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 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.

Dynamic impairment classification through arrayed comparisons

“…Before identifying cognitive impairment prospectively, we assume that relevant population normative data are available. Following the notation from Wang et al, 6 $$$ n $$$ participants enrolled in a healthy reference group and were evaluated on $$$ q $$$ cognitive domains over $$$ {m}_i $$$ assessments. Cognitive domain $$$ j $$$ is measured as $$$ {Y}_{ijk},i=1,\dots, n;j=1,\dots, q;k=1,\dots, {m}_i $$$ for participant $$$ i $$$ at $$$ k $$$th assessment.…”

“…Under the multivariate normal assumption on the $$$ q $$$ longitudinal cognitive functioning scores, Wang et al 6 proposed a LMNC test statistic for participant $$$ d $$$ at assessment $$$ \omega $$$ as $$$$ {G}_{\omega}^d={\left({\boldsymbol{U}}_{\omega}^d-{\hat{\boldsymbol{\mu}}}_{\omega}^d\right)}^{\intercal }{\left({\hat{\boldsymbol{\varPsi}}}_{\omega}^d\right)}^{-1}\left({\boldsymbol{U}}_{\omega}^d-{\hat{\boldsymbol{\mu}}}_{\omega}^d\right)\sim {\chi}_{q\omega}^2,\kern1em \omega =1,\dots, {m}_d, $$$$ and used it to classify prior impairment status on retrospectively collected data. In order to identify cognitive impairment at each assessment $$$ \omega $$$, we create DAC test statistics as the difference between two consecutive LMNC test statistics and set $$$ {S}_{\omega}^d={G}_{\omega}^d-{G}_{\omega -1}^d $$$ for $$$ 2\le \omega \le {m}_d $$$ and …”

“…Su et al 4 and Wang et al 5 have studied and demonstrated the effectiveness of the MNC with cross‐sectional neuropsychological data collected among persons infected with HIV. Wang et al 6 further extended the MNC method from cross‐sectional data to historically collected longitudinal data and proposed a longitudinal multivariate normative comparison (LMNC) method by modeling multiple neuropsychological scores with a multivariate linear mixed effects (MLME) model. Correlations among different brain domains and across all assessments within the same participant are explicitly considered within the model.…”

“…For research purposes, we often carry out analyses after all necessary information has been collected and then examine the data retrospectively. Thus, the static longitudinal MNC method in Wang et al 6 is adequate for providing classification of prior cognitive impairment with proper control of family‐wise error. In clinical practice, this is probably not sufficient, particularly when treatment should be prescribed in the early stage of cognitive decline.…”

Legacy effect on neuropsychological function in HIV-infected men on combination antiretroviral therapy

“…The MNC provides an overall metric of distance between each of an individual's multiple domain scores and the corresponding norms of healthy controls and this adjusts the family-wise error (and false positive errors) in a way that the Frascati and Gisslen methods cannot [23][24][25]. We have used this cross-sectional method in the MACS cohort [22], and also developed a longitudinal application of the MNC [26] with the same effectiveness at controlling the Family-Wise Error Rate. In this paper, we use MNC method to determine neuropsychological impairment and set the family-wise error rate at 0.05.…”