Dynamic impairment classification through arrayed comparisons

The multivariate normative comparison (MNC) method has been used for identifying cognitive impairment. When participants' cognitive brain domains are evaluated regularly, the longitudinal MNC (LMNC) has been introduced to correct for the intercorrelation among repeated assessments of multiple cognitive domains in the same participant. However, it may not be practical to wait until the end of study for diagnosis. For example, in participants of the Multicenter AIDS Cohort Study (MACS), cognitive functioning has been evaluated repeatedly for more than 35 years. Therefore, it is optimal to identify cognitive impairment at each assessment, while the family-wise error rate (FWER) is controlled with unknown number of assessments in future. In this work, we propose to use the difference of consecutive LMNC test statistics to construct independent tests. Frequency modeling can help predict how many assessments each participant will have, so Bonferroni-type correction can be easily adapted. A chi-squared test is used under the assumption of multivariate normality, and permutation test is proposed where this assumption is violated. We showed through simulation and the MACS data that our method controlled FWER below a predetermined level.