Simultaneous control on true positive rate (TPR) and false positive rate (FPR) is of significant importance in the performance evaluation of diagnostic tests. Most of the established literature utilizes partial area under the receiver operating characteristic (ROC) curve with restrictions only on FPR, called FPR pAUC, as a performance measure. However, its indirect control on TPR is conceptually and practically misleading. In this paper, a novel and intuitive performance measure, named as two-way pAUC, is proposed, which directly quantifies partial area under the ROC curve with explicit restrictions on both TPR and FPR. To estimate twoway pAUC, we devise a nonparametric estimator. Based on the estimator, a bootstrap-assisted testing method for two-way pAUC comparison is established. Moreover, to evaluate possible covariate effects on two-way pAUC, a regression analysis framework is constructed. Asymptotic normalities of the methods are provided. Advantages of the proposed methods are illustrated by simulation and Wisconsin Breast Cancer Data. We encode the methods as a publicly available R package tpAUC.

We consider the estimation and inference of graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we assume the data follow a tensor normal distribution whose covariance has a Kronecker product structure. A critical challenge in the estimation and inference of this model is the fact that its penalized maximum likelihood estimation involves minimizing a non-convex objective function. To address it, this paper makes two contributions: (i) In spite of the non-convexity of this estimation problem, we prove that an alternating minimization algorithm, which iteratively estimates each sparse precision matrix while fixing the others, attains an estimator with an optimal statistical rate of convergence. (ii) We propose a de-biased statistical inference procedure for testing hypotheses on the true support of the sparse precision matrices, and employ it for testing a growing number of hypothesis with false discovery rate (FDR) control. The asymptotic normality of our test statistic and the consistency of FDR control procedure are established. Our theoretical results are backed up by thorough numerical studies and our real applications on neuroimaging studies of Autism spectrum disorder and users' advertising click analysis bring new scientific findings and business insights. The proposed methods are encoded into a publicly available R package Tlasso.

Hepatitis B virus (HBV) infection is a major risk factor for the development of hepatocellular carcinoma (HCC) in China. At present, there still are 9.3 million chronic HBV-infected Chinese. Numerous studies have explored the association between possible factors and hepatocellular carcinoma risk, however, the results remains inconsistent. Therefore, we did this pooled analysis so as to get a precise result. Here, we took the chronic HBV-infected Chinese as the object. We systematically searched for studies evaluating whether the proposed factors changed HCC risk in PubMed, Chinese National Knowledge Infrastructure, VIP database and Wanfang data. Odds ratios (OR) with 95% confidence intervals (CI) were calculated by Review Manager 5.0 and publication bias was determined by Begg’s test and Egger’s test. In total, 3165 cases and 10,896 controls from 27 studies were included in this meta-analysis. Our results showed that pooled OR with 95% CI for each of the factors investigated were: non-antiviral treatment 2.70 (2.01, 3.62), high HBV DNA levels 2.61 (1.73, 3.94), alcohol consumption 2.19 (1.53, 3.13), a family history of HCC 3.58 (2.53, 5.06) and male gender 2.14 (1.68, 2.73), respectively. Our meta-analysis supports that high HBV DNA levels, non-antiviral treatment, alcohol consumption, a family history of HCC and male gender contributed to the risk of hepatocellular carcinoma in chronic HBV-infected Chinese from currently available evidence. Given the high prevalence of the non-antiviral treatment and alcohol drinking, behavior interventions for the two factors should be tackled first.

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