length (19 and 34 weeks' gestation); postnatally, infant length (birth, 6 and 12 months) and height (2 and 3 years) were measured. A residual growth model, two-stage multilevel linear spline model, joint multilevel linear spline model, SITAR and a growth mixture model were used to relate growth to 6-year BMC.

RESULTS

Results from the residual growth, two-stage and joint multilevel linear spline models were most comparable: an increase in length at all ages was positively associated with BMC, the strongest association being with later growth. Both SITAR and the growth mixture model demonstrated that length was positively associated with BMC.

CONCLUSIONS

Similarities and differences in results from a variety of analytic strategies need to be understood in the context of each statistical methodology.

Bayesian Piecewise Linear Mixed Models With a Random Change Point: An Application to BMI Rebound in Childhood

Background:

Body mass index (BMI) rebound refers to the beginning of the second rise in BMI during childhood. Accurate estimation of an individual’s timing of BMI rebound is important because it is associated with health outcomes in later life.

Methods:

We estimated BMI trajectories for 6545 children from the Avon Longitudinal Study of Parents and Children. We used a novel Bayesian two-phase piecewise linear mixed model where the “change point” was an individual-level random effect corresponding to the individual-specific timing of BMI rebound. The model’s individual-level random effects (intercept, prechange slope, postchange slope, change point) were multivariate normally distributed with an unstructured variance–covariance matrix, thereby, allowing for correlation between all random effects.

Results:

Average age at BMI rebound (mean change point) was 6.5 (95% credible interval: 6.4 to 6.6) years. The standard deviation of the individual-specific timing of BMI rebound (random effects) was 2.0 years for females and 1.6 years for males. Correlation between the prechange slope and change point was 0.57, suggesting that faster rates of decline in BMI prior to rebound were associated with rebound occurring at an earlier age. Simulations showed that estimates from the model were less biased than those from models, assuming a common change point for all individuals or a nonlinear trajectory based on fractional polynomials.

Conclusions:

Our model flexibly estimated the individual-specific timing of BMI rebound, while retaining parameters that are meaningful and easy to interpret. It is applicable in any situation where one wishes to estimate a change-point process which varies between individuals.

Preconceptional and gestational weight trajectories and risk of delivering a small-for-gestational-age baby in rural Gambia

Background: Maternal nutritional status is a key determinant of small for gestational age (SGA), but some knowledge gaps remain, particularly regarding the role of the energy balance entering pregnancy.Objective: We investigated how preconceptional and gestational weight trajectories (summarized by individual-level traits) are associated with SGA risk in rural Gambia.Design: The sample comprised 670 women in a trial with serial weight data (7310 observations) that were available before and during pregnancy. Individual trajectories from 6 mo before conception to 30 wk of gestation were produced with the use of multilevel modeling. Summary traits were expressed as weight z scores [weight z score at 3 mo preconception (zwt-3 mo), weight z score at conception, weight z score at 3 mo postconception, weight z score at 7 mo postconception (zwt+7 mo), and conditional measures that represented the change from the preceding time] and were related to SGA risk with the use of Poisson regression with confounder adjustment; linear splines were used to account for nonlinearity.Results: Maternal weight at each time point had a consistent nonlinear relation with SGA risk. For example, the zwt-3 mo estimate was stronger in women with values ≤0.5 (RR: 0.736; 95% CI: 0.594, 0.910) than in women with values >0.5 (RR: 0.920; 95% CI: 0.682, 1.241). The former group had the highest observed SGA prevalence. Focusing on weight change, only conditional zwt+7 mo was associated with SGA and only in women with values >-0.5 (RR: 0.579; 95% CI: 0.463, 0.724).Conclusions: Protection against delivering an SGA neonate offered by greater preconceptional or gestational weight may be most pronounced in more undernourished and vulnerable women. Independent of this possibility, greater second- and third-trimester weight gain beyond a threshold may be protective. This trial was registered at http://www.isrctn.com/ as ISRCTN49285450.

Multilevel growth curve models that incorporate a random coefficient model for the level 1 variance function

Aim

To present a flexible model for repeated measures longitudinal growth data within individuals that allows trends over time to incorporate individual-specific random effects. These may reflect the timing of growth events and characterise within-individual variability which can be modelled as a function of age.

Subjects and methods

A Bayesian model is developed that includes random effects for the mean growth function, an individual age-alignment random effect and random effects for the within-individual variance function. This model is applied to data on boys’ heights from the Edinburgh longitudinal growth study and to repeated weight measurements of a sample of pregnant women in the Avon Longitudinal Study of Parents and Children cohort.

Results

The mean age at which the growth curves for individual boys are aligned is 11.4 years, corresponding to the mean ‘take off’ age for pubertal growth. The within-individual variance (standard deviation) is found to decrease from 0.24 cm2 (0.50 cm) at 9 years for the ‘average’ boy to 0.07 cm2 (0.25 cm) at 16 years. Change in weight during pregnancy can be characterised by regression splines with random effects that include a large woman-specific random effect for the within-individual variation, which is also correlated with overall weight and weight gain.

Conclusions

The proposed model provides a useful extension to existing approaches, allowing considerable flexibility in describing within- and between-individual differences in growth patterns.

Potential selection effects when estimating associations between the infancy peak or adiposity rebound and later body mass index in children

INTRODUCTION

This study aims to evaluate a potential selection effect caused by exclusion of children with non-identifiable infancy peak (IP) and adiposity rebound (AR) when estimating associations between age and body mass index (BMI) at IP and AR and later weight status.

SUBJECTS AND METHODS

In 4744 children with at least 4 repeated measurements of height and weight in the age interval from 0 to 8 years (37 998 measurements) participating in the IDEFICS (Identification and Prevention of Dietary- and Lifestyle-Induced Health Effects in Children and Infants)/I.Family cohort study, fractional polynomial multilevel models were used to derive individual BMI trajectories. Based on these trajectories, age and BMI at IP and AR, BMI values and growth velocities at selected ages as well as the area under the BMI curve were estimated. The BMI growth measures were standardized and related to later BMI z-scores (mean age at outcome assessment: 9.2 years).

RESULTS

Age and BMI at IP and AR were not identifiable in 5.4% and 7.8% of the children, respectively. These groups of children showed a significantly higher BMI growth during infancy and childhood. In the remaining sample, BMI at IP correlated almost perfectly (r⩾0.99) with BMI at ages 0.5, 1 and 1.5 years, whereas BMI at AR correlated perfectly with BMI at ages 4-6 years (r⩾0.98). In the total study group, BMI values in infancy and childhood were positively associated with later BMI z-scores where associations increased with age. Associations between BMI velocities and later BMI z-scores were largest at ages 5 and 6 years. Results differed for children with non-identifiable IP and AR, demonstrating a selection effect.

CONCLUSIONS

IP and AR may not be estimable in children with higher-than-average BMI growth. Excluding these children from analyses may result in a selection bias that distorts effect estimates. BMI values at ages 1 and 5 years might be more appropriate to use as predictors for later weight status instead.

Pathways between Socioeconomic Disadvantage and Childhood Growth in the Scottish Longitudinal Study, 1991-2001

Socioeconomically disadvantaged children are more likely to be of shorter stature and overweight, leading to greater risk of obesity in adulthood. Disentangling the mediatory pathways between socioeconomic disadvantage and childhood size may help in the development of appropriate policies aimed at reducing these health inequalities. We aimed to elucidate the putative mediatory role of birth weight using a representative sample of the Scottish population born 1991-2001 (n = 16,628). Estimated height and overweight/obesity at age 4.5 years were related to three measures of socioeconomic disadvantage (mother's education, Scottish Index of Multiple Deprivation, synthetic weekly income). Mediation was examined using two approaches: a 'traditional' mediation analysis and a counterfactual-based mediation analysis. Both analyses identified a negative effect of each measure of socioeconomic disadvantage on height, mediated to some extent by birth weight, and a positive 'direct effect' of mother's education and Scottish Index of Multiple Deprivation on overweight/obesity, which was partly counterbalanced by a negative 'indirect effect'. The extent of mediation estimated when adopting the traditional approach was greater than when adopting the counterfactual-based approach because of inappropriate handling of intermediate confounding in the former. Our findings suggest that higher birth weight in more disadvantaged groups is associated with reduced social inequalities in height but also with increased inequalities in overweight/obesity.

Variability and rapid increase in body mass index during childhood are associated with adult obesity

BACKGROUND

Body mass index (BMI) in childhood predicts obesity in adults, but it is unknown whether rapid increase and variability in BMI during childhood are independent predictors of adult obesity.

METHODS

The study cohort consisted of 1622 Bogalusa Heart Study participants (aged 20 to 51 years at follow-up) who had been screened at least four times during childhood (aged 4-19 years). BMI rate of change during childhood for each individual was assessed by mixed models; BMI residual standard deviation (RSD) during childhoodwas used as a measure of variability. The average follow-up period was 20.9 years.

RESULTS

One standard deviation increase in rate of change in BMI during childhood was associated with 1.39 [95% confidence interval (CI): 1.17-1.61] kg/m(2) increase in adult BMI and 2.98 (95% CI: 2.42-3.56) cm increase in adult waist circumference, independently of childhood mean BMI. Similarly, one standard deviation increase in RSD in BMI during childhood was associated with 0.46 (95% CI: 0.23-0.69) kg/m(2) increase in adult BMI and 1.42 (95% CI: 0.82-2.02) cm increase in adult waist circumference. Odds ratio for adult obesity progressively increased from the lowest to the highest quartile of BMI rate of change or RSD during childhood (P for trend < 0.05 for both).

CONCLUSIONS

Rapid increase and greater variability in BMI during childhood appear to be independent risk factors for adult obesity. Our findings have implications for understanding body weight regulation and obesity development from childhood to adulthood.

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.