Empirical Bayes estimation of individual growth-curve parameters and their relationship to covariates

The analysis of growth curves has long been important in biostatistics. Work has focused on two problems: the estimation of individual curves based on many data points, and the estimation of the mean growth curve for a group of individuals. This paper extends a recent approach that seeks to combine data from a group of individuals in order to improve the estimates of individual growth parameters. Growth is modeled as polynomial in time, and the group model is also linear, incorporating growth-related covariates into the model. The estimation used is empirical Bayes. The estimation formulas are illustrated with a set of data on rat growth, originally presented by Box (1950, Biometrics 6, 362-389).