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Summary The net reclassification improvement (NRI) and the integrated discrimination improvement (IDI) were originally proposed to characterize accuracy improvement in predicting a binary outcome, when new biomarkers are added to regression models. These two indices have been extended from binary outcomes to multi-categorical and survival outcomes. Working on an AIDS study where the onset of cognitive impairment is competing risk censored by death, we extend the NRI and the IDI to competing risk outcomes, by using cumulative incidence functions to quantify cumulative risks of competing events, and adopting the definitions of the two indices for multi-category outcomes. The “missing” category due to independent censoring is handled through inverse probability weighting. Various competing risk models are considered, such as the Fine and Gray, multistate, and multinomial logistic models. Estimation methods for the NRI and the IDI from competing risk data are presented. The inference for the NRI is constructed based on asymptotic normality of its estimator, and the bias-corrected and accelerated bootstrap procedure is used for the IDI. Simulations demonstrate that the proposed inferential procedures perform very well. The Multicenter AIDS Cohort Study is used to illustrate the practical utility of the extended NRI and IDI for competing risk outcomes. 

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.