On the problem of optimal inference for time heterogeneous data with error components regression structure

Abstract

Time heterogeneity, or the fact that subjects are measured at different times, occurs frequently in non-experimental situations. For time heterogeneous data having error components regression structure it is demonstrated that under customary normality assumptions there is no estimation method based on Maximum Likelihood, Least Squares, Within-subject or Between-subject comparisons that is generally superior when estimating the slope of the regression line. However, in some situations it is possible to give guidelines for the choice of an optimal procedure. These are expressed in terms of the variability of the times for the measurements and also of the inter-subject correlation. The results are demonstrated on data from a longitudinal medical study.