Methodological study demonstrates penalized likelihood cubic spline smoothing for LMS curves across human growth data, highlighting an effective way to construct clinical reference percentiles.
Refence centile curves show the distribution of a measurement as it changes according to some covariate, often age. The LMS method summarizes the changing distribution by three curves representing the median, coefficient of variation and skewness, the latter expressed as a Box-Cox power. Using penalized likelihood the three curves can be fitted as cubic splines by non-linear regression, and the extent of smoothing required can be expressed in terms of smoothing parameters or equivalent degrees of freedom. The method is illustrated with data on triceps skinfold in Gambian girls and women, and body weight in U.S.A. girls.
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Cole et al. (1992) studied this question.
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