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Fitting Smoothed Centile Curves to Reference Data

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  • T. J. Cole

Abstract

A general method is described for fitting smooth centile curves to reference data, based on the power transformation family of Box and Cox. The data are defined by values or ranges of values of the independent variable t, and best fitting powers ̂λi assuming normality are estimated for each group i. Corresponding estimates for the generalized mean and coefficient of variation ̂μi and ̂σi are also obtained. The ̂λi, ̂μi and ̂σi plotted against ti are fitted by smooth curves L(t), M(t) and S(t) respectively, which together define a smooth curve for the 100αth centile given by C100α(t)=M(t)[1+L(t)S(t)zα]1/L(t), where zα is the normal equivalent deviate for tail area α. The method is validated by comparison with published growth standards and illustrated on weight and height data in children. A section describing the practical details of the method is also included.

Suggested Citation

  • T. J. Cole, 1988. "Fitting Smoothed Centile Curves to Reference Data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 151(3), pages 385-406, May.
    • Handle: RePEc:bla:jorssa:v:151:y:1988:i:3:p:385-406
    DOI: 10.2307/2982992
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    1. Alok Bhargava, 2006. "Modelling the Health of Filipino Children," World Scientific Book Chapters, in: Econometrics, Statistics And Computational Approaches In Food And Health Sciences, chapter 11, pages 153-168, World Scientific Publishing Co. Pte. Ltd..
    2. Yu, Keming, 2002. "Quantile regression using RJMCMC algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 40(2), pages 303-315, August.
    3. Sandra Stanković & Saša Živić & Aleksandra Ignjatović & Mariola Stojanović & Dragan Bogdanović & Sonja Novak & Jelena Vučić & Miodrag Stanković & Ljiljana Šaranac & Cvetković Vesna & Predrag Miljković, 2016. "Comparison of weight and length at birth of non-Roma and Roma newborn in Serbia," International Journal of Public Health, Springer;Swiss School of Public Health (SSPH+), vol. 61(1), pages 69-73, January.
    4. Melissa Gladstone & Gillian Lancaster & Gareth McCray & Vanessa Cavallera & Claudia R. L. Alves & Limbika Maliwichi & Muneera A. Rasheed & Tarun Dua & Magdalena Janus & Patricia Kariger, 2021. "Validation of the Infant and Young Child Development (IYCD) Indicators in Three Countries: Brazil, Malawi and Pakistan," IJERPH, MDPI, vol. 18(11), pages 1-19, June.
    5. Marc Hallin & Zudi Lu & Davy Paindaveine & Miroslav Siman, 2012. "Local Constant and Local Bilinear Multiple-Output Quantile Regression," Working Papers ECARES ECARES 2012-003, ULB -- Universite Libre de Bruxelles.
    6. John Komlos & Marek Brabec, 2010. "The Trend of BMI Values by Centiles of US Adults, Birth Cohorts 1882-1986," CESifo Working Paper Series 3132, CESifo.
    7. V. Chernozhukov & I. Fernández-Val & A. Galichon, 2009. "Improving point and interval estimators of monotone functions by rearrangement," Biometrika, Biometrika Trust, vol. 96(3), pages 559-575.
    8. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    9. George Vamvakas & Courtenay Frazier Norbury & Silia Vitoratou & Debbie Gooch & Andrew Pickles, 2019. "Standardizing test scores for a target population: The LMS method illustrated using language measures from the SCALES project," PLOS ONE, Public Library of Science, vol. 14(3), pages 1-17, March.
    10. He, Yaoyao & Zheng, Yaya, 2018. "Short-term power load probability density forecasting based on Yeo-Johnson transformation quantile regression and Gaussian kernel function," Energy, Elsevier, vol. 154(C), pages 143-156.
    11. Songhao Wang & Szu Hui Ng & William Benjamin Haskell, 2022. "A Multilevel Simulation Optimization Approach for Quantile Functions," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 569-585, January.
    12. Zhang, Linwan & Wu, Weixing & Wei, Ying & Pan, Rulu, 2015. "Stock holdings over the life cycle: Who hesitates to join the market?," Economic Systems, Elsevier, vol. 39(3), pages 423-438.
    13. Bosch, Ronald J. & Ye, Yinyu & Woodworth, George G., 1995. "A convergent algorithm for quantile regression with smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 19(6), pages 613-630, June.
    14. Y. Andriyana & I. Gijbels & A. Verhasselt, 2018. "Quantile regression in varying-coefficient models: non-crossing quantile curves and heteroscedasticity," Statistical Papers, Springer, vol. 59(4), pages 1589-1621, December.
    15. T. J. Cole, 2022. "A celebration of Harvey Goldstein’s lifetime contributions: Harvey Goldstein and his time at the Institute of Child Health," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 748-752, July.
    16. Angela Noufaily & M. C. Jones, 2013. "Parametric quantile regression based on the generalized gamma distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(5), pages 723-740, November.
    17. Tarozzi, Alessandro, 2008. "Growth reference charts and the nutritional status of Indian children," Economics & Human Biology, Elsevier, vol. 6(3), pages 455-468, December.
    18. N. Salvati & N. Tzavidis & M. Pratesi & R. Chambers, 2012. "Small area estimation via M-quantile geographically weighted regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 1-28, March.
    19. Jayabrata Biswas & Hemant Kulkarni & Kiranmoy Das, 2017. "Quantile Regression in Biostatistics," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 2(5), pages 102-105, August.
    20. Gannoun, Ali & Girard, Stephane & Guinot, Christiane & Saracco, Jerome, 2004. "Sliced inverse regression in reference curves estimation," Computational Statistics & Data Analysis, Elsevier, vol. 46(1), pages 103-122, May.
    21. John Komlos & Marek Brabec, 2010. "The Trend of BMI Values of US Adults by Centiles, birth cohorts 1882-1986," NBER Working Papers 16252, National Bureau of Economic Research, Inc.

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