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

Task

GAMLSS

Age (years) Age (years)

Wa

ist

(cm

)

Wa

ist

(cm

)

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

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

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

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

Sensitivity analysis

Shape parameter

Shape parameter

Shape: kurtosis