Longitudinal multivariate normative comparisons.

Motivated by the Multicenter AIDS Cohort Study (MACS), we develop classification procedures for cognitive impairment based on longitudinal measures. To control family-wise error, we adapt the cross-sectional multivariate normative comparisons (MNC) method to the longitudinal setting. The cross-sectional MNC was proposed to control family-wise error by measuring the distance between multiple domain scores of a participant and the norms of healthy controls and specifically accounting for intercorrelations among all domain scores. However, in a longitudinal setting where domain scores are recorded multiple times, applying the cross-sectional MNC at each visit will still have inflated family-wise error rate due to multiple testing over repeated visits. Thus, we propose longitudinal MNC procedures that are constructed based on multivariate mixed effects models. A χ2 test procedure is adapted from the cross-sectional MNC to classify impairment on longitudinal multivariate normal data. Meanwhile, a permutation procedure is proposed to handle skewed data. Through simulations we show that our methods can effectively control family-wise error at a predetermined level. A dataset from a neuropsychological substudy of the MACS is used to illustrate the applications of our proposed classification procedures.