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Obstetrics and gynaecology
Original research
Application of multilevel linear spline models for analysis of growth trajectories in a cohort with repeat antenatal and postnatal measures of growth: a prospective cohort study
  1. Linda M O'Keeffe1,2,3,
  2. Cara A Yelverton4,
  3. Helena C Bartels4,
  4. Kate N O'Neill1,
  5. Ciara McDonnell5,6,
  6. Fionnuala M McAuliffe4
  1. 1School of Public Health, University College Cork, Cork, Ireland
  2. 2MRC Integrative Epidemiology Unit at the University of Bristol, University of Bristol, Bristol, UK
  3. 3Population Health Sciences, University of Bristol, Bristol Medical School, Bristol, UK
  4. 4UCD Perinatal Research Centre, School of Medicine, University College Dublin, Dublin, Ireland
  5. 5Department of Paediatric Endocrinology & Diabetes, Children's Health Ireland at Temple Street, Dublin, Ireland
  6. 6Discipline of Paediatrics, School of Medicine, Trinity College Dublin, Dublin, Ireland
  1. Correspondence to Dr Linda M O'Keeffe; Linda.okeeffe{at}ucc.ie; Linda.okeeffe{at}bristol.ac.uk

Abstract

Objectives To model trajectories of antenatal and postnatal growth using linear spline multilevel models.

Design Prospective cohort study.

Setting Maternity hospital in Dublin, Ireland.

Participants 720–759 mother–child pairs from the ROLO study (initially a randomised control trial of a low glycaemic index diet in pregnancy to prevent recurrence of macrosomia [birth weight >4 kg]).

Primary outcomes Trajectories of growth from 20 weeks gestation (abdominal circumference [AC], head circumference [HC] and weight) or birth (length/height) to 5 years.

Results Over 50% of women had third-level education and 90% were of white ethnicity. Women were a mean (SD) age of 32 years (4.2) at recruitment. The best fitting model for AC, HC and weight included a model with 5 linear spline periods. The best fitting models for length/height included a model with 3 linear spline periods from birth to 6 months, 6 months to 2 years and 2 years to 5 years. Comparison of observed and predicted values for each model demonstrated good model fit. For all growth measures, growth rates were generally fastest in pregnancy or immediately post partum (for length/height), with rates of growth slowing after birth and becoming slower still as infancy and childhood progressed.

Conclusion We demonstrate the application of multilevel linear spline models for examining growth trajectories when both antenatal and postnatal measures of growth are available. The approach may be useful for cohort studies or randomised control trials with repeat prospective assessments of growth.

  • PAEDIATRICS
  • EPIDEMIOLOGY
  • OBSTETRICS

Data availability statement

Data are available on reasonable request. Data are available on submission and approval of a research proposal to the PI of ROLO, FM. Email Fionnuala.McAuliffe@ucd.ie.

http://creativecommons.org/licenses/by-nc/4.0/

This is an open access article distributed in accordance with the Creative Commons Attribution Non Commercial (CC BY-NC 4.0) license, which permits others to distribute, remix, adapt, build upon this work non-commercially, and license their derivative works on different terms, provided the original work is properly cited, appropriate credit is given, any changes made indicated, and the use is non-commercial. See: http://creativecommons.org/licenses/by-nc/4.0/.

https://doi.org/10.1136/bmjopen-2022-065701

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    STRENGTHS AND LIMITATIONS OF THIS STUDY

    • Using prospective follow up of a randomised control trial of predominantly macrocsomic infants, trajectories of antenatal and postnatal growth up to age 5 years were modelled as a single trajectory.

    • The linear spline multilevel modelling method used maximises sample sizes for analyses, reduces selection bias and produces more precise standard errors compared with single-level approaches.

    • We were not able to explore non-linear growth due to the sparsity of repeated measures and this cohort is unlikely to represent the growth rates of a general population since their development is above average due to the high prevalence of macrosomia.

    Introduction

    Antenatal and childhood growth are important indicators of fetal and child health and development and are associated with health in adult life.1 2 Consequently, modelling of growth trajectories, identifying causes and predictors of different growth trajectories and relating growth trajectories in the early life course to later life health is important for informing a life course approach to disease prevention.3–5

    A key aspect of understanding growth patterns, their causes, predictors and outcomes includes appropriate modelling of longitudinal growth data.3 Since repeated measures of growth within individuals are not independent of each other and the scale and variance of growth measures often changes over time, traditional approaches to analysis of growth data, such as single-level multiple regression, do not take account of the clustering of repeated measures within individuals.3 Moreover, the true shape of growth over time cannot be modelled using such approaches. While appropriate methods for the study of longitudinal growth data have been applied to antenatal and childhood growth measures in many cohort studies, most studies to date have examined antenatal growth6 7 or postnatal growth as separate processes/trajectories.8–14 Appropriate modelling of growth data as a continuum from antenatal to postnatal life is important to accurately characterise the shape of growth from early gestation into childhood to better understand it’s aetiology. In addition, it also enables such trajectories to be examined as outcomes for preconception or early pregnancy exposures or to be examined themselves as exposures for later health outcomes.3

    Using data from the prospective follow up of the Randomised cOntrol Trial of LOw glycaemic diet in pregnancy (ROLO) study, we demonstrate the application of linear spline multilevel models for modelling antenatal and postnatal growth trajectories using 4 measures of anthropometry (abdominal circumference [AC], head circumference [HC], weight and length/height) from 20 weeks’ gestation to age 5 years.

    Methods

    Study population

    The ROLO study is a randomised control trial of a low glycaemic index diet in pregnancy that recruited 800 secundigravid women who had previously given birth to a baby weighing over 4 kg between 2007 and 2011 at the National Maternity Hospital, Dublin, Ireland.15 Women were recruited at first antenatal consultation. Women with any underlying medical disorders, including a history of gestational diabetes, those on any drugs, those unable to give full informed consent, aged less than 18 years, of gestation greater than 18 weeks, and having multiple pregnancies were excluded. Women were randomised to either the intervention group which received dietary advice on a low glycaemic diet, or the control group who received routine antenatal care.

    Patient and public involvement

    None.

    Measurement of anthropometry

    Antenatal measures

    Fetal measurements were obtained from ultrasound scans performed on mothers at medians of 20+6 (IQR 20+1–21+5) and 34+1 (IQR: 33+5–34+5) weeks’ gestation, including AC and HC. An estimated fetal weight at 20 and 34 weeks’ gestation was calculated using the Hadlock 4-parameter formula. Ultrasound measurements were taken by 2 ultrasonographers using a Voluson 730 Expert (GE Medical Systems, Germany) using standard procedures.

    Postnatal measures

    At delivery, infants’ AC, HC, weight and length were recorded. Follow-up anthropometry assessments were also obtained in childhood at 6 months, 2 years and 5 years.15–17 All measurements were obtained and calculated by a trained member of the research team. At 6 months, 2 years and 5 years, weight (kg) of the child was measured using a calibrated stand on digital weighing scale (SECA 813) to the nearest 0.1 kg by a trained research team member. Children were measured in light clothing without shoes. Standing height was measured, without shoes, with head aligned in the Frankfort plain, using a free-standing stadiometer (SECA 217) and measurements recorded to the nearest 0.1 cm. The child’s HC and AC were measured using a SECA ergonomic circumference measuring tape, to the nearest 0.1 cm. All measurements were recorded 3 times and the average calculated to improve reliability.

    Statistical analysis

    We used multilevel models to examine trajectories of change in AC, HC, weight and length/height from 20 weeks gestation to age 5 years.18 19 Multilevel models (MLMs) estimate mean trajectories of the outcome while accounting for the non-independence (ie, clustering) of repeated measurements within individuals, change in scale and variance of measures over time and differences in the number and timing of measurements between individuals (using all available data from all eligible participants under a missing at random [MAR] assumption).3 20Table 1 shows the measures available at each occasion, demonstrating differences in the number of measurements available between individuals over time. The MLM approach used here, therefore, was advantageous as it allowed us to include data from all participants, regardless of whether they had 1 or multiple measures as shown in table 1.

    View this table:
    Table 1

    N repeated measures included in analyses for each growth measure

    Change in all 4 growth measures was estimated here using linear spline multilevel models (2 levels: measurement occasion and individual).3 Linear splines allow knot points to be fit at different ages to derive periods in which change is approximately linear. The optimal linear spline model for each growth measure was selected by examining observed data for each growth measure and comparing model fit statistics of different models. Model fit statistics examined included Akaike’s information criterion and observed and predicted values of each growth measure across the age range of the model. For AC, HC and weight, we compared the following models; models that assumed linear change over time, models with knots placed at birth and 5 years only (2 spline periods), models with knots placed at birth, 2 years and 5 years (3 spline periods), models with knots placed at birth, 6 months, 2 years and 5 years (4 spline periods) and finally a model which knots at 34 weeks, birth, 6 months, 2 years and 5 years. The best fitting model for these included a model with knots at each measurement occasion giving rise to 5 linear spline periods from 20 weeks’ to 34 weeks’ gestation, 34 weeks’ gestation to birth, birth to 6 months, 6 months to 2 years and 2 years to 5 years. For length/height, we compared the following models; a model which assumed linear change over time, a model with knots at 2 and 5 years only (2 spline periods) and a model with knots at 6 months, 2 years and 5 years (3 spline periods). The best fitting model for length/height included a model with 3 linear spline periods from birth to 6 months, 6 months to 2 years and 2 years to 5 years.

    All outcomes were normally distributed at each measurement occasion. Except for length/height which did not include antenatal measures, trajectories were centred on the first available measure (20 weeks gestation) for AC, HC and weight. Length/height trajectories were centred at birth. For all models, we placed no restrictions on the variance–covariance matrices of level 2 (individual level) random effects. Given the substantial change in scale and variance of growth from antenatal to postnatal life, we also aimed to allow occasion level measurement error to vary with age (level 1 random effects for the slope). Therefore, all models included a level 1 random effect for the slope while the HC model also included a level 1 random effect for the intercept. The final models for AC, HC and weight trajectories from 20 weeks gestation each took the following form: growth trajectoryij= β0 + u0j + (β1+ u1j)sij1 + (β2+ u2j)sij2 + (β3 + u3j)sij3 + (β4 + u4j)sij4 + (β5 + u5j)sij5+eij where for person j at measurement occasion i; β0 represents the fixed effect coefficient for the average intercept, β1–β5 represent fixed effect coefficients for the average linear slopes of each linear spline, u0j–u5j indicate person-specific random effects for the intercept and slopes, respectively, and eij represents the occasion-specific residuals or measurement error which were allowed to vary with age. The final model for length took a similar form but with only 3 linear spline periods due to the absence of measures prior to birth. Code for the application of these models using the ‘runmlwin’ command from MlWin21 within Stata V.1622 is included in online supplemental material.

    Results

    A total of 754, 756 and 759 offspring were included in analyses of AC, HC and weight, respectively, while 720 offspring were included in analyses of length/height. Table 1 includes the number of measures of each growth measure at each measurement occasion with number of measures available broadly similar across growth measures; for example, weight measures available on each occasion included 655 measures at 20 weeks gestation, 730 at 34 weeks gestation, 756 at birth, 280 at 6 months, 339 at 2 years and 387 at 5 years.

    Of participants included in analyses (table 2), over 50% had completed third-level education and a majority (>90%) were of white ethnicity. Among mothers of male babies, mean age (SD) at delivery was approximately 32.3 (4.2) years, mean (SD) BMI at delivery was 27.1 (5.2) kg/m2, mean (SD) birth weight at delivery was 4.1 (0.5) kg and median (IQR) gestational age was 40.4 (39.6, 41.1) weeks. Mothers of male babies had relatively low levels of deprivation as indicated by the mean (SD) Pobal HP (Haase and Pratschke) index of 5.3 (10.8) (note the Pobal HP index is a census-based deprivation index in Ireland which has a mean of 0 (SD=10) in the general population and ranges from −39 [most deprived] to 40 [most affluent])23 Characteristics were broadly similar for mothers of female babies though mothers of female babies had somewhat higher levels of third-level education (~60%). Model fit as judged by differences between observed growth measures and those predicted by the models for AC, HC, weight and length are shown in tables 3–6. Overall, our models have good fit as all reference ranges for the difference between observed and predicted are less than the SD of the observed or less than 10% of the observed value which can be used as a rule of thumb for the assessment of model fit.

    View this table:
    Table 2

    Characteristics of ROLO participants included in the analysis of length/height, by sex

    View this table:
    Table 3

    Model details for abdominal circumference

    View this table:
    Table 4

    Model details for head circumference

    View this table:
    Table 5

    Model details for weight

    Trajectories of AC, HC and weight from 20 weeks’ gestation to 5 years and trajectories of length/height from birth to 5 years by intervention status and sex are shown in tables 7 and 8 and figures 1–4). AC and HC had the fastest rates (table 7) of growth from 20 to 34 weeks’ gestation with growth rates continuing to slow thereafter up to age 5 years. Weight had the fastest growth rate from 34 weeks’ gestation to birth with growth rates slowing somewhat from birth to 6 months and continuing to slow thereafter until 5 years. Length/height had the fastest growth rates from birth to 2 years, with the growth rate decreasing thereafter and slowing further from 2 to 5 years.

    View this table:
    Table 7

    Mean growth rates of anthropometry and mean difference in growth rates by intervention status and sex in the ROLO cohort from 20 weeks to 5 years

    View this table:
    Table 8

    Mean absolute growth measure and difference in absolute growth measure by intervention status and sex in the ROLO cohort at 20 weeks gestation, birth and 5 years

    View this table:
    Table 6

    Model details for length

    Figure 1
    Figure 1

    Trajectories of abdominal circumference from 20 weeks gestation to age 5 years by intervention status and sex. Note that X axis displays time in months because trajectory spans the antenatal and postnatal period.

    Figure 2
    Figure 2

    Trajectories of head circumference from 20 weeks gestation to age 5 years by intervention status and sex. Note that x-axis displays time in months because trajectory spans the antenatal and postnatal period.

    Figure 3
    Figure 3

    Trajectories of weight from 20 weeks gestation to age 5 years by intervention status and sex. Note that x- axis displays time in months because trajectory spans the antenatal and postnatal period.

    Figure 4
    Figure 4

    Trajectories of length/height from birth to age 5 years by intervention status and sex. Note that x-axis displays time in months.

    We found no strong evidence of differences in trajectories of AC, weight and length/height between the intervention and control group, but we found some evidence of slightly greater HC (difference 0.27 cm (95% CI 0.03 to 0.51) emerging among the control group at 5 years (table 8). AC trajectories did not differ between males and females, though we found some evidence of modest differences in HC, weight and length/height trajectories between males and females. Females had lower HC at 20 weeks gestation with this difference widening at birth and persisting at age 5 years (difference at 5 years: −0.91 cm, 95% CI −1.14 to –0.68). Females had −0.15 kg (95% CI −0.21 to –0.08) lower birth weight and slower postnatal growth rates in weight leading to −0.50 kg (95% CI −0.96 to –0.05) lower weight among females at 5 years. Similarly, females were −0.83 cm (95% CI −1.17 to –0.48) shorter in length at birth and had slower postnatal growth rates in length/height leading to −1.22 cm (95% CI −2.01 to –0.43) shorter height among females at 5 years.

    Discussion

    In this prospective follow up of a randomised control trial of approximately 750 predominantly macrosomic infants, we demonstrated the use of linear spline multilevel modelling to examine trajectories of AC, HC, weight and length/height from 20 weeks’ gestation to age 5 years. We showed their applicability to data with repeated measures of growth which span the antenatal and postnatal period, even when as few as 4 repeat assessments are available (in the case of length/height) and measures are sparse.

    All women in this study previously had a macrosomic infant, and over half of infants had a birth weight in the macrosomic range (>4 kg). To our knowledge, previous analyses have not examined antenatal and postnatal growth trajectories together. Other cohorts have examined the antenatal or postnatal trajectories of infants like ours,24 25 but differences in methodological approaches such as the use of a group-based approach in the LIFECODES cohort make comparisons challenging.25 Our findings for antenatal growth are, however, broadly similar to a study examining the growth trajectories of AC in macrosomic infants from 20 weeks gestation to birth in 244 singleton pregnancies.26 For example, the macrosomic infants of mothers with gestational diabetes had a fetal AC of approximately 1.3 cm at 20 weeks, increasing linearly leading to an AC of 3.6 cm at birth, which is broadly comparable with the growth rates for AC found in our study. In comparison with findings from analyses of growth in the Avon Longitudinal Study of Parents and Children (ALSPAC), Born in Bradford, Generation XXI, Pelotas and PROBIT cohorts,3 our postnatal growth rates are expectedly slower than the growth rates of these general population cohorts. This is consistent with the ‘catch-down’ or slower postnatal growth expected in our high birth weight cohort.27 For example, infants in our cohort were born 52.8 cm in length and grew at 2.85 cm per month in the first 3 months after birth; this growth rate is slower than that of infants in the ALSPAC cohort, born 50 cm in length and growing at the faster rate of 3.57 cm per month in the 3 months after birth. Our growth rates are more comparable to those of the PROBIT cohort which included only infants greater than 2500 g birth weight and is the cohort in this analysis likely to be most similar to ours (birth length 51.4 cm and growth rate of 2.96 cm per month in the 3 months after birth). However, comparisons with previous studies should be undertaken with caution due to population differences (high birth weight vs general populations) and differences in methodological approaches.

    There are several strengths to the general approach of multilevel models taken here; these include the ability to maximise sample sizes for analyses and reduce selection bias compared with single-level approaches since multilevel models can include all participants with at least 1 growth measure under an MAR assumption.3 This is particularly advantageous where attrition rates from cohorts are high. Further advantages include more precise standard errors which consider the non-independence of repeated measures. There are also additional advantages to the approach of modelling antenatal and postnatal growth together in our cohort. A practical advantage includes the ability to examine this trajectory as a single trajectory outcome for prepregnancy or gestational exposures, thereby providing insights into the timing of the impact of exposures during pregnancy that analyses of summary birth anthropometry measures alone (such as birth weight) cannot provide. Moreover, because the associations of prepregnancy or gestational exposures can be examined with antenatal and postnatal growth rates in a single model it is possible to gain insights into whether associations have intrauterine mechanisms, intrauterine and postnatal mechanisms or perhaps intrauterine mechanisms that persist in postnatal life. Importantly, this latter finding would be overlooked entirely in a model which examines postnatal growth trajectories alone. In addition, the modelling of antenatal and postnatal growth together allows participants with only 1 antenatal measure and no postnatal measure or vice versa to be included in analyses, with a full trajectory estimated for that participant under the previously discussed MAR assumption. This can boost sample sizes28 and reduce selection bias induced by analysing antenatal and postnatal trajectories separately because participants with no antenatal or no postnatal measure would be excluded from their respective trajectory analyses whereas in the joint-modelling approach a full trajectory (from antenatal to postnatal life) can be estimated for these participants. Limitations of this work include an inability to explore other non-linear growth patterns such as fractional polynomials due to the sparsity of measures which did not allow a range of possible shapes of growth trajectories to be explored.3 In cohorts with greater numbers of repeated measures and density of repeats, linear spline multilevel modelling can be implemented and compared with other possible shapes include fractional polynomials which have been shown to provide a more biologically intuitive shape of change.3 However, the linear spline approach demonstrated here provides many practical advantages including being more easily interpretable, allowing analysts to split trajectories into distinct periods of change that can then be easily related to exposures and outcomes. It should be noted that this cohort are unlikely to represent the growth rates or trajectories of a general population since their development is above average compared with what would be expected from an age-and gender-matched general population (the cohort is roughly approximated to the 75th centile based on a crude comparison of means and SDs on the UK-WHO [Ireland] chart).29

    Conclusion

    We demonstrate the application of multilevel linear spline models for examining growth trajectories when both antenatal and postnatal measures of growth are available. The approach may be useful for cohort studies or randomised control trials with repeat prospective assessments of growth spanning pregnancy and childhood.

    Data availability statement

    Data are available on reasonable request. Data are available on submission and approval of a research proposal to the PI of ROLO, FM. Email Fionnuala.McAuliffe@ucd.ie.

    Ethics statements

    Patient consent for publication

    Ethics approval

    This study involves human participants and was approved by National Maternity Hospital, Dublin, Ireland. Ethical approval reference/ID:ROLO received institutional ethical approval and maternal written consent carried out at the National Maternity Hospital, Dublin, Ireland. A reference or ID for this is not available. Participants gave informed consent to participate in the study before taking part.

    Acknowledgments

    The authors would like to thank all the ROLO participants for their involvement and all the staff of the National Maternity Hospital and the Perinatal Research Centre.

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    Supplementary materials

    • Supplementary Data

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    Footnotes

    • Contributors LMO'K and FMM designed and planned the study. LM'OK conducted the analyses and wrote the paper up for publication. CAY, HCB, KNO'N and CM provided input on the modelling strategy, contributed to interpretation of data and provided critical revisions to the manuscript. LMO'K accepts full responsibility for the work published in this manuscript, had access to the data, and controlled the decision to publish.

    • Funding LMO'K and KO'N are supported by a Health Research Board of Ireland Emerging Investigator Award (EIA-FA-2019-007 SCaRLeT). The ROLO study was funded by the Health Research Board of Ireland, Health Research Centre for Health and Diet Research, and the European Union’s Seventh Framework Programme (FP7/2007-2013), project Early Nutrition under grant agreement no. 289346.

    • Competing interests None declared.

    • Patient and public involvement Patients and/or the public were not involved in the design, or conduct, or reporting, or dissemination plans of this research.

    • Provenance and peer review Not commissioned; externally peer reviewed.

    • Supplemental material This content has been supplied by the author(s). It has not been vetted by BMJ Publishing Group Limited (BMJ) and may not have been peer-reviewed. Any opinions or recommendations discussed are solely those of the author(s) and are not endorsed by BMJ. BMJ disclaims all liability and responsibility arising from any reliance placed on the content. Where the content includes any translated material, BMJ does not warrant the accuracy and reliability of the translations (including but not limited to local regulations, clinical guidelines, terminology, drug names and drug dosages), and is not responsible for any error and/or omissions arising from translation and adaptation or otherwise.