Computation of hypervolume under ROC manifold (HUM) is necessary to evaluate biomarkers for their capability to discriminate among multiple disease types or diagnostic groups. However the original definition of HUM involves multiple integration and thus a medical investigation for multi-class receiver operating characteristic (ROC) analysis could suffer from huge computational cost when the formula is implemented naively. We introduce a novel graph-based approach to compute HUM efficiently in this article. The computational method avoids the time-consuming multiple summation when sample size or the number of categories is large. We conduct extensive simulation studies to demonstrate the improvement of our method over existing R packages. We apply our method to two real biomedical data sets to illustrate its application.

Ischemic stroke (IS) is often comorbid with type 2 diabetes mellitus (T2DM) wherein the determinants of long-term outcomes, beyond the acute stroke phase, are not adequately known. This study identified the determinants of long-term outcomes for diabetic IS patients through a prospective nested case-control study in 624 patients treated with conservative measures (38.60% females, mean age: 63.85 years). After 36-month follow-up, 117 (18.8%) patients with poor outcome were enrolled in the case group. The poor outcome was defined with a modified Rankin Scale (mRS) score ≥3. Meanwhile, 374 (59.9%) patients with good outcome, defined as (mRS score <3), were included in the control group. Patients who died (n = 32) or lost to follow-up (n = 101) were excluded in analysis. Poor prognostic outcome was positively associated with (1) the pulse rate at admission, (2) diastolic blood pressure (DBP), and (3) fasting blood glucose (FBG) during follow-up, whereas physical activity and lipid-lowering treatment during follow-up were negatively associated. Importantly, a forecasting model with these indicators distinguished the patients with good versus poor outcomes with 70.1% sensitivity and 73.5% specificity. Health care professionals and laboratory medicine scholars may want to monitor an increase in DBP and FBG during follow-up, as well as physical activity and lipid-lowering treatment, in relationship to the prognosis of IS with comorbid T2DM after conservative therapies. The proposed predictive model for personalized/precision medicine requires field testing in independent studies, and might help risk stratification with theranostic tests for patients with acute IS who also have a diagnosis of T2DM.

In prognosis studies to evaluate association between a continuous biomarker and a survival outcome, investigators often classify subjects into two subclasses of the high- and low-expression groups and apply simple survival analysis techniques of the Kaplan-Meier method and the logrank test. The high- and low-expressions are defined according to whether or not the observation of the biomarker is higher than the cut-off value, which is heterogeneous across studies. The heterogeneous definitions of the cut-off value make it difficult to apply the standard meta-analysis techniques. We propose a method to estimate the concordance index for a survival outcome synthesizing published prognosis studies, in which the Kaplan-Meier estimates for the high- and low-expression groups are reported. We illustrate our proposed method with a real dataset for meta-analysis of prognosis studies evaluating Ki-67 in early breast cancer and evaluate its performance with a simulation study.

We respond here on a recent letter in this journal, on the transformation based on likelihood ratio.

We propose a non-monotone transformation to biomarkers in order to improve the diagnostic and screening accuracy. The proposed quadratic transformation only involves modeling the distribution means and variances of the biomarkers and is therefore easy to implement in practice. Mathematical justification was rigorously established to support the validity of the proposed transformation. We conducted extensive simulation studies to assess the performance of the proposed method and compared the new method with the traditional methods. Case studies on real biomedical and epigenetics data were provided to illustrate the proposed transformation. In particular, the proposed method improved the AUC values for a large number of markers in a DNA methylation study and consequently led to the identification of greater number of important biomarkers and biologically meaningful genetic pathways.

Chronic hepatitis B (CHB) is a major global health burden. Liver fibrosis, an insidious process, is the main histopathological change in CHB that might lead to the end-stage liver disease if left untreated. The intermediate liver fibrosis (S2) is the optimal time to start antiviral therapy. The aim of the present study was to examine the proteomic changes in patients with CHB at different fibrotic stages, with a view to identify future serum biomarkers for S2. Ninety CHB patients were grouped into mild (S0-1), intermediate (S2), and severe liver fibrosis (S3-4) (61 men and 29 women; age 25-63 years). Isobaric tagging for relative and absolute quantitation was applied to screen proteins differentially expressed among the patient groups. Another 46 patients with CHB (age 25-59 years; 31 men and 15 women), and 16 healthy controls (age 26-61 years; 11 men and 5 women) were enrolled in a validation group. Enzyme-linked immunosorbent assay was used to verify the diagnostic value of the candidate biomarkers. We found 139 proteins that were differentially expressed between various fibrotic stage-paired comparisons. Five protein candidates were selected as potential biomarkers of S2 for further verification. Notably, ficolin-2 (FCN2) and carboxypeptidase B2 (CPB2) showed differential expression between patients and healthy controls. In conclusion, serum proteomic changes reported here offer new molecular leads for future research on biomarker candidates to identify liver fibrotic stages in CHB. In particular, FCN2 and CPB2 warrant further research on their possible mechanistic involvement in CHB pathogenesis.

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.

Networked 21st century society, globalization, and communications technologies are paralleled by the rise of electromagnetic energy intensity in our environments and the growing pressure of the environtome on human biology and health. The latter is the entire complement of environmental factors, including the electromagnetic energy and the technologies that generate them, enacting on the digital citizen in the new century. Electromagnetic pulse (EMP) irradiation might have serious damaging effects not only on electronic equipment but also in the whole organism and reproductive health, through nonthermal effects and oxidative stress. We sought to determine whether EMP exposure (1) induces biological damage on reproductive health and (2) the extent to which selenium-rich Cordyceps fungi (daily coadministration) offer protection on the testicles and spermatozoa. In a preclinical randomized study, 3-week-old male BALB/c mice were repeatedly exposed to EMP (peak intensity 200 kV/m, pulse edge 3.5 ns, pulse width 15 ns, 0.1 Hz, and 400 pulses/day) 5 days per week for four consecutive weeks, with or without coadministration of daily selenium-rich Cordyceps fungi (100 mg/kg). Testicular index and spermatozoa formation were measured at baseline and 1, 7, 14, 28, and 60 day time points after EMP exposure. The group without Cordyceps cotreatment displayed decreased spermatozoa formation, shrunk seminiferous tubule diameters, and diminished antioxidative capacity at 28 and 60 days after exposure (p < 0.05). The Cordyceps daily cotreatment alleviated the testicular damage by EMP exposure, increased spermatozoa formation, and reduced apoptotic spermatogenic cells. These observations warrant further preclinical and clinical studies as an innovative approach for potential protection against electromagnetic radiation in the current age of networked society and digital citizenship.

Polytomous discrimination index is a novel and important diagnostic accuracy measure for multi-category classification. After reconstructing its probabilistic definition, we propose a nonparametric approach to the estimation of polytomous discrimination index based on an empirical sample of biomarker values. In this paper, we provide the finite-sample and asymptotic properties of the proposed estimators and such analytic results may facilitate the statistical inference. Simulation studies are performed to examine the performance of the nonparametric estimators. Two real data examples are analysed to illustrate our methodology.

Diagnostic tests are often compared in multi-reader multi-case (MRMC) studies in which a number of cases (subjects with or without the disease in question) are examined by several readers using all tests to be compared. One of the commonly used methods for analyzing MRMC data is the Obuchowski-Rockette (OR) method, which assumes that the true area under the receiver operating characteristic curve (AUC) for each combination of reader and test follows a linear mixed model with fixed effects for test and random effects for reader and the reader-test interaction. This article proposes generalized linear mixed models which generalize the OR model by incorporating a range-appropriate link function that constrains the true AUCs to the unit interval. The proposed models can be estimated by maximizing a pseudo-likelihood based on the approximate normality of AUC estimates. A Monte Carlo expectation-maximization algorithm can be used to maximize the pseudo-likelihood, and a non-parametric bootstrap procedure can be used for inference. The proposed method is evaluated in a simulation study and applied to an MRMC study of breast cancer detection.