Maximum likelihood estimation of reference centiles
We propose the use of centile estimates which are based on the fitting of appropriate densities by maximum likelihood. In the case of cross-sectional centile estimation, we show that this approach will generally lead to more precise estimates than would result from the use of non-parametric centile estimates. When longitudinal data are available or a series of cross-sectional data at different time points, the maximum likelihood approach can be used to simultaneously fit densities to each cross-section, subject to constraints (for example, smoothness constraints) on the parameters. The variances of these centile estimates are readily obtained and missing values and unequally spaced records are easily accommodated. We illustrate the procedure by means of an application using the Johnson family of densities to a study of weight gain in pregnancy.