P-splines with derivative based penalties and tensor product smoothing of unevenly distributed data

The P-splines of Eilers and Marx (1996) combine a B-spline basis with a discrete quadratic penalty on the basis coefficients, to produce a reduced rank spline like smoother. P-splines have three properties that make them very popular as reduced rank smoothers: i) the basis and the penalty are sparse, enabling efficient computation, especially for Bayesian stochastic simulation; ii) it is possible to flexibly `mix-and-match' the order of B-spline basis and penalty, rather than the order of penalty controlling the order of the basis as in spline smoothing; iii) it is very easy to set up the B-spline basis functions and penalties. The discrete penalties are somewhat less interpretable in terms of function shape than the traditional derivative based spline penalties, but tend towards penalties proportional to traditional spline penalties in the limit of large basis size. However part of the point of P-splines is not to use a large basis size. In addition the spline basis functions arise from solving functional optimization problems involving derivative based penalties, so moving to discrete penalties for smoothing may not always be desirable. The purpose of this note is to point out that the three properties of basis-penalty sparsity, mix-and-match penalization and ease of setup are readily obtainable with B-splines subject to derivative based penalization. The penalty setup typically requires a few lines of code, rather than the two lines typically required for P-splines, but this one off disadvantage seems to be the only one associated with using derivative based penalties. As an example application, it is shown how basis-penalty sparsity enables efficient computation with tensor product smoothers of scattered data

Increased vascular contractility in hypertension results from impaired endothelial calcium signaling

Endothelial cells line all blood vessels and are critical regulators of vascular tone. In hypertension, disruption of endothelial function alters the release of endothelial-derived vasoactive factors and results in increased vascular tone. Although the release of endothelial-derived vasodilators occurs in a Ca2+-dependent manner, little is known on how Ca2+ signaling is altered in hypertension. A key element to endothelial control of vascular tone is Ca2+ signals at specialized regions (myoendothelial projections) that connect endothelial cells and smooth muscle cells. This work describes disruption in the operation of this key Ca2+ signaling pathway in hypertension. We show that vascular reactivity to phenylephrine is increased in hypertensive (spontaneously hypertensive rat) when compared with normotensive (Wistar Kyoto) rats. Basal endothelial Ca2+ activity limits vascular contraction, but that Ca2+-dependent control is impaired in hypertension. When changes in endothelial Ca2+ levels are buffered, vascular contraction to phenylephrine increased, resulting in similar responses in normotension and hypertension. Local endothelial IP3(inositol trisphosphate)-mediated Ca2+ signals are smaller in amplitude, shorter in duration, occur less frequently, and arise from fewer sites in hypertension. Spatial control of endothelial Ca2+ signaling is also disrupted in hypertension: local Ca2+ signals occur further from myoendothelial projections in hypertension. The results demonstrate that the organization of local Ca2+ signaling circuits occurring at myoendothelial projections is disrupted in hypertension, giving rise to increased contractile responses

Selection of tuning parameters in bridge regression models via Bayesian information criterion

We consider the bridge linear regression modeling, which can produce a sparse or non-sparse model. A crucial point in the model building process is the selection of adjusted parameters including a regularization parameter and a tuning parameter in bridge regression models. The choice of the adjusted parameters can be viewed as a model selection and evaluation problem. We propose a model selection criterion for evaluating bridge regression models in terms of Bayesian approach. This selection criterion enables us to select the adjusted parameters objectively. We investigate the effectiveness of our proposed modeling strategy through some numerical examples.Comment: 20 pages, 5 figure

Bayesian DNA copy number analysis

<p>Abstract</p> <p>Background</p> <p>Some diseases, like tumors, can be related to chromosomal aberrations, leading to changes of DNA copy number. The copy number of an aberrant genome can be represented as a piecewise constant function, since it can exhibit regions of deletions or gains. Instead, in a healthy cell the copy number is two because we inherit one copy of each chromosome from each our parents.</p> <p>Bayesian Piecewise Constant Regression (BPCR) is a Bayesian regression method for data that are noisy observations of a piecewise constant function. The method estimates the unknown segment number, the endpoints of the segments and the value of the segment levels of the underlying piecewise constant function. The Bayesian Regression Curve (BRC) estimates the same data with a smoothing curve. However, in the original formulation, some estimators failed to properly determine the corresponding parameters. For example, the boundary estimator did not take into account the dependency among the boundaries and succeeded in estimating more than one breakpoint at the same position, losing segments.</p> <p>Results</p> <p>We derived an improved version of the BPCR (called mBPCR) and BRC, changing the segment number estimator and the boundary estimator to enhance the fitting procedure. We also proposed an alternative estimator of the variance of the segment levels, which is useful in case of data with high noise. Using artificial data, we compared the original and the modified version of BPCR and BRC with other regression methods, showing that our improved version of BPCR generally outperformed all the others. Similar results were also observed on real data.</p> <p>Conclusion</p> <p>We propose an improved method for DNA copy number estimation, mBPCR, which performed very well compared to previously published algorithms. In particular, mBPCR was more powerful in the detection of the true position of the breakpoints and of small aberrations in very noisy data. Hence, from a biological point of view, our method can be very useful, for example, to find targets of genomic aberrations in clinical cancer samples.</p

Comparison of Several Methods of Chromatographic Baseline Removal with a New Approach Based on Quantile Regression

The article is intended to introduce and discuss a new quantile regression method for baseline detrending of chromatographic signals. It is compared with current methods based on polynomial fitting, spline fitting, LOESS, and Whittaker smoother, each with thresholding and reweighting approach. For curve flexibility selection in existing algorithms, a new method based on skewness of the residuals is successfully applied. The computational efficiency of all approaches is also discussed. The newly introduced methods could be preferred to visible better performance and short computational time. The other algorithms behave in comparable way, and polynomial regression can be here preferred due to short computational time

Supervised learning for the automated transcription of spacer classification from spoligotype films

<p>Abstract</p> <p>Background</p> <p>Molecular genotyping of bacteria has revolutionized the study of tuberculosis epidemiology, yet these established laboratory techniques typically require subjective and laborious interpretation by trained professionals. In the context of a Tuberculosis Case Contact study in The Gambia we used a reverse hybridization laboratory assay called spoligotype analysis. To facilitate processing of spoligotype images we have developed tools and algorithms to automate the classification and transcription of these data directly to a database while allowing for manual editing.</p> <p>Results</p> <p>Features extracted from each of the 1849 spots on a spoligo film were classified using two supervised learning algorithms. A graphical user interface allows manual editing of the classification, before export to a database. The application was tested on ten films of differing quality and the results of the best classifier were compared to expert manual classification, giving a median correct classification rate of 98.1% (inter quartile range: 97.1% to 99.2%), with an automated processing time of less than 1 minute per film.</p> <p>Conclusion</p> <p>The software implementation offers considerable time savings over manual processing whilst allowing expert editing of the automated classification. The automatic upload of the classification to a database reduces the chances of transcription errors.</p

An iterative block-shifting approach to retention time alignment that preserves the shape and area of gas chromatography-mass spectrometry peaks

<p>Abstract</p> <p>Background</p> <p>Metabolomics, petroleum and biodiesel chemistry, biomarker discovery, and other fields which rely on high-resolution profiling of complex chemical mixtures generate datasets which contain millions of detector intensity readings, each uniquely addressed along dimensions of <it>time </it>(<it>e.g.</it>, <it>retention time </it>of chemicals on a chromatographic column), a <it>spectral value </it>(<it>e.g., mass-to-charge ratio </it>of ions derived from chemicals), and the <it>analytical run number</it>. They also must rely on data preprocessing techniques. In particular, inter-run variance in the retention time of chemical species poses a significant hurdle that must be cleared before feature extraction, data reduction, and knowledge discovery can ensue. <it>Alignment methods</it>, for calibrating retention reportedly (and in our experience) can misalign matching chemicals, falsely align distinct ones, be unduly sensitive to chosen values of input parameters, and result in distortions of peak shape and area.</p> <p>Results</p> <p>We present an iterative block-shifting approach for retention-time calibration that detects chromatographic features and qualifies them by retention time, spectrum, and the effect of their inclusion on the quality of alignment itself. Mass chromatograms are aligned pairwise to one selected as a reference. In tests using a 45-run GC-MS experiment, block-shifting reduced the absolute deviation of retention by greater than 30-fold. It compared favourably to COW and XCMS with respect to alignment, and was markedly superior in preservation of peak area.</p> <p>Conclusion</p> <p>Iterative block-shifting is an attractive method to align GC-MS mass chromatograms that is also generalizable to other two-dimensional techniques such as HPLC-MS.</p

Alternative regression models to assess increase in childhood BMI

<p>Abstract</p> <p>Background</p> <p>Body mass index (BMI) data usually have skewed distributions, for which common statistical modeling approaches such as simple linear or logistic regression have limitations.</p> <p>Methods</p> <p>Different regression approaches to predict childhood BMI by goodness-of-fit measures and means of interpretation were compared including generalized linear models (GLMs), quantile regression and Generalized Additive Models for Location, Scale and Shape (GAMLSS). We analyzed data of 4967 children participating in the school entry health examination in Bavaria, Germany, from 2001 to 2002. TV watching, meal frequency, breastfeeding, smoking in pregnancy, maternal obesity, parental social class and weight gain in the first 2 years of life were considered as risk factors for obesity.</p> <p>Results</p> <p>GAMLSS showed a much better fit regarding the estimation of risk factors effects on transformed and untransformed BMI data than common GLMs with respect to the generalized Akaike information criterion. In comparison with GAMLSS, quantile regression allowed for additional interpretation of prespecified distribution quantiles, such as quantiles referring to overweight or obesity. The variables TV watching, maternal BMI and weight gain in the first 2 years were directly, and meal frequency was inversely significantly associated with body composition in any model type examined. In contrast, smoking in pregnancy was not directly, and breastfeeding and parental social class were not inversely significantly associated with body composition in GLM models, but in GAMLSS and partly in quantile regression models. Risk factor specific BMI percentile curves could be estimated from GAMLSS and quantile regression models.</p> <p>Conclusion</p> <p>GAMLSS and quantile regression seem to be more appropriate than common GLMs for risk factor modeling of BMI data.</p