Transcript Iris Pigeot
The GAMLSS An innovative approach for
calculating reference values
Iris Pigeot and Timm Intemann
Leibniz 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
Funded by the EC, FP 6, Contract No. 016181 (FOOD)
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 Dietaryand 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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Waist (cm)
Waist (cm)
Task
Age (years)
Age (years)
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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GAMLSS
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
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Definition of GAMLSS
A semi-parametric GAMLSS assumes:
𝑦𝑖 , 𝑖 = 1, … , 𝑁, independent observations with probability
density function 𝑓(𝑦𝑖 |𝜽𝑖 ) conditional on 𝜽𝑖 which is vector
of 𝐾 parameters related to the covariates
𝐽𝑘
𝑔𝑘 𝜽𝑘 = 𝑿𝑘 𝛽𝑘 +
𝒉𝑗𝑘𝑘 (𝒙𝑗𝑘𝑘 )
𝑗𝑘 =1
Link function 𝑔𝑘 , 𝑘 = 1, … , 𝐾
Parameter 𝜽 = 𝜃1 , … , 𝜃𝐾 of a distribution 𝐷(𝜽)
Design matrix 𝑿𝑘 with paramter vector 𝛽𝑘
Spline 𝒉𝑗𝑘𝑘 of a vector 𝒙𝑗𝑘𝑘 𝜖 ℝ𝑁 of 1, … , 𝐽𝑘
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Four distribution parameters
For 𝑲 = 𝟒
Location:
𝐽1
𝑔1 𝝁 = 𝑿1 𝛽1 +
𝒉𝑗1 1 (𝒙𝑗1 1 )
𝑗1 =1
𝐽2
Scale:
𝑔2 𝝈 = 𝑿2 𝛽2 +
𝒉𝑗2 2 (𝒙𝑗2 2 )
𝑗2 =1
𝐽3
Skewness:
𝑔3 (𝝂) = 𝑿3 𝛽3 +
𝒉𝑗3 3 (𝒙𝑗3 3 )
𝑗3 =1
𝐽4
Kurtosis:
𝑔4 𝝉 = 𝑿4 𝛽4 +
𝒉𝑗44 (𝒙𝑗4 4 )
𝑗4 =1
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Shape
Distributions in GAMLSS
BCCG (LMS)
BCPE
Cole and Green (1992) Rigby and Stasinopoulos (2004)
transformed normal
transformed power exponential
𝐾=3
𝐾=4
1 shape parameter
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2 shape parameters
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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References
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: 30533076.
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.
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Thank you for your
attention!
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Appendix
Funded by the EC, FP 6, Contract No. 016181 (FOOD)
Modelling bone stiffness index
For boys
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
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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
Shape parameter
Shape parameter
Shape: kurtosis