Fitting Smoothed Centile Curves to Reference Data

SUMMARY 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 ̂λ i assuming normality are estimated for each group i. Corresponding estimates for the generalized mean and coefficient of variation ̂μ i and ̂σ i are also obtained. The ̂λ i , ̂μ i and ̂σ i plotted against t i are fitted by smooth curves L ( t ), M ( t ) and S ( t ) respectively, which together define a smooth curve for the 100αth centile given byC 100 α ( t ) = M ( t ) [ 1 + L ( t ) S ( t ) z α ] 1 / L ( t ) ,where z α 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.