Recent eLetters

We thank Dr. Johnson for his interest in our paper [1] and for the opportunity to discuss methods for modelling child growth. Many methods for modelling repeated measures data are available, and the strengths and limitations of each method will depend on many factors, including the specific research question of interest and the structure of the data being analysed.[2] In our analysis, we used linear spline multilevel models. Such models divide age into separate 'pieces' joined with knot points, and model a different linear slope between each pair of knots. Individual- level random effects allow individuals to differ in both starting size (birth length or weight) and in their rate of growth in each period of childhood. Clearly, such a piecewise linear model is an approximation of the true complex underlying growth pattern. However, a key advantage of using linear splines to model infant and child growth is that they are easy to interpret. As well as being a useful way of creating interpretable summaries of growth trajectories, the linear spline approach provided good fit to our data, for all ethnic and sex groups, as seen in Supplementary web table 2 of our original paper.

Selection of knot points for linear spline models is an important issue. However, Dr. Johnson is incorrect when he states that we used the same knot points that had been derived from the Avon Longitudinal Study of Parents and Children (ALSPAC) data. As reported in the statistical analysis section of our paper, [1] we considered a series of models with knot points at different ages, and selected the best fitting models for the Born in Bradford data. These knot points were slightly different to those used in the ALSPAC study. However, it is interesting to note that this methodology has now been employed in several cohorts in varied geographical settings and with different ethnic and socioeconomic composition and that in each case, similar knot points that best fit the data in these different studies have been identified.[3-8] The fact that best-fitting models using data from very different populations have such similar knot points gives some biological credibility to the periods of growth identified by these models.

In the Born in Bradford cohort we had insufficient data in the first month of life to model neonatal weight loss. When these methods are applied to datasets with a greater number of measurements in early life, it is possible to model neonatal weight loss. For example in the Generation XXI cohort, based in Porto, Portugal, a median of ten growth measures are available for each child within the first few years of life, with almost all children having multiple growth measurements recorded in the first months of life. In this cohort, linear spline multilevel models with knot points at 10 days, 3 months and 1 year fit the data well.[8]

Dr. Johnson suggests that individual knot points should have been used in our study. In contrast to our analyses, such models allow the age of change points within growth trajectories to vary between individuals. Allowing for individual-specific knot points may result in better fit of the statistical model to the data.[9] But this increased model fit comes at the cost of complexity and interpretability. The timing of knot points is likely to be related to the rate of change before and after that knot point, and thus these quantities would need to be interpreted carefully. The potential added benefits of using this approach to address our question of ethnic differences in growth depend on two main factors: how variable knot points are likely to be between individuals, and whether the timing of individual-specific knot points is of interest in its own right. We do not feel that either of these actually support the use of this method to address the research question we were answering. Individual variation in, for example, the timing of puberty onset or the timing of cognitive decline in older age [10] is likely to be considerably greater than individual variation in the timing of changes in growth velocity in infancy and early childhood; therefore models incorporating individual- specific knot points may be more useful in the former situations than in the latter. Likewise, our research question concerned describing ethnic differences in rates of growth and was not concerned with ethnic differences in the timing of features of early growth. Such an approach would be useful when the research question centres on the timing of change and how this timing relates to earlier exposures or later outcomes, for example, when assessing whether age at puberty is associated with later cardiovascular health, one would need to estimate individual age at onset of puberty rather than assuming that this was constant across the population.

We once again thank Dr. Johnson for his interest in our paper. Whilst we recognise that linear spline models represent a simplification of the true underlying growth process, we feel that they are a suitable compromise between model fit, which was good in our study, and interpretability. Examination of growth using different models is important for triangulation, and different methods will be relevant for different research questions.

Reference List

1. Fairley L, Petherick ES, Howe LD, Tilling K, Cameron N, Lawlor DA, et al. Describing differences in weight and length growth trajectories between white and Pakistani infants in the UK: analysis of the Born in Bradford birth cohort study using multilevel linear spline models. Arch Dis Child 2013,98:274-279.

2. Hauspie R, Cameron N, Molinari L. Methods in Human Growth Research: Cambridge University Press; 2004.

3. Howe LD, Tilling K, Galobardes B, Smith GD, Gunnell D, Lawlor DA. Socioeconomic differences in childhood growth trajectories: at what age do height inequalities emerge? J.Epidemiol.Community Health 2012,66:143-148.

4. Paternoster L, Howe LD, Tilling K, Weedon MN, Freathy RM, Frayling TM, et al. Adult height variants affect birth length and growth rate in children. Hum.Mol.Genet. 2011,20:4069-4075.

5. Matijasevich A, Howe LD, Tilling K, Santos IS, Barros AJ, Lawlor DA. Maternal education inequalities in height growth rates in early childhood: 2004 Pelotas birth cohort study. Paediatr.Perinat.Epidemiol. 2012,26:236-249.

6. Tilling K, Davies N, Windmeijer F, Kramer MS, Bogdanovich N, Matush L, et al. Is infant weight associated with childhood blood pressure? Analysis of the Promotion of Breastfeeding Intervention Trial (PROBIT) cohort. Int.J.Epidemiol. 2011,40:1227-1237.

7. Tilling K, Davies NM, Nicoli E, Ben-Shlomo Y, Kramer MS, Patel R, et al. Associations of growth trajectories in infancy and early childhood with later childhood outcomes. Am.J.Clin.Nutr. 2011,94:1808S-1813S.

8. Howe LD. Individual trajectories of childhood growth in five cohorts: the application of linear spline multi-level models. In: EUCCONET/ Society for Longitudinal and Life Course Studies. Paris; 2012.

9. Bellera CA, Hanley JA, Joseph L, Albertsen PC. Hierarchical changepoint models for biochemical markers illustrated by tracking postradiotherapy prostate-specific antigen series in men with prostate cancer. Ann Epidemiol 2008,18:270-282.

10. van den Hout A, Muniz-Terrera G, Matthews FE. Change point models for cognitive tests using semi-parametric maximum likelihood. Comput Stat Data Anal 2013,57:684-698.

Conflict of Interest:

None declared

Dear Ed Gill [1] and Powell [2] state there is little data on delivery of unscheduled care. We would like to share our learning.

To improve paediatric training in primary care one of us (SC) has worked with Advanced Life Support Group (ALSG) led by SW and piloted a, "Poorly Child Pathway Course." This one day course deals with the most common acute childhood presentations and uses a traffic light system (green, amber, red) to classify patients. It aims to improve the management of children presenting to Urgent Care and Out of Hours and communication between primary and secondary care.

23 candidates were taught by 8 faculty. Candidate and Faculty feedback is ongoing, early results show: 80% agreed that a one day course worked well; confidence improved from 2.7/4 to 3.8/4. Primary Care facilities do not have the facility to review patients so hospitals see all amber patients

The second intervention was to pilot a, "Front of House," (FoH) model of care where children were seen and assessed by either a consultant paediatrician, paediatric middle grade or Advanced Nurse Practitioner Students (APNPs) prior to admission. There are two 24 hour paediatric units within CDDFT separated by 22 miles, University Hospital North Durham (UHND) and Darlington Memorial Hospital (DMH). The pilot ran at DMH over a 3 week period between 5th to 23rd November, 2013 on Mondays to Fridays 9:00 to 21:00. There was insufficient staff to run this model at weekends.

During November there were 391 admissions under 18 years of age compared to 406 in November 2012. The data is not scientific. Considering successive 8% annual increases in admissions it suggests a decrease in admissions.

We plan to perform a 6 month, "trial," at UHND using the system 7 days a week with consultants triaging calls.

References

1. Gill PJ, Goldacre MJ, Mant D et al. Increase in Emergency Admissions to Hospital for Children aged under 15 in Emgland, 199-2010: National Database Analysis. Arch. Dis Child 2013; 98: 328-334 2. Powell C Do we need to change the way we deliver unscheduled care? Arch. Dis Child 2013; 98: 319-320

With sincere thanks to the faculty of the pilot Poorly Child Pathway Course: Prof. Peter Driscoll (IDP) Dr. Martin Samuels (Stoke-on-Trent) Paul Lattimer (CDDFT) Dr Leigh Simmonds (CDDFT) Dr John Holmes (CDDFT) Dr Barbara Phillips (IDP) Dr David Ratcliffe (Manchster)

and to our APNPs: Lisa German-Phillips Amanda Dunn Susie Watson Shona Sangster Meg Davies Cheryl Peart

Conflict of Interest:

None declared

We read Ladhani and Ramsay's editorial with great interest. Whilst we agree on the need for the delivery of a completed course of Hepatitis B vaccinations in infants of high-risk mothers where the fourth vaccination is administration by their first birthday, in order to improve uptake of vaccines it is essential to recognise factors preventing this occurring.

Firstly, Hepatitis B positive mothers diagnosed in antenatal services may give birth in a labour unit outside of their local area due to bed pressures and newborns may not receive their first vaccination. This should, however, be limited by the use of patient-held maternity records.

The initial Hepatitis B vaccination is often administered by maternity or neonatal paediatric staff under a hospital doctor prescription. Subsequent vaccines are currently offered by a variety of healthcare professionals such as general practitioners (GP) or community paediatricians. Yates et al[1] showed a high level of participation at the first vaccination but large numbers of infants did not have follow-up vaccines. Reasons for this may include poor transfer of information and clinical records between providers. Also, the administration of infant Hepatitis B vaccinations does not result in item of service payments for GPs and as such GP may be less likely to offer follow up vaccinations. Similarly, acquisition of vaccines, blood test sampling, sample handling practices and pathology systems may vary among GP practices, thus posing additional barriers to the completion of vaccination schedules and serological testing.

In the North London Borough of Enfield, a number of children under the age of 2 years old move in and out of area making follow-up more challenging. However, in 2004 in this borough, 80% of all high-risk neonates of Hepatitis B positive mothers registered at Chase Farm Hospital during antenatal testing received the full vaccination course and serology[2]. This success has been attributed to the use of a named clinical lead conducting an integrated immunisation clinic with a clinic nurse. The team would recall and follow up patients to offer immunisation and serological testing while considering migration, language and access barriers. In a resource-limited health system such immunisation clinics may not be feasible. Universal vaccination of children with Hepatitis B vaccines is not practical or more effective than a targeted approach[3]. Therefore, we would recommend that follow-up Hepatitis B vaccinations and serology are performed by incentivised GPs as a new 'item of service' payment.

1. Yates TA, Paranthaman K, Yu L-M, et al. UK vaccination schedule: persistence of immunity to hepatitis B in children vaccinated after perinatal exposure. Arch Dis Child 2013;98:429-33. 2. Giroudon I. Immunization Coverage in Infants at Risk of Perinatal Transmission of Hepatitis B: A London Study (LANSSG). HPA London Regional Epidemiology Unit. 2008. 3. Balogum MA, Parry JV, Mutton K, et al. Hepatitis B virus transmission in pre-adolescent schoolchildren in four multi-ethnic areas of England. Epidemiol Infect 2013; 141(5):916-25

Conflict of Interest:

None declared

We are grateful to Dr Ladhani and Dr Ramsay [1] for their thoughtful editorial that accompanied the publication of our paper [2]. We would agree that, despite discrepant observational data in the UK regarding the waning of antibody titres [2, 3], there is now a large body of evidence [4] demonstrating that, even where antibody titres have waned, booster doses are not required if an adequate primary schedule has been completed.

As discussed in the editorial, the pragmatic priority is to ensure that all children complete the course and receive at least one further dose after their initial (accelerated) schedule at 0, 1, 2 months.

Routine immunisation visits are a convenient time to do this, and the pre-school booster presents one such opportunity. However, as Dr Ladhani and Dr Ramsay have noted elsewhere, almost all UK children diagnosed with chronic hepatitis B infection acquire this through vertical transmission [5]. Having a named clinician responsible for delivery of the 0, 1, 2 month schedule can improve its delivery , and the 12 month routine vaccine visit is more timely than the pre-school booster for ensuring its completion.

1. Ladhani SN, Ramsay ME. The importance of a preschool booster for children born to hepatitis B-positive mothers. Arch Dis Child. 2013; 98: 395-396. 2. Yates TA, Paranthaman K, Yu LM, et al. UK vaccination schedule: persistence of immunity to hepatitis B in children vaccinated after perinatal exposure. Arch Dis Child. 2013; 98: 429-433. 3. Boxall EH, A Sira J, El-Shuhkri N, et al. Long-term persistence of immunity to hepatitis B after vaccination during infancy in a country where endemicity is low. J Infect Dis. 2004; 190(7): 1264-9. 4. Leuridan E, Van Damme P. Hepatitis B and the need for a booster dose. Clin Infect Dis. 2011; 53(1): 68-75. 5. Flood J, Amirthalingam G, Ramsay ME, et al. The diagnosis of chronic Hepatitis B infection among children born in England after introduction of universal antenatal HBV screening programme. Poster presented at the European Society of Paediatric Infectious Disease Meeting, The Hague, June 2011. http://www.kenes.com/ espid2011/cd/pdf/P774.pdf.

Conflict of Interest:

Our study was supported by the NIHR Oxford Biomedical Research Centre and GlaxoSmithKline Biologicals. SL has undertaken paid work for vaccine manufacturers for provision of travel health training and attendance at advisory group meetings. AJP and MDS have conducted clinical trials on behalf of Oxford University sponsored by manufacturers of vaccines. AJP and MDS do not accept any personal payments from vaccine manufacturers: grants for support of educational activities are paid to an educational/administrative fund held by the Department of Paediatrics, Oxford University. MDS has received support from vaccine manufacturers to attend academic conferences. ED, SBW, SJH, KP and TAY declare no conflicts of interest besides funding received for the study.

Fairley et al(1) describe differences in growth between White and Pakistani infants in the BiB study using mixed effects linear splines, an approach becoming popular in the analysis of serial anthropometry. Linear splines were used because they summarize noisy data in meaningful parameters: an intercept and linear slope terms (connected by knots) governing different age sections. Adding an exposure obtained estimates of differences between ethnicities in size at the intercept and in rate of change for each age section. Linear splines are an appealing analytical choice, but their biological and statistical limitations are often overlooked.

Growth follows a complex pattern of age related change and linear splines (by their very nature) have limited ability to describe this process. A traditional structural growth model (e.g., Berkey-Reed 1st order(2)) may be a better choice to "describe the growth pattern". Careful selection of knots might have improved matters (e.g., given neonatal weight loss, a knot at age two weeks would make sense). Instead, knots developed in the ALSPAC study were used, thereby assuming that the growth process was the same for BiB infants (with different defining characteristics) compared to ALSPAC infants. Further, when investigating the effects of an exposure on growth, does it make sense to impose the same inflection points (i.e., knots) on each response of that exposure? A major assumption of the mixed effects linear splines used by Fairley et al(1) was that all individuals shared the same inflection points. Applying conventional regression to hierarchical data produces incorrect standard errors(3) and linear spline specification that does not account for between individual variation may have similar consequences.

Methods in other disciplines(4) have extended the flexibility of linear splines to incorporate individual level inflection points at knots that do not need to be specified a priori, but instead are data driven. A promising avenue of research is to extend mixed effects linear splines for growth modelling to include individual level inflection points; this could be done in existing Bayesian modelling framework software(5).

1. Fairley L, Petherick ES, Howe LD, Tilling K, Cameron N, Lawlor DA, et al. Describing differences in weight and length growth trajectories between white and Pakistani infants in the UK: analysis of the Born in Bradford birth cohort study using multilevel linear spline models. Archives of Disease in Childhood 2013;98:274-9. 2. Berkey CS, Reed RB. A model for describing normal and abnormal growth in early childhood. Human Biology 1987;59:973-87. 3. Goldstein H. Efficient statistical modelling of longitudinal data. Annals of Human Biology 1986;13:129-41. 4. van den Hout A, Muniz-Terrera G, Matthews FE. Change point models for cognitive tests using semi-parametric maximum likelihood. Computational Statistics & Data Analysis 2013;57:684-98. 5. Lunn DJT, A. Best, N. Spiegelhalter, D. WinBUGS - a Bayesian modelling framework: concepts, structure, and extensibility. Statistics and Computing 2000;10:325-37.

Conflict of Interest:

None declared