It is often necessary to differentiate subjects from multiple categories using medical tests. We may then adopt statistical measures to characterize the performance of these tests. The three-way ROC analysis has been proposed to evaluate the diagnostic accuracy of medical tests with three categories, reflecting the correct classification probabilities across all possible decision thresholds. The geometry of the ROC surface is carefully studied, leading to numerical summary measures such as the volume under the surface. This paper generalizes the global volume under the surface of three-way ROC analysis to the weighted volume under the surface (WVUS) by introducing a weight function emphasizing particular regions of correct classification probabilities. This generalization practically allows researchers to calculate the diagnostic accuracy for a medical or clinical biomarker while satisfactorily high probabilities of correct classification for one or two classes are conditionally ensured. We provide the asymptotic properties of the proposed nonparametric and parametric estimators of WVUS, which could easily lend support to statistical inferences. Some simulations have been conducted to assess the proposed estimators and also to demonstrate the necessity of WVUS. A real data analysis about liver cancer illustrates our methodology.

Ordered multiple categorical (MC) variable has been widely considered and studied as response variable, and few studies have carefully considered it as a predictor in linear regression. When doing this, the existence of some pseudo-categories may result in overfitting, and to detect those pseudo-categories by hypothesis test of all dummy variables might have low specificity. In this paper, we propose a transformation method of dummy variables for such ordered MC predictors, after which a model selection method combined with BIC will be elaborated. Theoretical consistency of our model selection method is established under some common assumptions. Both simulation studies and real data analysis of a medical survey indicate that our method provides good performance and is applicable to a wide range of biomedical research.

Discovering a medication that suitable for all patients is not possible due to the fact that the reaction to medication may differ significantly across different patient subgroups. The heterogeneity of treatment effects is central to the agenda for both personalized medicine and treatment selection. To expedite the development of tailored therapies and improve the treatment efficacy, identification of subgroups that exhibit different treatment effects is thus playing an essential role. In this paper, we consider high-dimensional dense longitudinal observations which have frequent and large number of measurements with high-dimensional covariates. We offer a data-driven subgroup identification method, which incorporates the sparse boosting algorithm into homogeneity pursuit via change point detection. Extensive simulations are carried out to examine the performance of our proposed approach. We further illustrate our method by analyzing a wallaby growth dataset.