Prediction and Creation of Smooth Curves for Temporally Correlated Longitudinal Data

Abstract

This article presents a method of obtaining smoothed curves for a sample of individuals that permits an arbitrary number and spacing of observations for each individual. We consider the case where each individual's curve cannot be separately estimated because either the n _i 's are too small or no suitable parametric forms for the random effects are available. The model assumes a parametric form for the population mean curve and the correlation of the repeated measures. The assumed correlation structure is evaluated using the empirical semivariogram, a function of the sum of the squared differences of within-individual residuals. A method is proposed to validate the form and stationarity of the correlation structure. Maximum likelihood estimates for the population mean parameters and variance components are obtained simultaneously. These estimates may be used to create a semiparametric differentiable curve and to predict future values for each individual using a method called kriging. This method also yields instantaneous estimates of growth velocity. An example of this method is presented, and connections to kriging are discussed.

Key Words:

• Growth curves
• Growth velocity
• Kriging
• Semi-variogram