Two-Sample Tests Based on Data Depth.

In this paper, we focus on the homogeneity test that evaluates whether two multivariate samples come from the same distribution. This problem arises naturally in various applications, and there are many methods available in the literature. Based on data depth, several tests have been proposed for this problem but they may not be very powerful. In light of the recent development of data depth as an important measure in quality assurance, we propose two new test statistics for the multivariate two-sample homogeneity test. The proposed test statistics have the same χ2(1) asymptotic null distribution. The generalization of the proposed tests into the multivariate multisample situation is discussed as well. Simulations studies demonstrate the superior performance of the proposed tests. The test procedure is illustrated through two real data examples.

EM-test for homogeneity in a two-sample problem with a mixture structure.

In many applications such as case-control studies with contaminated controls, or the test of a treatment effect in the presence of nonresponders in biological experiments or clinical trials, a two-sample problem with one of the samples having a mixture structure often arises. Due to the importance and wide applications of scale mixtures and location mixtures, we consider in this paper the case that the component densities differ only in scale parameters and the case that the component densities differ only in location parameters, and further construct an EM-test for the two-sample problem under each case. We show that both the EM-tests possess a chi-squared null limiting distribution. The local power analysis and sample size calculations are also investigated. Finally, the simulation studies and real data analysis demonstrate that the proposed EM-tests have better performance than the existing methods.

Detecting Differentially Variable MicroRNAs via Model-Based Clustering.

Identifying differentially variable (DV) genomic probes is becoming a new approach to detect novel genomic risk factors for complex human diseases. The F test is the standard equal-variance test in statistics. For high-throughput genomic data, the probe-wise F test has been successfully used to detect biologically relevant DNA methylation marks that have different variances between two groups of subjects (e.g., cases versus controls). In addition to DNA methylation, microRNA (miRNA) is another important mechanism of epigenetics. However, to the best of our knowledge, no studies have identified DV miRNAs. In this article, we proposed a novel model-based clustering method to improve the power of the probe-wise F test to detect DV miRNAs. We imposed special structures on covariance matrices for each cluster of miRNAs based on the prior information about the relationship between variances in cases and controls and about the independence among them. Simulation studies showed that the proposed method seems promising in detecting DV probes. Based on two real datasets about human hepatocellular carcinoma (HCC), we identified 7 DV-only miRNAs (hsa-miR-1826, hsa-miR-191, hsa-miR-194-star, hsa-miR-222, hsa-miR-502-3p, hsa-miR-93, and hsa-miR-99b) using the proposed method, one (hsa-miR-1826) of which has not yet been reported to be related to HCC in the literature.

Robust joint score tests in the application of DNA methylation data analysis.

BACKGROUND: Recently differential variability has been showed to be valuable in evaluating the association of DNA methylation to the risks of complex human diseases. The statistical tests based on both differential methylation level and differential variability can be more powerful than those based only on differential methylation level. Anh and Wang (2013) proposed a joint score test (AW) to simultaneously detect for differential methylation and differential variability. However, AW's method seems to be quite conservative and has not been fully compared with existing joint tests. RESULTS: We proposed three improved joint score tests, namely iAW.Lev, iAW.BF, and iAW.TM, and have made extensive comparisons with the joint likelihood ratio test (jointLRT), the Kolmogorov-Smirnov (KS) test, and the AW test. Systematic simulation studies showed that: 1) the three improved tests performed better (i.e., having larger power, while keeping nominal Type I error rates) than the other three tests for data with outliers and having different variances between cases and controls; 2) for data from normal distributions, the three improved tests had slightly lower power than jointLRT and AW. The analyses of two Illumina HumanMethylation27 data sets GSE37020 and GSE20080 and one Illumina Infinium MethylationEPIC data set GSE107080 demonstrated that three improved tests had higher true validation rates than those from jointLRT, KS, and AW. CONCLUSIONS: The three proposed joint score tests are robust against the violation of normality assumption and presence of outlying observations in comparison with other three existing tests. Among the three proposed tests, iAW.BF seems to be the most robust and effective one for all simulated scenarios and also in real data analyses.

Adjusted Empirical Likelihood Method in the Presence of Nuisance Parameters with Application to the Sharpe Ratio.

The Sharpe ratio is a widely used risk-adjusted performance measurement in economics and finance. Most of the known statistical inferential methods devoted to the Sharpe ratio are based on the assumption that the data are normally distributed. In this article, without making any distributional assumption on the data, we develop the adjusted empirical likelihood method to obtain inference for a parameter of interest in the presence of nuisance parameters. We show that the log adjusted empirical likelihood ratio statistic is asymptotically distributed as the chi-square distribution. The proposed method is applied to obtain inference for the Sharpe ratio. Simulation results illustrate that the proposed method is comparable to Jobson and Korkie's method (1981) and outperforms the empirical likelihood method when the data are from a symmetric distribution. In addition, when the data are from a skewed distribution, the proposed method significantly outperforms all other existing methods. A real-data example is analyzed to exemplify the application of the proposed method.

A Comparative Study of Tests for Homogeneity of Variances with Application to DNA Methylation Data.

Variable DNA methylation has been associated with cancers and complex diseases. Researchers have identified many DNA methylation markers that have different mean methylation levels between diseased subjects and normal subjects. Recently, researchers found that DNA methylation markers with different variabilities between subject groups could also have biological meaning. In this article, we aimed to help researchers choose the right test of equal variance in DNA methylation data analysis. We performed systematic simulation studies and a real data analysis to compare the performances of 7 equal-variance tests, including 2 tests recently proposed in the DNA methylation analysis literature. Our results showed that the Brown-Forsythe test and trimmed-mean-based Levene's test had good performance in testing for equality of variance in our simulation studies and real data analyses. Our results also showed that outlier profiles could be biologically very important.

Far infrared-assisted extraction followed by MEKC for the simultaneous determination of flavones and phenolic acids in the leaves of Rhododendron mucronulatum Turcz.

A method based on micellar electrokinetic chromatography with amperometric detection and far infrared-assisted extraction has been developed for the simultaneous determination of two flavones (rutin and farrerol) and three phenolic acids (syringic acid, vanillic acid, and 4-hydroxybenzoic acid) in the dried leaves of Rhododendron mucronulatum Turcz., a commonly used traditional Chinese medicine. The effects of some important factors such as the voltage applied on the infrared generator, irradiation time, the concentration of borate and sodium dodecylsulfate (SDS), separation voltage, and detection potential were investigated to acquire the optimum conditions. The detection electrode was a 300-µm diameter carbon disc electrode. The five analytes could be well separated within 8 min in a 40 cm-long capillary at a separation voltage of 12 kV in a 50 mM borate buffer (pH 9.2) containing 50 mM SDS. The relationship between peak current and analyte concentration was linear over about three orders of magnitude with the detection limits (S/N=3) ranging from 0.20 to 0.46 µM. The results indicated that far infrared irradiations significantly enhanced the extraction efficiency. The extraction time was substantially reduced to 6 min compared with 3 h for conventional hot solvent extraction.

Determination of carbohydrates in Folium Lysium Chinensis using capillary electrophoresis combined with far-infrared light irradiation-assisted extraction.

In this work, a method based on capillary electrophoresis with amperometric detection and far-infrared-assisted extraction has been developed for the determination of mannitol, sucrose, glucose and fructose in Folium Lysium Chinensis, a commonly used traditional Chinese medicine. The water-soluble constituents in the herbal drug were extracted with double distilled water with the assistance of far-infrared radiations. The effects of detection potential, irradiation time, and the voltage applied on the infrared generator were investigated to acquire the optimum analysis conditions. The detection electrode was a 300-µm-diameter copper disk electrode at a detection potential of +0.65 V. The four carbohydrates could be well separated within 18 min in a 50-cm length fused-silica capillary at a separation voltage of 9 kV in a 50-mM NaOH aqueous solution. The relation between peak current and analyte concentration was linear over about three orders of magnitude with detection limits (S/N=3) ranging from 0.66 to 1.15 µM for all analytes. The results indicated that far infrared significantly enhanced the extraction efficiency of the carbohydrates in Folium Lysium Chinensis. The extraction time was significantly reduced to 7 min compared with several hours for conventional hot solvent extraction.

Functional mixture regression.

In functional linear models (FLMs), the relationship between the scalar response and the functional predictor process is often assumed to be identical for all subjects. Motivated by both practical and methodological considerations, we relax this assumption and propose a new class of functional regression models that allow the regression structure to vary for different groups of subjects. By projecting the predictor process onto its eigenspace, the new functional regression model is simplified to a framework that is similar to classical mixture regression models. This leads to the proposed approach named as functional mixture regression (FMR). The estimation of FMR can be readily carried out using existing software implemented for functional principal component analysis and mixture regression. The practical necessity and performance of FMR are illustrated through applications to a longevity analysis of female medflies and a human growth study. Theoretical investigations concerning the consistent estimation and prediction properties of FMR along with simulation experiments illustrating its empirical properties are presented in the supplementary material available at Biostatistics online. Corresponding results demonstrate that the proposed approach could potentially achieve substantial gains over traditional FLMs.

Heterogeneity Between Ducts of the Same Nuclear Grade Involved by Duct Carcinoma In Situ (DCIS) of the Breast.

PURPOSE: Nuclear grade of breast DCIS is considered during patient management decision-making although it may have only a modest prognostic association with therapeutic outcome. We hypothesized that visual inspection may miss substantive differences in nuclei classified as having the same nuclear grade. To test this hypothesis, we measured subvisual nuclear features by quantitative image cytometry for nuclei with the same grade, and tested for statistical differences in these features. EXPERIMENTAL DESIGN AND STATISTICAL ANALYSIS: Thirty-nine nuclear digital image features of about 100 nuclei were measured in digital images of H&E stained slides of 81 breast biopsy specimens. One field with at least 5 ducts was evaluated for each patient. We compared features of nuclei with the same grade in multiple ducts of the same patient with ANOVA (or Welch test), and compared features of nuclei with the same grade in two ducts of different patients using 2-sided t-tests (P ≤ 0.05). Also, we compared image features for nuclei in patients with single grade to those with the same grade in patients with multiple grades using t-tests. RESULTS: Statistically significant differences were detected in nuclear features between ducts with the same nuclear grade, both in different ducts of the same patient, and between ducts in different patients with DCIS of more than one grade. CONCLUSION: Nuclei in ducts visually described as having the same nuclear grade had significantly different subvisual digital image features. These subvisual differences may be considered additional manifestations of heterogeneity over and above differences that can be observed microscopically. This heterogeneity may explain the inconsistency of nuclear grading as a prognostic factor.

Effect of quantitative nuclear image features on recurrence of Ductal Carcinoma In Situ (DCIS) of the breast.

BACKGROUND: Nuclear grade has been associated with breast DCIS recurrence and progression to invasive carcinoma; however, our previous study of a cohort of patients with breast DCIS did not find such an association with outcome. Fifty percent of patients had heterogeneous DCIS with more than one nuclear grade. The aim of the current study was to investigate the effect of quantitative nuclear features assessed with digital image analysis on ipsilateral DCIS recurrence. METHODS: Hematoxylin and eosin stained slides for a cohort of 80 patients with primary breast DCIS were reviewed and two fields with representative grade (or grades) were identified by a Pathologist and simultaneously used for acquisition of digital images for each field. Van Nuys worst nuclear grade was assigned, as was predominant grade, and heterogeneous grading when present. Patients were grouped by heterogeneity of their nuclear grade: Group A: nuclear grade 1 only, nuclear grades 1 and 2, or nuclear grade 2 only (32 patients), Group B: nuclear grades 1, 2 and 3, or nuclear grades 2 and 3 (31 patients), Group 3: nuclear grade 3 only (17 patients). Nuclear fine structure was assessed by software which captured thirty-nine nuclear feature values describing nuclear morphometry, densitometry, and texture. Step-wise forward Cox regressions were performed with previous clinical and pathologic factors, and the new image analysis features. RESULTS: Duplicate measurements were similar for 89.7% to 97.4% of assessed image features. The rate of correct classification of nuclear grading with digital image analysis features was similar in the two fields, and pooled assessment across both fields. In the pooled assessment, a discriminant function with one nuclear morphometric and one texture feature was significantly (p = 0.001) associated with nuclear grading, and provided correct jackknifed classification of a patient's nuclear grade for Group A (78.1%), Group B (48.4%), and Group C (70.6%). The factors significantly associated with DCIS recurrence were those previously found, type of initial presentation (p = 0.03) and amount of parenchymal involvement (p = 0.05), along with the morphometry image feature of ellipticity (p = 0.04). CONCLUSION: Analysis of nuclear features measured by image cytometry may contribute to the classification and prognosis of breast DCIS patients with more than one nuclear grade.

Ductal carcinoma in situ of the breast (DCIS) with heterogeneity of nuclear grade: prognostic effects of quantitative nuclear assessment.

BACKGROUND: Previously, 50% of patients with breast ductal carcinoma in situ (DCIS) had more than one nuclear grade, and neither worst nor predominant nuclear grade was significantly associated with development of invasive carcinoma. Here, we used image analysis in addition to histologic evaluation to determine if quantification of nuclear features could provide additional prognostic information and hence impact prognostic assessments. METHODS: Nuclear image features were extracted from about 200 nuclei of each of 80 patients with DCIS who underwent lumpectomy alone, and received no adjuvant systemic therapy. Nuclear images were obtained from 20 representative nuclei per duct, from each of a group of 5 ducts, in two separate fields, for 10 ducts. Reproducibility of image analysis features was determined, as was the ability of features to discriminate between nuclear grades. Patient information was available about clinical factors (age and method of DCIS detection), pathologic factors (DCIS size, nuclear grade, margin size, and amount of parenchymal involvement), and 39 image features (morphology, densitometry, and texture). The prognostic effects of these factors and features on the development of invasive breast cancer were examined with Cox step-wise multivariate regression. RESULTS: Duplicate measurements were similar for 89.7% to 97.4% of assessed image features. For the pooled assessment with approximately 200 nuclei per patient, a discriminant function with one densitometric and two texture features was significantly (p < 0.001) associated with nuclear grading, and provided 78.8% correct jackknifed classification of a patient's nuclear grade. In multivariate assessments, image analysis nuclear features had significant prognostic associations (p