A comparison of statistical methods for age-specific reference values of discrete scales

References

• Altman, D., E. Ohuma, I. Fetal, and for the International Fetal and Newborn Growth Consortium for the 21st Century (INTERGROWTH-21st). 2013. Statistical considerations for the development of prescriptive fetal and newborn growth standards in the intergrowth-21st project. BJOG: An International Journal of Obstetrics & Gynaecology 120:71–6. doi:10.1111/1471-0528.12031.
   PubMed Web of Science ®Google Scholar
• Andersen, P. K., and L. T. Skovgaard. 2010. Regression with linear predictors. New York: Springer-Verlag.
   Google Scholar
• Binder, H., W. Sauerbrei, and P. Royston. 2013. Comparison between splines and fractional polynomials for multivariable model building with continuous covariates: A simulation study with continuous response. Statistics in Medicine 32 (13):2262–77. doi:10.1002/sim.5639.
   PubMed Web of Science ®Google Scholar
• Bollaerts, K., P. H. Eilers, and M. Aerts. 2006. Quantile regression with monotonicity restrictions using p-splines and the l1-norm. Statistical Modelling 6 (3):189–207. doi:10.1191/1471082X06st118oa.
   Web of Science ®Google Scholar
• Bondell, H. D., B. J. Reich, and H. Wang. 2010. Noncrossing quantile regression curve estimation. Biometrika 97 (4):825–38. doi:10.1093/biomet/asq048.
   PubMed Web of Science ®Google Scholar
• Borghi, E., M. de Onis, C. Garza, J. Van den Broeck, E. A. Frongillo, L. Grummer-Strawn, S. Van Buuren, H. Pan, L. Molinari, R. Martorell, WHO Multicentre Growth Reference Study Group, et al. 2006. Construction of the world health organization child growth standards: Selection of methods for attained growth curves. Statistics in Medicine 25 (2):247–65. doi:10.1002/sim.2227.
   PubMed Web of Science ®Google Scholar
• Cole, T. J. 2012. The development of growth references and growth charts. Annals of Human Biology 39 (5):382–94. doi:10.3109/03014460.2012.694475.
   PubMed Web of Science ®Google Scholar
• Cole, T. J., and P. J. Green. 1992. Smoothing reference centile curves: The lms method and penalized likelihood. Statistics in Medicine 11 (10):1305–19. doi:10.1002/sim.4780111005.
   PubMed Web of Science ®Google Scholar
• Eilers, P. H. C., and B. D. Marx. 1996. Flexible smoothing with b -splines and penalties. Statistical Science 11 (2):89–121. doi:10.1214/ss/1038425655.
   Web of Science ®Google Scholar
• Fernández, C., and M. F. J. Steel. 1998. On Bayesian modelling of fat tails and skewness. Journal of the American Statistical Association 93 (441):359–71. doi:10.1080/01621459.1998.10474117.
   Web of Science ®Google Scholar
• Geraci, M., and M. Bottai. 2014. Linear quantile mixed models. Statistics and Computing 24 (3):461–79. doi:10.1007/s11222-013-9381-9.
   Web of Science ®Google Scholar
• Heineman, K. R., A. F. Bos, and M. Hadders-Algra. 2008. The Infant Motor Profile: A standardized and qualitative method to assess motor behaviour in infancy. Developmental Medicine & Child Neurology 50 (4):275–82. doi:10.1111/j.1469-8749.2008.02035.x.
   PubMed Web of Science ®Google Scholar
• Heineman, K. R., P. Schendelaar, E. R. Van den Heuvel, and M. Hadders-Algra. 2018. Motor development in infancy is related to cognitive function at 4 years of age. Developmental Medicine and Child Neurology 60 (11):1149–55. doi:10.1111/dmcn.13761.
   PubMed Web of Science ®Google Scholar
• Hossain, A., R. Rigby, M. Stasinopoulos, and M. Enea. 2016. Centile estimation for a proportion response variable. Statistics in Medicine 35 (6):895–904. doi:10.1002/sim.6748.
   PubMed Web of Science ®Google Scholar
• Koenker, R., and K. F. Hallock. 2001. Quantile regression. Journal of Economic Perspectives 15 (4):143–56. doi:10.1257/jep.15.4.143.
   Web of Science ®Google Scholar
• Koenker, R., P. Ng, and S. Portnoy. 1994. Quantile smoothing splines. Biometrika 81 (4):673–80. doi:10.1093/biomet/81.4.673.
   Web of Science ®Google Scholar
• O’Sullivan, F. 1986. A statistical perspective on ill-posed inverse problems. Statistical Science 1 (4):502–18.
   Google Scholar
• O’Sullivan, F. 1988. Fast computation of fully automated log-density and log-hazard estimators. SIAM Journal on Scientific and Statistical Computing 9 (2):363–79. doi:10.1137/0909024.
   Web of Science ®Google Scholar
• Papageorghiou, A. T., E. O. Ohuma, D. G. Altman, T. Todros, L. Cheikh Ismail, A. Lambert, Y. A. Jaffer, E. Bertino, M. G. Gravett, M. Purwar, and for the 21st Century (INTERGROWTH-21st), N. G. C., et al. 2014. International standards for fetal growth based on serial ultrasound measurements: The fetal growth longitudinal study of the intergrowth-21st project. The Lancet 384 (9946):869–79. doi:10.1016/S0140-6736(14)61490-2.
   PubMed Web of Science ®Google Scholar
• R Core Team. 2019. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Rigby, R. A., and D. M. Stasinopoulos. 2004. Smooth centile curves for skew and kurtotic data modelled using the Box-Cox power exponential distribution. Statistics in Medicine 23 (19):3053–76. doi:10.1002/sim.1861.
   PubMed Web of Science ®Google Scholar
• Rigby, R. A., and D. M. Stasinopoulos. 2005. Generalized additive models for location, scale and shape. Journal of the Royal Statistical Society: Series C (Applied Statistics) 54 (3):507–54. doi:10.1111/j.1467-9876.2005.00510.x.
   Web of Science ®Google Scholar
• Rigby, R. A., and D. M. Stasinopoulos. 2006. Using the Box-Cox t distribution in GAMLSS to model skewness and kurtosis. Statistical Modelling 6 (3):209–29. doi:10.1191/1471082X06st122oa.
   Web of Science ®Google Scholar
• Royston, P., and D. G. Altman. 1994. Regression using fractional polynomials of continuous covariates: Parsimonious parametric modelling. Applied Statistics 43 (3):429. doi:10.2307/2986270.
   Web of Science ®Google Scholar
• Royston, P., and D. G. Altman. 1997. Approximating statistical functions by using fractional polynomial regression. Journal of the Royal Statistical Society: Series D (the Statistician) 46 (3):411–22. doi:10.1111/1467-9884.00093.
   Google Scholar
• Royston, P., and W. Sauerbrei. 2008. Multivariable model-building: A pragmatic approach to regression anaylsis based on fractional polynomials for modelling continuous variables, Vol. 777. Chichester, UK: Wiley.
   Google Scholar
• Royston, P., and E. M. Wright. 1998. A method for estimating age-specific reference intervals (“normal ranges”) based on fractional polynomials and exponential transformation. Journal of the Royal Statistical Society: Series A (Statistics in Society) 161 (1):79–101. doi:10.1111/1467-985X.00091.
   Google Scholar
• Ryoo, J. H., T. R. Konold, J. D. Long, V. J. Molfese, and X. Zhou. 2017. Nonlinear growth mixture models with fractional polynomials: An illustration with early childhood mathematics ability. Structural Equation Modeling: A Multidisciplinary Journal 24 (6):897–910. doi:10.1080/10705511.2017.1335206.
   Web of Science ®Google Scholar
• SAS Institute Inc. 2012. Copyright© 2002-2012 SAS and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc., Cary, NC, USA.
   Google Scholar
• Schnabel, S. K., and P. H. Eilers. 2013. Simultaneous estimation of quantile curves using quantile sheets. AStA Advances in Statistical Analysis 97 (1):77–87. doi:10.1007/s10182-012-0198-1.
   Web of Science ®Google Scholar
• Silverwood, R. J., and T. J. Cole. 2007. Statistical methods for constructing gestational age-related reference intervals and centile charts for fetal size. Ultrasound in Obstetrics & Gynecology: The Official Journal of the International Society of Ultrasound in Obstetrics and Gynecology 29 (1):6–13. doi:10.1002/uog.3911.
   PubMed Web of Science ®Google Scholar
• Stasinopoulos, M. D., R. A. Rigby, G. Z. Heller, V. Voudouris, and F. De Bastiani. 2017. Flexible regression and smoothing: Using GAMLSS in R. Boca Raton, FL: Chapman and Hall/CRC.
   Google Scholar
• Tan, Q., Thomassen, M. Hjelmborg, v B. J. Clemmensen, A. Andersen, K. E. Petersen, T. K. McGue, M. Christensen, K. Kruse. and T. A. 2011. A growth curve model with fractional polynomials for analysing incomplete time-course data in microarray gene expression studies. Advances in Bioinformatics 20112011:261514–6.
   PubMedGoogle Scholar
• Tilling, K., C. Macdonald-Wallis, D. A. Lawlor, R. A. Hughes, and L. D. Howe. 2014. Modelling childhood growth using fractional polynomials and linear splines. Annals of Nutrition & Metabolism 65 (2–3):129–38. doi:10.1159/000362695.
   PubMed Web of Science ®Google Scholar
• Wei, Y., and X. He. 2006. Conditional growth charts. The Annals of Statistics 34 (5):2069–131. With discussions and a rejoinder by the authors. doi:10.1214/009053606000000623.
   Google Scholar