Iris Pigeot

Report
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
2
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
3
Waist (cm)
Waist (cm)
Task
Age (years)
Age (years)
Publication
5
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.
6
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
7
Definition of GAMLSS
A semi-parametric GAMLSS assumes:
  ,  = 1, … , , independent observations with probability
density function ( | ) conditional on  which is vector
of  parameters related to the covariates

  =   +
 ( )
 =1
Link function  ,  = 1, … , 
Parameter  = 1 , … ,  of a distribution ()
Design matrix  with paramter vector 
Spline  of a vector   ℝ of 1, … , 




8
Four distribution parameters
For  = 
Location:
1
1  = 1 1 +
1 1 (1 1 )
1 =1
2
Scale:
2  = 2 2 +
2 2 (2 2 )
2 =1
3
Skewness:
3 () = 3 3 +
3 3 (3 3 )
3 =1
4
Kurtosis:
4  = 4 4 +
44 (4 4 )
4 =1
9
Shape
Distributions in GAMLSS
BCCG (LMS)
BCPE
Cole and Green (1992) Rigby and Stasinopoulos (2004)
transformed normal
transformed power exponential
=3
=4
1 shape parameter
10
2 shape parameters
Median : location parameter
11
Median : location parameter
12
Median : location parameter
13
Coefficient of variation  :
scale parameter
14
Coefficient of variation  :
scale parameter
15
Coefficient of variation  :
scale parameter
16
Skewness : shape parameter
17
Skewness : shape parameter
18
Skewness : shape parameter
19
Kurtosis  : shape parameter
 Special feature of GAMLSS
20
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
21
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)
22
Model diagnostics
23
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
24
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.
25
Thank you for your
attention!
26
27
28
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
29
Bone stiffness index (SI)
 Percentiles depending on height: P3, Median, P97
30
Bone stiffness index (SI)
 Age- and height-specific
50th percentiles for girls
31
Sensitivity analysis
Shape parameter 
Shape parameter 
Shape: kurtosis

similar documents