Fitting Smoothed Centile Curves to Reference Data

T. J. Cole

Journal of the Royal Statistical Society Series A, 1988, vol. 151, issue 3, 385-406

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.

Date: 1988
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