Mathematical methods in the assessment of human growth

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

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.