Centile and growth curves estimation
Submitting InstitutionLondon Metropolitan University
Unit of AssessmentMathematical Sciences
Summary Impact TypeHealth
Research Subject Area(s)
Mathematical Sciences: Statistics
Information and Computing Sciences: Information Systems
Summary of the impact
The methodology for growth curve estimation developed by Rigby and
Stasinopoulos (2004,2006) has been used worldwide. The World Health
Organisation used the methodology and the related software exclusively for
developing child growth standards, WHO (2006, 2007, 2009). The Global Lung
Function Initiative (GLFI), (www.lungfunction.org,
Stanojevic et al. 2008, Cole et al. 2009, ) use it for
providing a unified worldwide approach to lung function in growth and
ageing. The methodology is now the gold standard for developing growth
The most popular method for growth curve estimation was the LMS method
developed by Cole and Green (1992). Rigby and Stasinopoulos (2004, 2005,
2006) extended the LMS method (which allows for location, scale and
skewness but not for kurtosis in the data), by introducing the 4-
parameter Box-Cox power exponential (BCPE) and the Box-Cox t (BCT)
distributions and called the resulting centile and quantile estimation
methods LMSP and LMST, respectively. The BCCG (equivalent to the LMS
method), BCPE and BCT distributions are part of the GAMLSS general
framework of models. The GAMLSS methodology for growth curves also
generalised the LMS method by allowing multiple explanatory variables and
factors in the model for each of the four parameters of the BCPE or BCT
distributions something which was found useful in the GLFI. The interest
of the two researchers in growth curve methodology started around 2000. In
September 2002 Dr Rigby and Prof. Stasinopoulos were contacted by the
Department of Nutrition for Health and Development of the World Health
Organisation, expressing an interest in the then little known GAMLSS
models as a potential method for the construction of growth curves. This
resulted in a close collaboration, which led to improvements in the GAMLSS
software with the inclusion of several diagnostic techniques appropriate
for comparing and evaluating the fitted growth curves. In the summer of
2003 the decision was taken by WHO that the LMSP method using the BCPE
distribution was the most appropriate method for the construction of the
standard growth curves for the merged data collected from six
representative countries of the world. The arguments for choosing the
GAMLSS methodology for constructing the growth curves, as opposed to at
least 30 other competing methodologies, were published by Borghi et
al. (2006). The WHO subsequently published the actual child growth
standards curves in three volumes, WHO (2006, 2007, 2009).
Another example of worldwide application of the GAMLSS methodology is the
Global Lung Function Initiative (GLFI). The GLFI aim is to set a unified
worldwide approach to lung function in growth and ageing. The GAMLSS
methodology was used to provide equations for obtaining the lung function
centile 'z-score' given values of age, height, ethnic group and gender.
These are two major applications of the GAMLSS methodology in growth curve
fitting, although the method is also now used widely for the construction
of growth curves.
Both Dr Rigby and Prof. Stasinopoulos have been researching continuously
at London Metropolitan University (University of North London before 2001)
for more than twenty years.
References to the research
2005 Rigby R. A. and Stasinopoulos M.D. Generalised additive models for
location scale and shape, (with discussion), Appl. Statist., 54, part 3,
2006 Rigby R. A. and Stasinopoulos M.D. (2006) Using the Box-Cox t
distribution in GAMLS modelling of skewness and kurtosis. Statistical
Modelling, 6, pp 209-229.
2006 Borghi E, de Onis M, Garza C, Van den Broeck J, Frongillo EA,
Grummer-Strawn L, Van Buuren S, Pan H, Molinari L, Martorell R, Onyango
AW, Martines JC, Construction of the World Health Organization child
growth standards: selection of methods for attained growth curves Statistics
in Medicine 2006;25(2):247-65.
(the first three papers were submitted in that last RAF)
Details of the impact
The GAMLSS growth curve methodology has improved and extended the
previous major existing methodology of the LMS method. The researchers
also provide free appropriate software for fitting the models and most
importantly checking their adequacy. This allows the user to find the most
appropriate model for their data.
The impact of any statistical methodological contribution, such as the
GAMLSS growth curve methodology, can only be measured by its usefulness in
practical applications and the impact those applications have to the wider
community. In what it follows we will argue that this is the case with
GAMLSS methodology. Firstly, we will consider the impact that the WHO
Growth Reference Study has and will have upon world health.
The following quote from their website explains the aims of their study:
"The WHO Multicentre Growth Reference Study (MGRS) was undertaken between
1997 and 2003 to generate new growth curves for assessing the growth and
development of infants and young children around the world. The MGRS
collected primary growth data and related information from approximately
8500 children from widely different ethnic backgrounds and cultural
settings (Brazil, Ghana, India, Norway, Oman and the USA). The new growth
curves are expected to provide a single international standard that
represents the best description of physiological growth for all children
from birth to five years of age and to establish the breastfed infant as
the normative model for growth and development."
Upon the completion of the analysis WHO published three books, WHO (2006,
2007, 2009), which are available from their website http://www.who.int/childgrowth/standards/en/.
The impact of the release of Growth Reference Study curves is explained by
the article "Worldwide implementation of the WHO Child Growth Standards"
of de Onis et al. (2012) from which the following quote is taken
"By April 2011, 125 countries had adopted the WHO standards, another
twenty-five were considering their adoption and thirty had not adopted
them. Preference for local references was the main reason for
non-adoption." The article also provided a map to show which countries
adopted the WHO standards curves.
The important point to make here is that results, from applying the
GAMLSS methodology, are used and will be used for the next decades in a
majority of countries of the world for checking the health and the
wellbeing of children.
A further major application of the methodology is its use by the Global
Lung Function Initiative. The initiative uses GAMLSS methodology to
provide equations for obtaining the lung function centile 'z- score' given
values of age, height, ethnic group and gender, Quanjer et al. (2012a).
The equations have been adopted by a variety of commercial companies, as
can be seen in the page 'Manufacturers'
in the www.lungfunction.org
Sources to corroborate the impact
The following three volumes provide evidence for the use of the GAMLSS
methodology and software in the creation of the child growth standards by
Child Growth Standards: Methods and development: Length/height-for-age,
weight-for- age, weight-for-length, weight-for-height and body mass
index-for-age. (2006) Geneva: World Health Organization
Child Growth Standards: Methods and development: Head
circumference-for-age, arm circumference-for-age, triceps
skinfold-for-age and subscapular skinfold-for-age. (2007) Geneva:
World Health Organization,
Child Growth Standards: Methods and development (2009) Growth
velocity based on weight, length and head circumference. Geneva: World
The following articles support the use of the GAMLSS methodology and
software by the Global Lung Function Initiative:
Cole, T. J., Stanojevic, S., Stocks, J., Coats, A. L., Hankinson, J. L.
and Wade, A. M. (2009) Age-
and size related reference ranges: A case study of spirometry through
childhood and adulthood. Statistics in Medicine,28,
Stanojevic, S., Wade, A.M., Stocks, J., Hankinson, J.L., Allan, L.,
Coates, A.L., Pan, H., Rosenthal, M., Corey, M., Lebecque, B., and Cole,
T.J. (2008) Reference
ranges for spirometry across all ages: a new approach. American
Journal of Respiratory and Critical Care Medicine, 177,
Quanjer, P.H., Stanojevic, S., Cole, T.J., Baur, X., Hall, G.L., Culver,
B.H., Enright, P.L., Hankinson, J.L., Ip, I.M.S.M. Zheng, J., Stocks, J.
and the ERS Global Lung Function Initiative (2012a Multi-ethnic
reference values for spirometry for the 3-95-yr age range: the global
lung function 2012 equations. European Respiratory Journal,
Quanjer, P.H., Stanojevic, S., Stocks, J. and Cole, T.J. (2012b) GAMLSS
in action. Available from www.lungfunction.org