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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.

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.

BackgroundNuclear 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.MethodsHematoxylin 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.ResultsDuplicate 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).ConclusionAnalysis of nuclear features measured by image cytometry may contribute to the classification and prognosis of breast DCIS patients with more than one nuclear grade.

Directional data are often collected in applications such as in genetics, geology and astrolomy. One particular statistical problem of interest is whether the data are from a mixture of two von Mises distributions or a single von Mises distribution. Motivating examples including a DNA microarray experiment where it is suggested that a proportion of circadian genes have systematically different phase/peak expressions in two different tissues. We study the use of modified likelihood ratio test (MLRT) to this class of problems. The MLRT statistic is shown to have a simple χ 2 1 null limiting distribution. The result is extended to general parametric kernels. The simulation study gives additional insight into the finite-sample performance of the test. For illustration, two real data examples are also given.

We study a two-sample homogeneity testing problem, in which one sample comes from a population with density f x and the other is from a mixture population with mixture density 1−λ f x λg x . This problem arises naturally from many statistical applications such as test for partial differential gene expression in microarray study or genetic studies for gene mutation. Under the semiparametric assumption g x f x e α βx , a penalized empirical likelihood ratio test could be constructed, but its implementation is hindered by the fact that there is neither feasible algorithm for computing the test statistic nor available research results on its theoretical properties. To circumvent these difficulties, we propose an EM test based on the penalized empirical likelihood. We prove that the EM test has a simple chi-square limiting distribution, and we also demonstrate its competitive testing performances by simulations. A real-data example is used to illustrate the proposed methodology.

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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.