Circular piecewise regression with applications to cell-cycle data

Applications of circular regression models appear in many different fields such as evolutionary psychology, motor behavior, biology, and, in particular, in the analysis of gene expressions in oscillatory systems. Specifically, for the gene expression problem, a researcher may be interested in modeling the relationship among the phases of cell-cycle genes in two species with differing periods. This challenging problem reduces to the problem of constructing a piecewise circular regression model and, with this objective in mind, we propose a flexible circular regression model which allows different parameter values depending on sectors along the circle. We give a detailed interpretation of the parameters in the model and provide maximum likelihood estimators. We also provide a model selection procedure based on the concept of generalized degrees of freedom. The model is then applied to the analysis of two different cell-cycle data sets and through these examples we highlight the power of our new methodology

Difference-based clustering of short time-course microarray data with replicates

<p>Abstract</p> <p>Background</p> <p>There are some limitations associated with conventional clustering methods for short time-course gene expression data. The current algorithms require prior domain knowledge and do not incorporate information from replicates. Moreover, the results are not always easy to interpret biologically.</p> <p>Results</p> <p>We propose a novel algorithm for identifying a subset of genes sharing a significant temporal expression pattern when replicates are used. Our algorithm requires no prior knowledge, instead relying on an observed statistic which is based on the first and second order differences between adjacent time-points. Here, a pattern is predefined as the sequence of symbols indicating direction and the rate of change between time-points, and each gene is assigned to a cluster whose members share a similar pattern. We evaluated the performance of our algorithm to those of K-means, Self-Organizing Map and the Short Time-series Expression Miner methods.</p> <p>Conclusions</p> <p>Assessments using simulated and real data show that our method outperformed aforementioned algorithms. Our approach is an appropriate solution for clustering short time-course microarray data with replicates.</p

A biclustering algorithm based on a Bicluster Enumeration Tree: application to DNA microarray data

<p>Abstract</p> <p>Background</p> <p>In a number of domains, like in DNA microarray data analysis, we need to cluster simultaneously rows (genes) and columns (conditions) of a data matrix to identify groups of rows coherent with groups of columns. This kind of clustering is called <it>biclustering</it>. Biclustering algorithms are extensively used in DNA microarray data analysis. More effective biclustering algorithms are highly desirable and needed.</p> <p>Methods</p> <p>We introduce <it>BiMine</it>, a new enumeration algorithm for biclustering of DNA microarray data. The proposed algorithm is based on three original features. First, <it>BiMine </it>relies on a new evaluation function called <it>Average Spearman's rho </it>(ASR). Second, <it>BiMine </it>uses a new tree structure, called <it>Bicluster Enumeration Tree </it>(BET), to represent the different biclusters discovered during the enumeration process. Third, to avoid the combinatorial explosion of the search tree, <it>BiMine </it>introduces a parametric rule that allows the enumeration process to cut tree branches that cannot lead to good biclusters.</p> <p>Results</p> <p>The performance of the proposed algorithm is assessed using both synthetic and real DNA microarray data. The experimental results show that <it>BiMine </it>competes well with several other biclustering methods. Moreover, we test the biological significance using a gene annotation web-tool to show that our proposed method is able to produce biologically relevant biclusters. The software is available upon request from the authors to academic users.</p

One year symptom severity and health-related quality of life changes among Black African patients undergoing uterine fibroid embolisation.

BACKGROUND: The main aim in the treatment of symptomatic fibroids by various modalities including uterine fibroid embolisation (UFE) is to alleviate symptoms and ultimately improve the quality of life. The efficacy of this modality of treatment in Black African women with significant fibroid burden and large uterine volumes is not clear. The main objective of the study was to examine potential changes in symptom severity among Black African patients 1 year following UFE for symptomatic uterine fibroids in a resource-constrained setting, rated using a validated questionnaire (UFS-QOL). Secondary outcomes examined were changes in quality of life and potential associations with age, parity, uterine volume and fibroid number prior to UFE. Additional interventions after UFE were also recorded. METHODS: A prospective before and after study of Black African patients undergoing UFE was undertaken. Participants underwent pelvic MR imaging prior to UFE and completed the UFS-QOL, a validated condition-specific questionnaire at baseline and at 1 year. Ninety five participants were recruited and data from 80 completing 1 year of follow up were available for analysis of changes in the symptom severity scores. RESULTS: The mean reduction in symptom severity score was 29.6 [95% CI 23.6 to 35.6, P < 0.001] and the mean improvement in HRQOL score was 35.7 [95% CI 28.4 to 42.9, P < 0.001]. A greater number of fibroids identified prior to UFE was associated with a more substantial improvement in symptom severity score (rs = 0.28, n = 80, P = 0.013) and participants of higher parity reported a greater improvement in HRQOL score (r = 0.336, P = 0.002). Major and minor surgical interventions were needed in 5 (6.3%) and 10 (12.5%) participants respectively. CONCLUSIONS: UFE is associated with clinically useful and statistically significant symptom relief in Black African patients. Symptom improvement following UFE is not compromised by a large fibroid burden and the rate of subsequent intervention is within an acceptable range. UFE is a safe alternative and efforts are needed to widen access to this non-surgical treatment modality

Post hoc pattern matching: assigning significance to statistically defined expression patterns in single channel microarray data

<p>Abstract</p> <p>Background</p> <p>Researchers using RNA expression microarrays in experimental designs with more than two treatment groups often identify statistically significant genes with ANOVA approaches. However, the ANOVA test does not discriminate which of the multiple treatment groups differ from one another. Thus, <it>post hoc </it>tests, such as linear contrasts, template correlations, and pairwise comparisons are used. Linear contrasts and template correlations work extremely well, especially when the researcher has <it>a priori </it>information pointing to a particular pattern/template among the different treatment groups. Further, all pairwise comparisons can be used to identify particular, treatment group-dependent patterns of gene expression. However, these approaches are biased by the researcher's assumptions, and some treatment-based patterns may fail to be detected using these approaches. Finally, different patterns may have different probabilities of occurring by chance, importantly influencing researchers' conclusions about a pattern and its constituent genes.</p> <p>Results</p> <p>We developed a four step, <it>post hoc </it>pattern matching (PPM) algorithm to automate single channel gene expression pattern identification/significance. First, 1-Way Analysis of Variance (ANOVA), coupled with <it>post hoc </it>'all pairwise' comparisons are calculated for all genes. Second, for each ANOVA-significant gene, all pairwise contrast results are encoded to create unique pattern ID numbers. The # genes found in each pattern in the data is identified as that pattern's 'actual' frequency. Third, using Monte Carlo simulations, those patterns' frequencies are estimated in random data ('random' gene pattern frequency). Fourth, a Z-score for overrepresentation of the pattern is calculated ('actual' against 'random' gene pattern frequencies). We wrote a Visual Basic program (StatiGen) that automates PPM procedure, constructs an Excel workbook with standardized graphs of overrepresented patterns, and lists of the genes comprising each pattern. The visual basic code, installation files for StatiGen, and sample data are available as supplementary material.</p> <p>Conclusion</p> <p>The PPM procedure is designed to augment current microarray analysis procedures by allowing researchers to incorporate all of the information from post hoc tests to establish unique, overarching gene expression patterns in which there is no overlap in gene membership. In our hands, PPM works well for studies using from three to six treatment groups in which the researcher is interested in treatment-related patterns of gene expression. Hardware/software limitations and extreme number of theoretical expression patterns limit utility for larger numbers of treatment groups. Applied to a published microarray experiment, the StatiGen program successfully flagged patterns that had been manually assigned in prior work, and further identified other gene expression patterns that may be of interest. Thus, over a moderate range of treatment groups, PPM appears to work well. It allows researchers to assign statistical probabilities to patterns of gene expression that fit <it>a priori </it>expectations/hypotheses, it preserves the data's ability to show the researcher interesting, yet unanticipated gene expression patterns, and assigns the majority of ANOVA-significant genes to non-overlapping patterns.</p

Quantitative Serial MRI of the Treated Fibroid Uterus

There are no long-term medical treatments for uterine fibroids, and non-invasive biomarkers are needed to evaluate novel therapeutic interventions. The aim of this study was to determine whether serial dynamic contrast-enhanced MRI (DCE-MRI) and magnetization transfer MRI (MT-MRI) are able to detect changes that accompany volume reduction in patients administered GnRH analogue drugs, a treatment which is known to reduce fibroid volume and perfusion. Our secondary aim was to determine whether rapid suppression of ovarian activity by combining GnRH agonist and antagonist therapies results in faster volume reduction.Forty women were assessed for eligibility at gynaecology clinics in the region, of whom thirty premenopausal women scheduled for hysterectomy due to symptomatic fibroids were randomized to three groups, receiving (1) GnRH agonist (Goserelin), (2) GnRH agonist+GnRH antagonist (Goserelin and Cetrorelix) or (3) no treatment. Patients were monitored by serial structural, DCE-MRI and MT-MRI, as well as by ultrasound and serum oestradiol concentration measurements from enrolment to hysterectomy (approximately 3 months).A volumetric treatment effect assessed by structural MRI occurred by day 14 of treatment (9% median reduction versus 9% increase in untreated women; P = 0.022) and persisted throughout. Reduced fibroid perfusion and permeability assessed by DCE-MRI occurred later and was demonstrable by 2-3 months (43% median reduction versus 20% increase respectively; P = 0.0093). There was no apparent treatment effect by MT-MRI. Effective suppression of oestradiol was associated with early volume reduction at days 14 (P = 0.041) and 28 (P = 0.0061).DCE-MRI is sensitive to the vascular changes thought to accompany successful GnRH analogue treatment of uterine fibroids and should be considered for use in future mechanism/efficacy studies of proposed fibroid drug therapies. GnRH antagonist administration does not appear to accelerate volume reduction, though our data do support the role of oestradiol suppression in GnRH analogue treatment of fibroids.ClinicalTrials.gov NCT00746031

Bayes Discriminant Rules with Ordered Predictors

Discriminant analysis, Latent space, Misclassification probability, Order restrictions, Restricted estimation,