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Semiparametric estimation of regression quantiles with application to standardizing weight for height and age in US children

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  • P. J. Heagerty
  • M. S. Pepe

Abstract

The appropriate interpretation of measurements often requires standardization for concomitant factors. For example, standardization of weight for both height and age is important in obesity research and in failure‐to‐thrive research in children. Regression quantiles from a reference population afford one intuitive and popular approach to standardization. Current methods for the estimation of regression quantiles can be classified as nonparametric with respect to distributional assumptions or as fully parametric. We propose a semiparametric method where we model the mean and variance as flexible regression spline functions and allow the unspecified distribution to vary smoothly as a function of covariates. Similarly to Cole and Green, our approach provides separate estimates and summaries for location, scale and distribution. However, similarly to Koenker and Bassett, we do not assume any parametric form for the distribution. Estimation for either cross‐sectional or longitudinal samples is obtained by using estimating equations for the location and scale functions and through local kernel smoothing of the empirical distribution function for standardized residuals. Using this technique with data on weight, height and age for females under 3 years of age, we find that there is a close relationship between quantiles of weight for height and age and quantiles of body mass index (BMI=weight/height2) for age in this cohort.

Suggested Citation

  • P. J. Heagerty & M. S. Pepe, 1999. "Semiparametric estimation of regression quantiles with application to standardizing weight for height and age in US children," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(4), pages 533-551.
    • Handle: RePEc:bla:jorssc:v:48:y:1999:i:4:p:533-551
    DOI: 10.1111/1467-9876.00170
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    Cited by:

    1. Yingye Zheng & Patrick J. Heagerty, 2007. "Prospective Accuracy for Longitudinal Markers," Biometrics, The International Biometric Society, vol. 63(2), pages 332-341, June.
    2. Lori E. Dodd & Margaret S. Pepe, 2003. "Partial AUC Estimation and Regression," Biometrics, The International Biometric Society, vol. 59(3), pages 614-623, September.
    3. Tianxi Cai & Yingye Zheng, 2007. "Model Checking for ROC Regression Analysis," Biometrics, The International Biometric Society, vol. 63(1), pages 152-163, March.
    4. Margaret Sullivan Pepe & Tianxi Cai, 2004. "The Analysis of Placement Values for Evaluating Discriminatory Measures," Biometrics, The International Biometric Society, vol. 60(2), pages 528-535, June.
    5. Margaret Sullivan Pepe, 2000. "An Interpretation for the ROC Curve and Inference Using GLM Procedures," Biometrics, The International Biometric Society, vol. 56(2), pages 352-359, June.
    6. Hemant Kulkarni & Jayabrata Biswas & Kiranmoy Das, 2019. "A joint quantile regression model for multiple longitudinal outcomes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(4), pages 453-473, December.
    7. Holly Janes & Gary Longton & Margaret S. Pepe, 2009. "Accommodating covariates in receiver operating characteristic analysis," Stata Journal, StataCorp LP, vol. 9(1), pages 17-39, March.
    8. Ying Huang & Margaret Sullivan Pepe & Ziding Feng, 2007. "Evaluating the Predictiveness of a Continuous Marker," Biometrics, The International Biometric Society, vol. 63(4), pages 1181-1188, December.
    9. Isabelle Charlier & Davy Paindaveine, 2014. "Conditional Quantile Estimation through Optimal Quantization," Working Papers ECARES ECARES 2014-28, ULB -- Universite Libre de Bruxelles.
    10. Y. Huang & M. S. Pepe, 2010. "Semiparametric methods for evaluating the covariate‐specific predictiveness of continuous markers in matched case–control studies," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(3), pages 437-456, May.
    11. Yingye Zheng & Tianxi Cai & Yuying Jin & Ziding Feng, 2012. "Evaluating Prognostic Accuracy of Biomarkers under Competing Risk," Biometrics, The International Biometric Society, vol. 68(2), pages 388-396, June.
    12. Ziyi Li & Yijian Huang & Dattatraya Patil & Martin G. Sanda, 2023. "Covariate adjustment in continuous biomarker assessment," Biometrics, The International Biometric Society, vol. 79(1), pages 39-48, March.
    13. Ilaria Lucrezia Amerise, 2013. "Weighted Non-Crossing Quantile Regressions," Working Papers 201308, Università della Calabria, Dipartimento di Economia, Statistica e Finanza "Giovanni Anania" - DESF.
    14. Jooyong Shim & Changha Hwang & Kyungha Seok, 2016. "Support vector quantile regression with varying coefficients," Computational Statistics, Springer, vol. 31(3), pages 1015-1030, September.
    15. Jooyong Shim & Changha Hwang & Kyungha Seok, 2014. "Composite support vector quantile regression estimation," Computational Statistics, Springer, vol. 29(6), pages 1651-1665, December.
    16. Ying Huang & Peter B. Gilbert, 2011. "Comparing Biomarkers as Principal Surrogate Endpoints," Biometrics, The International Biometric Society, vol. 67(4), pages 1442-1451, December.
    17. Yingye Zheng & Tianxi Cai & Janet L. Stanford & Ziding Feng, 2010. "Semiparametric Models of Time-Dependent Predictive Values of Prognostic Biomarkers," Biometrics, The International Biometric Society, vol. 66(1), pages 50-60, March.
    18. Jayabrata Biswas & Kiranmoy Das, 2021. "A Bayesian quantile regression approach to multivariate semi-continuous longitudinal data," Computational Statistics, Springer, vol. 36(1), pages 241-260, March.
    19. Ying Yuan & Guosheng Yin, 2010. "Bayesian Quantile Regression for Longitudinal Studies with Nonignorable Missing Data," Biometrics, The International Biometric Society, vol. 66(1), pages 105-114, March.
    20. Muhammad Amin & Lixin Song & Milton Abdul Thorlie & Xiaoguang Wang, 2015. "SCAD-penalized quantile regression for high-dimensional data analysis and variable selection," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(3), pages 212-235, August.
    21. Holly Janes & Margaret S. Pepe, 2008. "Matching in Studies of Classification Accuracy: Implications for Analysis, Efficiency, and Assessment of Incremental Value," Biometrics, The International Biometric Society, vol. 64(1), pages 1-9, March.

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