The analysis of repeated 'direct' measures of change illustrated with an application in longitudinal imaging

The use of repeated measures of an outcome variable to improve statistical power and precision in randomized clinical trials and cohort studies is well documented. Linear mixed models have great utility in the analysis of such studies in many medical applications including imaging. However, in imaging studies and other applications the basic outcome can be a 'direct' measure of change in a variable, as opposed to a difference calculated by subtraction of one measured value from another. The correlation structure of such repeated measures of 'direct' change, in particular the non-independence of within-person consecutive measures, adds complexity to the analysis. In this paper, we present a family of hierarchical mixed models for the analysis of such data and explain how to implement them using standard statistical software. We illustrate the use of our models with data from a cohort of patients with Alzheimer's disease.