Calculating centile curves using kernel density estimation methods with application to infant kidney lengths

Observing a clinical measurement for an individual is of little value, unless it can be compared with measurements obtained from a healthy population, thought of as standard. The range of measurements observed will, in general, vary with age or some function of time. The usual approach is to assume a distributional form for the population density, but this is inappropriate for variables which do not follow a simple distribution. A method of estimating the centiles of a conditional distribution using multi-dimensional kernel density estimation, to allow conditioning on the value of one or more covariates, is proposed. By careful choice of the kernel used, the percentiles may easily be calculated using a Newton-Raphson procedure. The method is illustrated using kidney lengths and birthweights of a sample of newborn infants.