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Funded by the EC, FP 6, Contract No. 016181 (FOOD)
The GAMLSS -An innovative approach for calculating reference values
Iris Pigeot and Timm IntemannLeibniz Institute for Prevention Research and Epidemiology − BIPS- on behalf of the IDEFICS consortium -
Symposium “Reference values for children´s metabolic health indicators from the IDEFICS study”
ECOG, Salzburg, 13 – 15 November 2014
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Reference curves
For many clinical parameters reference values are still missing in children
Due to physical development of children age-dependent growth curves (e.g. for height) are needed
Method of choice for estimating reference curves: GAMLSS
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Identification and prevention of Dietary- and lifestyle-induced health EFfects In Children and infantS
Objectives: Enhance knowledge of health effects of
changing diet & altered social environment & lifestyle of children, 2-10 years, in Europe,
Develop, implement & evaluate specific intervention approaches to reduce prevalence of diet- & lifestyle-related diseases & disorders.
Exhaustive examination programme including numerous biological/clinical parameters
Population-based sample of 18.745 children 2-10 years old
IDEFICS study valuable data source
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Task
GAMLSS
Age (years) Age (years)
Wa
ist
(cm
)
Wa
ist
(cm
)
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Publication
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Publication
Obesity determinants and reference standards for health parameters in pre-adolescent European children: Results from the IDEFICS study Blood lipids among young children in Europe: results from the European IDEFICS study Percentiles of fasting serum insulin, glucose, HbA1c and HOMA-IR in pre-pubertal normal-
weight European children from the IDEFICS cohort C-reactive protein reference percentiles among pre-adolescent children in Europe based on the
IDEFICS study population Reference values for leptin and adiponectin in children below the age of 10 based on the
IDEFICS cohort Percentile reference values for anthropometric body composition indices in European children
from the IDEFICS study Physical fitness reference standards in European children: The IDEFICS study Reference values of bone stiffness index and C-terminal telopeptide (CTX) in healthy European
children Blood pressure reference values for European non-overweight school children: The IDEFICS
study Reference values of whole-blood fatty acids by age and sex from European children aged 3-8
years Metabolic syndrome in young children: definitions and results of the IDEFICS study
Ahrens, W., Moreno, L. and Pigeot, I. (2014): Obesity determinants and reference standards for health parameters in pre-adolescent European children: Results from the IDEFICS study. International Journal of Obesity, 38.
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Generalised additive model for location, scale and shape Rigby and Stasinopoulos (2005) Regression model Generalisation of the LMS method (Cole and Green, 1992) General class of distribution:
Highly skew Kurtotic
More than one covariate gamlss package in the statistical software R Used by WHO for growth curves
GAMLSS
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Definition of GAMLSS
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A semi-parametric GAMLSS assumes: independent observations with probability density
function conditional on which is vector of parameters related to the covariates
Link function Parameter of a distribution Design matrix with paramter vector Spline of a vector of
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Four distribution parameters
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For
Location:
Shape
Scale:
Kurtosis:
Skewness:
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BCCG (LMS) BCPE
Cole and Green (1992) Rigby and Stasinopoulos (2004)
transformed normal transformed power exponential
1 shape parameter 2 shape parameters
Distributions in GAMLSS
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Median : location parameter
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Median : location parameter
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Median : location parameter
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Coefficient of variation : scale parameter
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Coefficient of variation : scale parameter
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Coefficient of variation : scale parameter
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Skewness : shape parameter
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Skewness : shape parameter
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Skewness : shape parameter
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Kurtosis : shape parameter
Special feature of GAMLSS
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Model selection
A variety of distributions at hand (e.g. BCPE, BCCG) Model influence on distribution parameters as
constant, linear function of age and height or cubic spline of age and height
Stepwise model selection using Bayesian Information Criterion (BIC)
Results in a model for each distribution with lowest BIC
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Model diagnostics
Information criterion: BIC Visual impression Comparison of models: boys girls Percentage of cases below the percentiles
Distribution of residuals Q-Q plots Wormplots (Buuren and Fredriks, 2001)
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Model diagnostics
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Conclusion
We applied GAMLSS successfully for more than 35 variables
Derivation of percentile curves and z-scores Particularly useful, if
Shape adjustments are required More than one covariate should be modeled (e.g. for blood
pressure)
Model diagnostic tools available to avoid overcomplex models
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Ahrens, W., Moreno, L. and Pigeot, I. (2014). Obesity determinants and reference standards for health parameters in pre-adolescent European children: Results from the IDEFICS study. International Journal of Obesity, 38.
Van Buuren, S., Fredriks, M. (2001). Worm plot: a simple diagnostic device for modelling growth reference curves. Statistics in Medicine 20: 1259-1277.
Cole, T.J. and Green, P.J. (1992). Smoothing reference centile curves: The LMS method and penalized likelihood. Statistics in Medicine 11: 1305-1319.
Rigby, R.A. & Stasinopoulos, D.M. (2004). Smooth centile curves for skew and kurtotic data modelled using the Box-Cox power exponential distribution. Statistics in Medicine 23: 3053-3076.
Rigby, R.A. & Stasinopoulos, D.M. (2005). Generalized additive models for location, scale and shape. Journal of the Royal Society: Series C (Applied Statistics) 54: 507-554.
References
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Thank you for your attention!
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Funded by the EC, FP 6, Contract No. 016181 (FOOD)
Appendix
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Modelling bone stiffness index
Distribution Parameter BIC
log() log()
BCCG age+cs(height)
cs(height) cs(height) - 42 652
BCPE age+cs(height)
cs(height) cs(height) 1 42 661
Normal distribution
age+cs(height)
cs(height) - - 43 154
For boys
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Bone stiffness index (SI)
Percentiles depending on height: P3, Median, P97
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Bone stiffness index (SI)
Age- and height-specific
50th percentiles for girls
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Sensitivity analysis
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Shape parameter
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Shape parameter
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Shape: kurtosis