Mathematical methods in the assessment of human growth
Lead Research Organisation:
University College London
Department Name: Unlisted
Abstract
Nearly all children grow, and healthy children grow well. This important principle distinguishes paediatrics from adult medicine, so that a simple and effective way to measure the health of children is to assess their size and growth over time. Growth charts are used throughout the world for this purpose by midwives, nurses, doctors and paediatricians, either at home, or the welfare clinic, doctor‘s surgery or in hospital. Growth is important in many areas of paediatrics and child health.
But growth assessment raises quite complex statistical questions about how the charts should be constructed and used. The grant aims to develop the science of growth assessment by building on previous work: improving statistical methods for their construction, devising new forms of chart to sharpen the assessment, and addressing underlying questions such as ‘What exactly is good growth?‘, or ‘Why are people taller now than last century?‘ or ‘How tall will my baby be?‘ A clue to the first question comes from babies followed up into later life, where their growth rate in infancy relates to their later health. There is increasing evidence that growing too fast too early leads to greater illness later, for reasons which are not well understood but which may relate to obesity. So this suggests that ‘good‘ growth is not necessarily ‘rapid‘ growth, and growth charts for babies should be able to test for this. Yet despite their name, growth charts are not good at measuring growth over time, instead they measure a child‘s size. This is just one area where the charts need to be improved.
Another area is child obesity, which has become a serious public health problem in recent years. Methods for measuring fatness, and for identifying overweight or obesity, involve similar statistical questions to those for growth, and are best answered by approaching them in the same way. For example recent work on the grant has led to a new definition of child obesity which is
But growth assessment raises quite complex statistical questions about how the charts should be constructed and used. The grant aims to develop the science of growth assessment by building on previous work: improving statistical methods for their construction, devising new forms of chart to sharpen the assessment, and addressing underlying questions such as ‘What exactly is good growth?‘, or ‘Why are people taller now than last century?‘ or ‘How tall will my baby be?‘ A clue to the first question comes from babies followed up into later life, where their growth rate in infancy relates to their later health. There is increasing evidence that growing too fast too early leads to greater illness later, for reasons which are not well understood but which may relate to obesity. So this suggests that ‘good‘ growth is not necessarily ‘rapid‘ growth, and growth charts for babies should be able to test for this. Yet despite their name, growth charts are not good at measuring growth over time, instead they measure a child‘s size. This is just one area where the charts need to be improved.
Another area is child obesity, which has become a serious public health problem in recent years. Methods for measuring fatness, and for identifying overweight or obesity, involve similar statistical questions to those for growth, and are best answered by approaching them in the same way. For example recent work on the grant has led to a new definition of child obesity which is
Technical Summary
Statistical anthropometry involves the assessment of size and shape, and their ‘growth‘ or rate of change over time, during fetal, infant, child, pubertal and adult life; the adjustment of whole-body and body-compartment physiological measures for body size and shape during both child and adulthood; and the investigation of factors relating to these quantities, particularly the prediction of later health from earlier size and growth. They all raise statistical issues where analysis is strengthened by being approached in a unified way. Previous work on this grant has established a set of statistical principles which have led to widespread advances in the treatment of such anthropometry data: the LMS method for fitting age-related reference ranges, used to construct growth charts and to convert anthropometry to age-sex adjusted SD scores; and a general definition of conditional growth based on SD scores which allows growth as well as size to be assessed using conventional charts.
The aims of the proposed research are to (i) identify new public health and clinical areas where the statistical tools can be applied; (ii) provide new insights into aspects of growth and nutrition through application of the tools, and (iii) improve and extend the tools. One particular aim will be to address the anthropometric transition from child to adult, both in terms of size and growth. These aims will be pursued mainly through the analysis of pre-existing data, often provided by collaborators.
Examples under (i) are infant weight gain charts for ethnic minorities, Down‘s syndrome and those born very premature; height gain charts adjusted for pubertal stage; and prediction equations for basal metabolic rate in children and adults. Examples under (ii) are refining the definition of child obesity using body mass index (BMI) and better understanding its age-related changes; and clarifying the life course importance of early size and growth on later health outcome. Under (iii) tnt aims to extend the methodology of the LMS method, upgrade the Windows program that has been written to apply it, and explore ways of using the LMS method to determine sample size in growth surveys.
The aims of the proposed research are to (i) identify new public health and clinical areas where the statistical tools can be applied; (ii) provide new insights into aspects of growth and nutrition through application of the tools, and (iii) improve and extend the tools. One particular aim will be to address the anthropometric transition from child to adult, both in terms of size and growth. These aims will be pursued mainly through the analysis of pre-existing data, often provided by collaborators.
Examples under (i) are infant weight gain charts for ethnic minorities, Down‘s syndrome and those born very premature; height gain charts adjusted for pubertal stage; and prediction equations for basal metabolic rate in children and adults. Examples under (ii) are refining the definition of child obesity using body mass index (BMI) and better understanding its age-related changes; and clarifying the life course importance of early size and growth on later health outcome. Under (iii) tnt aims to extend the methodology of the LMS method, upgrade the Windows program that has been written to apply it, and explore ways of using the LMS method to determine sample size in growth surveys.
Organisations
- University College London, United Kingdom (Collaboration, Lead Research Organisation)
- University of Leeds, United Kingdom (Collaboration)
- Guy's and St Thomas' NHS Foundation Trust, London (Collaboration)
- Centers for Disease Control and Prevention (CDC) (Collaboration)
- University of Bristol, United Kingdom (Collaboration)
- Great Ormond Street Hospital (GOSH) (Collaboration)
- London Sch of Hygiene and Trop Medicine, United Kingdom (Collaboration)
- University of Sheffield, United Kingdom (Collaboration)
- University of East Anglia, United Kingdom (Collaboration)
- Medical Research Council (Collaboration)
- University of Manchester, Manchester, United Kingdom (Collaboration)
- Johns Hopkins University, United States (Collaboration)
Publications

Hoo AF
(2002)
Sex-specific prediction equations for Vmax(FRC) in infancy: a multicenter collaborative study.
in American journal of respiratory and critical care medicine

Horta BL
(2003)
Early and late growth and blood pressure in adolescence.
in Journal of epidemiology and community health

Jackson LV
(2007)
Blood pressure centiles for Great Britain.
in Archives of disease in childhood

Jarjou LM
(2006)
Randomized, placebo-controlled, calcium supplementation study in pregnant Gambian women: effects on breast-milk calcium concentrations and infant birth weight, growth, and bone mineral accretion in the first year of life.
in The American journal of clinical nutrition

Jebb SA
(2000)
Evaluation of the novel Tanita body-fat analyser to measure body composition by comparison with a four-compartment model.
in The British journal of nutrition

Jebb SA
(2004)
Prevalence of overweight and obesity among young people in Great Britain.
in Public health nutrition

Joffe TH
(2003)
A new method for quantifying encephalization in the growing individual.
in Journal of theoretical biology

Lake JK
(2000)
Back pain and obesity in the 1958 British birth cohort. cause or effect?
in Journal of clinical epidemiology

Lanigan JA
(2004)
Number of days needed to assess energy and nutrient intake in infants and young children between 6 months and 2 years of age.
in European journal of clinical nutrition

Liao YF
(2006)
Hard palate repair timing and facial growth in unilateral cleft lip and palate: a longitudinal study.
in The Cleft palate-craniofacial journal : official publication of the American Cleft Palate-Craniofacial Association
Description | IOTF BMI cutoffs systematic review citations |
Geographic Reach | Multiple continents/international |
Policy Influence Type | Citation in systematic reviews |
Impact | My paper (Cole TJ, Bellizzi MC, Flegal KM, Dietz WH. Establishing a standard definition for child overweight and obesity: international survey. BMJ 2000;320:1240-3) gave a set of BMI cut-offs by age and sex to define overweight and obesity in children internationally. It has since been cited >3500 times, and Web of Science classifies 102 of these citations since 2006 as 'reviews'. A few highly cited examples of these reviews are (in November 2011): Title: Interventions for treating obesity in children Author(s): Luttikhuis HO, Baur L, Jansen H, et al. Source: COCHRANE DATABASE OF SYSTEMATIC REVIEWS Issue: 1 Article Number: CD001872 Published: 2009 Times Cited: 74 Title: Epidemiology of Obesity in the Western Hemisphere Author(s): Ford ES, Mokdad AH Source: JOURNAL OF CLINICAL ENDOCRINOLOGY & METABOLISM Volume: 93 Issue: 11 Pages: S1-S8 Supplement: Suppl. 1 Published: NOV 2008 Times Cited: 58 Title: Socioeconomic status and adiposity in childhood: A systematic review of cross-sectional studies 1990-2005 Author(s): Shrewsbury V, Wardle J Source: OBESITY Volume: 16 Issue: 2 Pages: 275-284 Published: FEB 2008 Times Cited: 95 Title: Assessment of child and adolescent overweight and obesity Author(s): Krebs NF, Himes JH, Jacobson D, et al. Source: PEDIATRICS Volume: 120 Pages: S193-S228 Supplement: Suppl. S Published: DEC 2007 Times Cited: 127 Title: Body mass index in children and adolescents: considerations for population-based applications Author(s): Must A, Anderson SE Source: INTERNATIONAL JOURNAL OF OBESITY Volume: 30 Issue: 4 Pages: 590-594 Published: APR 2006 Times Cited: 28 |
Description | Irish growth charts |
Geographic Reach | National |
Policy Influence Type | Participation in a national consultation |
Impact | discussion about changing the Irish national growth charts to include WHO, following the UK model. |
Description | LMS method applications |
Geographic Reach | Multiple continents/international |
Policy Influence Type | Influenced training of practitioners or researchers |
Impact | My LMS method (Cole TJ, Green PJ. 1992. Smoothing reference centile curves: the LMS method and penalized likelihood. Stat Med 11:1305-1319) has been cited 472 times to date, 278 times since 2006. It allows researchers to derive age-related reference ranges for measurements in children, such as height and weight growth charts, blood pressure centiles etc. The 278 citations show that the method has been applied, often using my software LMSchartmaker (licensed via MRC), in many countries and organisations e.g. USA, WHO, Germany, Italy, Netherlands, Norway, Denmark, Saudi Arabia, Kuwait, Bulgaria, Turkey, Greece, Poland, India and Argentina. Growth charts for the last three countries have been published in 2009/10 with Cole or Pan as co-authors. The measurements to which the method has been applied include anthropometry (weight, height, arm circumference, % body fat etc), blood pressure, heart rate, lung function, aerobic fitness, etc, for children at all ages from fetus through neonatal, infant, preschool and school age to adolescent. |
Description | SACN BMI cutoffs |
Geographic Reach | National |
Policy Influence Type | Participation in advisory committee |
Impact | The Department of Health uses BMI cutoffs for classifying overweight and obesity in children. The Standing Advisory Committee on Nutrition met to discuss changing the cutoffs. Another meeting has been called to finalise the decision, which will affect all national reporting of child obesity. |
Description | SACN growth charts |
Geographic Reach | National |
Policy Influence Type | Participation in a national consultation |
Impact | SACN published its report recommending that WHO charts be introduced to the UK. The new charts have since been designed, produced and launched nationally (May 2009). |
Description | UK-WHO growth charts |
Geographic Reach | National |
Policy Influence Type | Membership of a guidance committee |
Impact | I am a member of the Royal College of Paediatrics and Child Health expert group funded by the English Department of Health to design the new UK-WHO growth charts, which were launched nationally in May 2009. Some hundreds of thousands of printed growth charts are used in primary care, secondary care and by parents of young children. The expert group has continued to meet in 2011/12 to develop growth charts for the age group 4-18 years. This activity also appears under collaborations. |
Description | UK90 BMI centiles |
Geographic Reach | National |
Policy Influence Type | Citation in systematic reviews |
Impact | My paper (Cole TJ, Freeman JV, Preece MA. Body mass index reference curves for the UK, 1990. Arch Dis Child 1995;73:25-9) published BMI centiles for the UK and has been used since 1995 for national BMI assessment and screening. It has been cited 690 times to date, and Web of Science categorises 27 of these citations since 2006 as 'reviews'. Some highly cited examples of such review citations are as follows: Title: Body mass index in children and adolescents: considerations for population-based applications Author(s): Must A, Anderson SE Source: INTERNATIONAL JOURNAL OF OBESITY Volume: 30 Issue: 4 Pages: 590-594 Published: APR 2006 Times Cited: 24 Title: The evolution of human fatness and susceptibility to obesity: an ethological approach Author(s): Wells JCK Source: BIOLOGICAL REVIEWS Volume: 81 Issue: 2 Pages: 183-205 Published: MAY 2006 Times Cited: 30 Title: Metabolic risk-factor clustering estimation in children: to draw a line across pediatric metabolic syndrome Author(s): Brambilla P, Lissau I, Flodmark CE, et al. Source: INTERNATIONAL JOURNAL OF OBESITY Volume: 31 Issue: 4 Pages: 591-600 Published: APR 2007 Times Cited: 23 Title: Tracking of childhood overweight into adulthood: a systematic review of the literature Author(s): Singh AS, Mulder C, Twisk JWR, et al. Source: OBESITY REVIEWS Volume: 9 Issue: 5 Pages: 474-488 Published: SEP 2008 Times Cited: 41 |
Description | WHO growth velocity |
Geographic Reach | Multiple continents/international |
Policy Influence Type | Participation in a national consultation |
Description | Buchan |
Organisation | University of Manchester |
Department | School of Medicine Manchester |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | advice on growth and statistical analysis |
Collaborator Contribution | contribution of data and joint authorship |
Impact | publication: 16880777 |
Description | GOSH |
Organisation | Great Ormond Street Hospital (GOSH) |
Country | United Kingdom |
Sector | Hospitals |
PI Contribution | advice on aspects of growth and statistical analysis |
Collaborator Contribution | provision of data and joint authorship |
Impact | publications: 19875994 16552412 19183310 18043501 16986993 16936560 |
Description | Jackson |
Organisation | University of East Anglia |
Department | School of Medicine UEA |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | advice on growth and statistical analysis |
Collaborator Contribution | contribution of data and joint authorship |
Impact | publication: 16905566 |
Description | LSHTM |
Organisation | London School of Hygiene and Tropical Medicine (LSHTM) |
Department | Faculty of Epidemiology and Population Health |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | advice on growth and statistical analysis |
Collaborator Contribution | provision of data and joint authorship |
Impact | publications: 16306313 17200989 19564879 16570089 |
Description | MRC CECH |
Organisation | University College London |
Department | MRC Centre for Epidemiology for Child Health |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | advice on growth and statistical analysis |
Collaborator Contribution | provision of data and joint authorship |
Impact | publications: 18469281 16984935 19019884 17637703 19789171 18801795 18089633 18403500 19085539 16801947 |
Description | MRC HNR |
Organisation | Medical Research Council (MRC) |
Department | MRC Human Nutrition Research Unit |
Country | United Kingdom |
Sector | Public |
PI Contribution | advice on growth and statistical analysis |
Collaborator Contribution | provision of data and joint authorship |
Impact | publications: 19594476 18541591 16522914 22990031 |
Description | MRC Nutrition ICH |
Organisation | University College London |
Department | Institute of Child Health |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | advice on aspects of growth and statistical analysis |
Collaborator Contribution | provision of data and joint authorship |
Impact | publications: 17429924 17667912 18239656 16770333 16894361 17179023 17209191 23076617 22580078 27604768 |
Description | Martin |
Organisation | Guy's and St Thomas' NHS Foundation Trust |
Country | United Kingdom |
Sector | Public |
PI Contribution | advice on growth and statistical analysis |
Collaborator Contribution | provision of data and joint authorship |
Impact | publication: 17301110 |
Description | Portex |
Organisation | University College London |
Department | Institute of Child Health |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | advice on growth and statistical analysis |
Collaborator Contribution | provision of data and joint authorship |
Impact | publications: 19574442 19065626 17197485 18006882 20351026 20817707 23045209 22743675 22474159 22183491 25254426 25700391 25837028 26493801 27831907 |
Description | Rudolf |
Organisation | University of Leeds |
Department | Faculty of Medicine and Health |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | advice on growth and statistical analysis |
Collaborator Contribution | provision of data and joint authorship |
Impact | publication: 17763011 22529106 |
Description | SCHARR |
Organisation | University of Sheffield |
Department | School of Health and Related Research (ScHARR) |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | advice on growth |
Collaborator Contribution | joint authorship |
Impact | publications: 16724479 16551784 |
Description | Soc Med Bristol |
Organisation | University of Bristol |
Department | School of Social and Community Medicine |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | advice on growth and statistical analysis |
Collaborator Contribution | provision of data and joint authorship |
Impact | publications: 16344844 16720666 |
Description | UCL Epidemiology |
Organisation | University College London |
Department | Institute of Epidemiology and Health Care |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | advice on growth and statistical analysis |
Collaborator Contribution | provision of data and joint authorship |
Impact | publications: 19884892 16679329 |
Description | US CDC |
Organisation | Centers for Disease Control and Prevention (CDC) |
Country | United States |
Sector | Public |
PI Contribution | advice on growth and statistical analysis |
Collaborator Contribution | joint authorship |
Impact | publication: 17591624 |
Description | Wang |
Organisation | Johns Hopkins University |
Department | Department of International Health |
Country | United States |
Sector | Academic/University |
PI Contribution | advice on growth and statistical analysis |
Collaborator Contribution | joint authorship |
Impact | publication: 17361655 |
Title | International BMI cut-offs |
Description | A set of cut-off values for children's BMI by age and sex, identifying obesity, overweight, and thinness. They were described in BMJ articles in 2000 and 2007. |
Type | Diagnostic Tool - Non-Imaging |
Current Stage Of Development | Market authorisation |
Year Development Stage Completed | 2007 |
Development Status | Closed |
Impact | The international cut-offs have been widely cited (5000+ Web of Science citations, Oct 2014) and are regularly mentioned in systematic reviews of child obesity prevention and treatment. |
Title | LMSchartmaker software |
Description | The LMS method summarises the distribution of the measurement (e.g. weight) as it changes with age, in terms of the median, coefficient of variation and skewness (based on a Box-Cox power). The three quantities are modelled as cubic spline curves in age, and so summarise the whole distribution as it changes with age. The LMSchartmaker software makes this statistical analysis accessible to non-statisticians to construct growth centile charts. It is available on the web as a Windows program in two forms, Light (free) and Pro (paid for). The software has been continually developed since before 2006, but there have been notable improvements since then. |
Type Of Technology | Software |
Impact | The LMSchartmaker software is widely used for growth chart construction. The underlying statistical theory paper (Cole & Green, 1992) has been cited some 400 times, and the method has been used for national growth references in many countries including the UK, US, Netherlands and World Health Organization. Downloads of the Light version are not recorded, but the Pro version pays a royalty to the MRC under an agreement with Harlow Printing Ltd, who host the download site. |
Title | LMSgrowth Excel add-in |
Description | The LMSgrowth add-in allows users to manipulate growth references and growth charts fitted by the LMS method (e.g. using my LMSchartmaker software), allowing children's heights and weights etc to be converted to centiles and z-scores. |
Type Of Technology | Software |
Impact | The software is a free download from a website hosted by Harlow Printing, a company that sells growth charts. It is used by paediatric health professionals very widely in the UK, as a way to handle growth data as collected either in general practice, growth clinics or in research. |
Description | Breastfeeding Conference |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | National |
Primary Audience | Professional Practitioners |
Results and Impact | 300 health visitors and midwives at the UNICEF UK Baby Friendly Initiative Annual Conference heard me talk on the WHO growth charts: implications for practice in the UK lots of interest - the first they had heard of the new charts, based on breastfed infants |
Year(s) Of Engagement Activity | 2006 |
Description | Neonatal Update |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Type Of Presentation | Keynote/Invited Speaker |
Geographic Reach | Regional |
Primary Audience | Health professionals |
Results and Impact | In 2006 gave a talk to ~100 paediatricians attending the annual Neonatal Update conference about how to use growth charts. In 2011 gave another talk, on the subject of my SITAR growth curve analysis for developing longitudinal growth curve charts for very preterm infants. Both talks were very well received and generated a lot of interest and discussion. |
Year(s) Of Engagement Activity | 2006,2011 |
Description | Singapore |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | National |
Primary Audience | Public/other audiences |
Results and Impact | I was invited to Singapore to develop new growth charts there, and at the end of the week I gave two talks describing the charts - one for health professionals and the other for parents and the public. Both audiences were several hundred strong. I left the country immediately afterwards, so can't say what impact I made. |
Year(s) Of Engagement Activity | 2007 |