Funded by the EC, FP 6, Contract No (FOOD) 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

2 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

3 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 children 2-10 years old  IDEFICS study valuable data source

Task Age (years) Waist (cm)

Publication 5

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

7  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

Definition of GAMLSS 8

Four distribution parameters 9 Location: Shape Scale: Kurtosis: Skewness:

10 BCCG (LMS)BCPE Cole and Green (1992)Rigby and Stasinopoulos (2004) transformed normaltransformed power exponential 1 shape parameter2 shape parameters Distributions in GAMLSS

11 Median  : location parameter

12 Median  : location parameter

13 Median  : location parameter

14 Coefficient of variation  : scale parameter

15 Coefficient of variation  : scale parameter

16 Coefficient of variation  : scale parameter

17 Skewness : shape parameter

18 Skewness : shape parameter

19 Skewness : shape parameter

20 Kurtosis  : shape parameter  Special feature of GAMLSS

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

25 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: Cole, T.J. and Green, P.J. (1992). Smoothing reference centile curves: The LMS method and penalized likelihood. Statistics in Medicine 11: 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: 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: References

26 Thank you for your attention!

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Funded by the EC, FP 6, Contract No (FOOD) Appendix 28

29 Modelling bone stiffness index DistributionParameterBIC  log(  ) log(  ) BCCGage+cs(height)cs(height) BCPEage+cs(height)cs(height) Normal distribution age+cs(height)cs(height) For boys

30 Bone stiffness index (SI)  Percentiles depending on height: P3, Median, P97

31 Bone stiffness index (SI)  Age- and height-specific 50th percentiles for girls

Sensitivity analysis

Shape parameter 

Shape: kurtosis