Classifying individuals based on predictors of random effects. Multicenter AIDS Cohort Study.

Often one wishes to describe individuals according to whether their average exposure over a period of time is above or below some meaningful threshold. In this article, we treat predictors of random effects as diagnostic tools to aid in such classification, given that the true unobservable mean exposure for each of a set of individuals is defined according to a mixed linear model. Viewing candidate predictors in this light engenders the consideration of a unique set of performance criteria, and invites the use of nomenclature commonly used by epidemiologists and decision analysts to evaluate diagnostic techniques. We describe these criteria analytically and graphically under a random effects analysis of variance model, with the expressed goal of classifying subjects with regard to their true mean. Given knowledge of the model parameters, we compare typical predictors and illustrate the fact that completely new alternatives can arise depending on the particular set of criteria emphasized. We include a brief simulation study in which we also compare prediction methods according to various classification criteria, after incorporating estimates of the unknown model parameters. We provide two examples using data from participants in the Multicenter AIDS Cohort Study. In the first example, we seek to classify HIV seronegative individuals based on their mean diastolic blood pressure. In the second, via a natural extension to a randomized regression model, we classify HIV seropositive individuals according to their CD4+ slope over time.