Longitudinal multivariate normative comparisons

Abstract

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 ${\chi }^2$ 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.

Keywords: cognitive impairment; false discovery rate; family-wise error rate; longitudinal analysis; multivariate mixed-effect model.

FIGURE 1

The longitudinal multivariate normative comparison χ² test when data follow multivariate normal distribution

FIGURE 2

The longitudinal multivariate normative comparison χ² and permutation tests; the upper panel is when data follow multivariate t distributions (permutation test when df = 5 overlapped with the nominal α line); the bottom panel is when data are transformed from Gamma distributions

FIGURE 3

The longitudinal multivariate normative comparison χ² test and permutation test using multivariate t data when testing group has different visit frequencies

FIGURE 4

The longitudinal multivariate normative comparison (LMNC) χ² test and permutation test with different sample sizes under multivariate normality (left); the LMNC permutation test with different sample sizes and visit frequencies using multivariate t data (right); α = 0.05 represented as the horizontal dashed line

FIGURE 5

Q-Q plot of baseline motor score in the seronegative group and visit frequencies of two serostatus groups

FIGURE 6

Comparing proportion of cognitive impairment in seronegative and seropositive groups in the Multicenter AIDS Cohort Study