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Background Identifying gene interactions is a topic of great importance in genomics, and approaches based on network models provide a powerful tool for studying these. Assuming a Gaussian graphical model, a gene association network may be estimated from multiomic data based on the non-zero entries of the inverse covariance matrix. Inferring such biological networks is challenging because of the high dimensionality of the problem, making traditional estimators unsuitable. The graphical lasso is constructed for the estimation of sparse inverse covariance matrices in such situations, using $$L_1$$ L 1 -penalization on the matrix entries. The weighted graphical lasso is an extension in which prior biological information from other sources is integrated into the model. There are however issues with this approach, as it naïvely forces the prior information into the network estimation, even if it is misleading or does not agree with the data at hand. Further, if an associated network based on other data is used as the prior, the method often fails to utilize the information effectively. Results We propose a novel graphical lasso approach, the tailored graphical lasso, that aims to handle prior information of unknown accuracy more effectively. We provide an R package implementing the method, . Applying the method to both simulated and real multiomic data sets, we find that it outperforms the unweighted and weighted graphical lasso in terms of all performance measures we consider. In fact, the graphical lasso and weighted graphical lasso can be considered special cases of the tailored graphical lasso, and a parameter determined by the data measures the usefulness of the prior information. We also find that among a larger set of methods, the tailored graphical is the most suitable for network inference from high-dimensional data with prior information of unknown accuracy. With our method, mRNA data are demonstrated to provide highly useful prior information for protein–protein interaction networks. Conclusions The method we introduce utilizes useful prior information more effectively without involving any risk of loss of accuracy should the prior information be misleading.

In many statistical regression and prediction problems, it is reasonable to assume monotone relationships between certain predictor variables and the outcome. Genomic effects on phenotypes are, for instance, often assumed to be monotone. However, in some settings, it may be reasonable to assume a partially linear model, where some of the covariates can be assumed to have a linear effect. One example is a prediction model using both high-dimensional gene expression data, and low-dimensional clinical data, or when combining continuous and categorical covariates. We study methods for fitting the partially linear monotone model, where some covariates are assumed to have a linear effect on the response, and some are assumed to have a monotone (potentially nonlinear) effect. Most existing methods in the literature for fitting such models are subject to the limitation that they have to be provided the monotonicity directions a priori for the different monotone effects. We here present methods for fitting partially linear monotone models which perform both automatic variable selection, and monotonicity direction discovery. The proposed methods perform comparably to, or better than, existing methods, in terms of estimation, prediction, and variable selection performance, in simulation experiments in both classical and high-dimensional data settings.

The generation and systematic collection of genome-wide data is ever-increasing. This vast amount of data has enabled researchers to study relations between a variety of genomic and epigenomic features, including genetic variation, gene regulation and phenotypic traits. Such relations are typically investigated by comparatively assessing genomic co-occurrence. Technically, this corresponds to assessing the similarity of pairs of genome-wide binary vectors. A variety of similarity measures have been proposed for this problem in other fields like ecology. However, while several of these measures have been employed for assessing genomic co-occurrence, their appropriateness for the genomic setting has never been investigated. We show that the choice of similarity measure may strongly influence results and propose two alternative modelling assumptions that can be used to guide this choice. On both simulated and real genomic data, the Jaccard index is strongly altered by dataset size and should be used with caution. The Forbes coefficient (fold change) and tetrachoric correlation are less influenced by dataset size, but one should be aware of increased variance for small datasets. All results on simulated and real data can be inspected and reproduced at https://hyperbrowser.uio.no/sim-measure.

BackgroundIdentifying gene interactions is a topic of great importance in genomics, and approaches based on network models provide a powerful tool for studying these. Assuming a Gaussian graphical model, a gene association network may be estimated from multiomic data based on the non-zero entries of the inverse covariance matrix. Inferring such biological networks is challenging because of the high dimensionality of the problem, making traditional estimators unsuitable. The graphical lasso is constructed for the estimation of sparse inverse covariance matrices in Gaussian graphical models in such situations, using L1-penalization on the matrix entries. An extension of the graphical lasso is the weighted graphical lasso, in which prior biological information from other (data) sources is integrated into the model through the weights. There are however issues with this approach, as it naïvely forces the prior information into the network estimation, even if it is misleading or does not agree with the data at hand. Further, if an associated network based on other data is used as the prior, weighted graphical lasso often fails to utilize the information effectively.ResultsWe propose a novel graphical lasso approach, the tailored graphical lasso, that aims to handle prior information of unknown accuracy more effectively. We provide an R package implementing the method, tailoredGlasso. Applying the method to both simulated and real multiomic data sets, we find that it outperforms the unweighted and weighted graphical lasso in terms of all performance measures we consider. In fact, the graphical lasso and weighted graphical lasso can be considered special cases of the tailored graphical lasso, and a parameter determined by the data measures the usefulness of the prior information. With our method, mRNA data are demonstrated to provide highly useful prior information for protein-protein interaction networks.ConclusionsThe method we introduce utilizes useful prior information more effectively without involving any risk of loss of accuracy should the prior information be misleading.

Graph-based representations are considered to be the future for reference genomes, as they allow integrated representation of the steadily increasing data on individual variation. Currently available tools allow de novo assembly of graph-based reference genomes, alignment of new read sets to the graph representation as well as certain analyses like variant calling and haplotyping. We here present a first method for calling ChIP-Seq peaks on read data aligned to a graph-based reference genome. The method is a graph generalization of the peak caller MACS2, and is implemented in an open source tool, Graph Peak Caller. By using the existing tool vg to build a pan-genome of Arabidopsis thaliana, we validate our approach by showing that Graph Peak Caller with a pan-genome reference graph can trace variants within peaks that are not part of the linear reference genome, and find peaks that in general are more motif-enriched than those found by MACS2., Author summary The expression of genes is a tightly regulated process. A key regulatory mechanism is the modulation of transcription by a class of proteins called transcription factors that bind to DNA in the spatial proximity of regulated genes. Determining the binding locations of transcription factors for specific cell types and settings is thus a key step in understanding the dynamics of normal cells as well as disease states. Binding sites for a given transcription factor are typically obtained through an experimental technique called CHiP-seq, in which DNA binding locations are obtained by sequencing DNA fragments attached to the transcription factor and aligning these sequences to a reference genome. A computational technique known as peak calling is then used to separate signal from noise and predict where the protein binds. Current peak callers are based on linear reference genomes that do not contain known genetic variants from the population. They thus potentially miss cases where proteins bind to such alternative genome sequences. Recently, a new type of reference genomes based on graph representations have become popular, as they are able to also incorporate alternative genome sequences. We here present Graph Peak Caller, the first peak caller that is able to exploit such graph representations for the detection of transcription factor binding locations. Using a graph-based reference genome for Arabidopsis thaliana, we show that our peak caller can lead to better detection of transcription factor binding locations as compared to a similar existing peak caller that uses a linear reference genome representation.

We propose novel modifications to an anomaly detection methodology based on multivariate signal reconstruction followed by residuals analysis. The reconstructions are made using Auto Associative Kernel Regression (AAKR), where the query observations are compared to historical observations called memory vectors, representing normal operation. When the data set with historical observations grows large, the naive approach where all observations are used as memory vectors will lead to unacceptable large computational loads, hence a reduced set of memory vectors should be intelligently selected. The residuals between the observed and the reconstructed signals are analysed using standard Sequential Probability Ratio Tests (SPRT), where appropriate alarms are raised based on the sequential behaviour of the residuals. The modifications we introduce include: a novel cluster based method to select memory vectors to be considered by the AAKR, which gives an extensive reduction in computation time; a generalization of the distance measure, which makes it possible to distinguish between explanatory and response variables; and a regional credibility estimation used in the residuals analysis, to let the time used to identify if a sequence of query vectors represents an anomalous state or not, depend on the amount of data situated close to or surrounding the query vector. We demonstrate how the anomaly detection method and the proposed modifications can be successfully applied for anomaly detection on a set of imbalanced benchmark data sets, as well as on recent data from a marine diesel engine in operation.

In numerous problems where the aim is to estimate the effect of a predictor variable on a response, one can assume a monotone relationship. For example, dose-effect models in medicine are of this type. In a multiple regression setting, additive monotone regression models assume that each predictor has a monotone effect on the response. In this paper, we present an overview and comparison of very recent frequentist methods for fitting additive monotone regression models. Three of the methods we present can be used both in the high dimensional setting, where the number of parameters $p$ exceeds the number of observations $n$, and in the classical multiple setting where $1

BackgroundThe generation and systematic collection of genome-wide data is ever-increasing. This vast amount of data has enabled researchers to study relations between a variety of genomic and epigenomic features, including genetic variation, gene regulation, and phenotypic traits. Such relations are typically investigated by comparatively assessing genomic co-occurrence. Technically, this corresponds to assessing the similarity of pairs of genome-wide binary vectors. A variety of metrics have been proposed for this problem in other fields like ecology. However, while several of these metrics have been employed for assessing genomic co-occurrence, their appropriateness for the genomic setting has never been investigated.ResultsWe show that the choice of metric may strongly influence results and propose two alternative modelling assumptions that can be used to guide this choice. On both simulated and real genomic data, the Jaccard index is strongly affected by dataset size and should be used with caution. The Forbes coefficient (fold change) and tetrachoric correlation are less affected by dataset size, but one should be aware of increased variance for small datasets.AvailabilityAll results on simulated and real data can be inspected and reproduced athttps://hyperbrowser.uio.no/sim-measure

The continuous growth in maritime traffic and recent developments towards autonomous navigation have directed increasing attention to navigational safety in which new tools are required to identify real-time risk and complex navigation situations. These tools are of paramount importance to avoid potentially disastrous consequences of accidents and promote safe navigation at sea. In this study, an adaptive ship-safety-domain is proposed with spatial risk functions to identify both collision and grounding risk based on motion and maneuverability conditions for all vessels. The algorithm is designed and validated through extensive amounts of Automatic Identification System (AIS) data for decision support over a large area, while the integration of the algorithm with other navigational systems will increase effectiveness and ensure reliability. Since a successful evacuation of a potential vessel-to-vessel collision, or a vessel grounding situation, is highly dependent on the nearby maneuvering limitations and other possible accident situations, multi-vessel collision and grounding risk is considered in this work to identify real-time risk. The presented algorithm utilizes and exploits dynamic AIS information, vessel registry and high-resolution maps and it is robust to inaccuracies of position, course and speed over ground records. The computation-efficient algorithm allows for real-time situation risk identification at a large-scale monitored map up to country level and up to several years of operation with a very high accuracy.

Background Using high-dimensional penalized regression we studied genome-wide DNA-methylation in bone biopsies of 80 postmenopausal women in relation to their bone mineral density (BMD). The women showed BMD varying from severely osteoporotic to normal. Global gene expression data from the same individuals was available, and since DNA-methylation often affects gene expression, the overall aim of this paper was to include both of these omics data sets into an integrated analysis. Methods The classical penalized regression uses one penalty, but we incorporated individual penalties for each of the DNA-methylation sites. These individual penalties were guided by the strength of association between DNA-methylations and gene transcript levels. DNA-methylations that were highly associated to one or more transcripts got lower penalties and were therefore favored compared to DNA-methylations showing less association to expression. Because of the complex pathways and interactions among genes, we investigated both the association between DNA-methylations and their corresponding cis gene, as well as the association between DNA-methylations and trans-located genes. Two integrating penalized methods were used: first, an adaptive group-regularized ridge regression, and secondly, variable selection was performed through a modified version of the weighted lasso. Results When information from gene expressions was integrated, predictive performance was considerably improved, in terms of predictive mean square error, compared to classical penalized regression without data integration. We found a 14.7% improvement in the ridge regression case and a 17% improvement for the lasso case. Our version of the weighted lasso with data integration found a list of 22 interesting methylation sites. Several corresponded to genes that are known to be important in bone formation. Using BMD as response and these 22 methylation sites as covariates, least square regression analyses resulted in R2=0.726, comparable to an average R2=0.438 for 10000 randomly selected groups of DNA-methylations with group size 22. Conclusions Two recent types of penalized regression methods were adapted to integrate DNA-methylation and their association to gene expression in the analysis of bone mineral density. In both cases predictions clearly benefit from including the additional information on gene expressions.

In this paper we propose a cluster based version of the anomaly detection methodology based on signal reconstruction, using Auto Associative Kernel Regression (AAKR), combined with residuals analysis, using Sequential Probability Ratio Test (SPRT). We demonstrate how the proposed cluster based methodology can be successfully applied for anomaly detection on a marine diesel engine in operation. Furthermore, we demonstrate the vast reduction in computation time compared to the original framework, and discuss other possible advantages and disadvantages of the proposed methodology.

Background: Recent large-scale undertakings such as ENCODE and Roadmap Epigenomics have generated experimental data mapped to the human reference genome (as genomic tracks) representing a variety of functional elements across a large number of cell types. Despite the high potential value of these publicly available data for a broad variety of investigations, little attention has been given to the analytical methodology necessary for their widespread utilisation. Findings: We here present a first principled treatment of the analysis of collections of genomic tracks. We have developed novel computational and statistical methodology to permit comparative and confirmatory analyses across multiple and disparate data sources. We delineate a set of generic questions that are useful across a broad range of investigations and discuss the implications of choosing different statistical measures and null models. Examples include contrasting analyses across different tissues or diseases. The methodology has been implemented in a comprehensive open-source software system, the GSuite HyperBrowser. To make the functionality accessible to biologists, and to facilitate reproducible analysis, we have also developed a web-based interface providing an expertly guided and customizable way of utilizing the methodology. With this system, many novel biological questions can flexibly be posed and rapidly answered. Conclusions: Through a combination of streamlined data acquisition, interoperable representation of dataset collections, and customizable statistical analysis with guided setup and interpretation, the GSuite HyperBrowser represents a first comprehensive solution for integrative analysis of track collections across the genome and epigenome. The software is available at: https://hyperbrowser.uio.no., This work was supported by the Research Council of Norway (under grant agreements 221580, 218241, and 231217/F20), by the Norwegian Cancer Society (under grant agreements 71220’PR-2006-0433 and 3485238-2013), and by the South-Eastern Norway Regional Health Authority (under grant agreement 2014041).

DNA methylation affects expression of associated genes and may contribute to the missing genetic effects from genome-wide association studies of osteoporosis. To improve insight into the mechanisms of postmenopausal osteoporosis, we combined transcript profiling with DNA methylation analyses in bone. RNA and DNA were isolated from 84 bone biopsies of postmenopausal donors varying markedly in bone mineral density (BMD). In all, 2529 CpGs in the top 100 genes most significantly associated with BMD were analyzed. The methylation levels at 63 CpGs differed significantly between healthy and osteoporotic women at 10% false discovery rate (FDR). Five of these CpGs at 5% FDR could explain 14% of BMD variation. To test whether blood DNA methylation reflect the situation in bone (as shown for other tissues), an independent cohort was selected and BMD association was demonstrated in blood for 13 of the 63 CpGs. Four transcripts representing inhibitors of bone metabolism—MEPE, SOST, WIF1, and DKK1—showed correlation to a high number of methylated CpGs, at 5% FDR. Our results link DNA methylation to the genetic influence modifying the skeleton, and the data suggest a complex interaction between CpG methylation and gene regulation. This is the first study in the hitherto largest number of postmenopausal women to demonstrate a strong association among bone CpG methylation, transcript levels, and BMD/fracture. This new insight may have implications for evaluation of osteoporosis stage and susceptibility. The final version of this research has been published in Epigenetics. © 2017 Taylor & Francis

Background It has been proposed that future reference genomes should be graph structures in order to better represent the sequence diversity present in a species. However, there is currently no standard method to represent genomic intervals, such as the positions of genes or transcription factor binding sites, on graph-based reference genomes. Results We formalize offset-based coordinate systems on graph-based reference genomes and introduce methods for representing intervals on these reference structures. We show the advantage of our methods by representing genes on a graph-based representation of the newest assembly of the human genome (GRCh38) and its alternative loci for regions that are highly variable. Conclusion More complex reference genomes, containing alternative loci, require methods to represent genomic data on these structures. Our proposed notation for genomic intervals makes it possible to fully utilize the alternative loci of the GRCh38 assembly and potential future graph-based reference genomes. We have made a Python package for representing such intervals on offset-based coordinate systems, available at https://github.com/uio-cels/offsetbasedgraph . An interactive web-tool using this Python package to visualize genes on a graph created from GRCh38 is available at https://github.com/uio-cels/genomicgraphcoords .

Given two independent samples of size n and m drawn from univariate distributions with unknown densities f and g, respectively, we are interested in identifying subintervals where the two empirical densities deviate significantly from each other. The solution is built by turning the nonparametric density comparison problem into a comparison of two regression curves. Each regression curve is created by binning the original observations into many small size bins, followed by a suitable form of root transformation to the binned data counts. Turned as a regression comparison problem, several nonparametric regression procedures for detection of sparse signals can be applied. Both multiple testing and model selection methods are explored. Furthermore, an approach for estimating larger connected regions where the two empirical densities are significantly different is also derived, based on a scale-space representation. The proposed methods are applied on simulated examples as well as real-life data from biology.

Watson and Holmes propose ways of investigating robustness of statistical decisions by examining certain neighbourhoods around a posterior distribution. This may partly amount to ad hoc modelling of extra uncertainty. Instead of creating neighbourhoods around the posterior a posteriori, we argue that it might be more fruitful to model a layer of extra uncertainty first, in the model building process, and then allow the data to determine how big the resulting neighbourhoods ought to be. We develop and briefly illustrate a general strategy along such lines.

Genome-wide, cell-type-specific profiles are being systematically generated for numerous genomic and epigenomic features. There is, however, no universally applicable analytical methodology for such data. We present GSuite HyperBrowser, the first comprehensive solution for integrative analysis of dataset collections across the genome and epigenome. The GSuite HyperBrowser is an open-source system for streamlined acquisition and customizable statistical analysis of large collections of genome-wide datasets. The system is based on new computational and statistical methodologies that permit comparative and confirmatory analyses across multiple disparate data sources. Expert guidance and reproducibility are facilitated via a Galaxy-based web-interface. The software is available athttps://hyperbrowser.uio.no/gsuite

In this paper we present an application of sensorbased anomaly detection in maritime transport. The study is based on real sensor data streamed from a ship to shore, where the data is analysed through a big data analytics platform. The novelty of this work originates in the use of data from sensors covering different aspects of the ship operation, exemplified here by propulsion power, speed over ground and ship motion in four different degrees of freedom. The developed method employs Auto Associative Kernel Regression (AAKR) for signal reconstruction, and the Sequential Probability Ratio Test (SPRT) technique for anomaly detection, where different hypothesis tests looking both at mean and variance deviations have been tested. In order to compare different settings, formal state of the art performance metrics have been used. We demonstrate that the AAKR model produces good reconstructions when the observations are similar to observations represented in the training data, and for some examples of simulated anomalies, the method reveals the abnormal behaviour. As long as the parameters are tuned carefully, alarms are triggered appropriately by the SPRT.

We address the issue of variable preselection in high-dimensional penalized regression, such as the lasso, a commonly used approach to variable selection and prediction in genomics. Preselection—to start with a manageable set of covariates—is becoming increasingly necessary for enabling advanced analysis tasks to be carried out on data sets of huge size created by high throughput technologies. Preselection of features to be included in multivariate analyses based on simple univariate ranking is a natural strategy that has often been implemented despite its potential bias. We demonstrate this bias and propose a way to correct it. Starting with a sequential implementation of the lasso with increasing lists of predictors, we exploit a property of the set of corresponding cross-validation curves, a pattern that we call “freezing”. The ranking of the predictors to be included sequentially is based on simple measures of associations with the outcome, which can be pre-computed in an efficient way for ultra high dimensional data sets externally to the penalized regression implementation. We demonstrate by simulation that our sequential approach leads in a vast majority of cases to a safe and efficient way of focusing the lasso analysis on a smaller and manageable number of predictors. In situations where the lasso performs well, we need typically less than 20 % of the variables to recover the same solution as if using the full set of variables. We illustrate the applicability of our strategy in the context of a genome-wide association study and on microarray genomic data where we need just 2. 5 % and 13 % of the variables respectively. Finally we include an example where 260 million gene-gene interactions are ranked and we are able to recover the lasso solution using only 1 % of these. Freezing offers great potential for extending the applicability of penalized regressions to current and upcoming ultra high dimensional problems in bioinformatics. Its applicability is not limited to the standard lasso but is a generic property of many penalized approaches.

The symposium covered a broad spectrum of themes on High-Dimensional Statistics. We present here a short overview of some of the topics discussed at the symposium: high-dimensional inference in regression, high-dimensional causal inference, Bayesian variable selection for high-dimensional analysis, and integration of multiple high-dimensional data, but this categorization is not exhaustive. The contributions by some of the participants, appearing as chapters in the book, include both in-depth reviews and development of new statistical methodology, applications and theory.

Several old and new density estimators may have good theoretical performance, but are hampered by not being bona fide densities; they may be negative in certain regions or may not integrate to 1. One can therefore not simulate from them, for example. This paper develops general modification methods that turn any density estimator into one which is a bona fide density, and which is always better in performance under one set of conditions and arbitrarily close in performance under a complementary set of conditions. This improvement-for-free procedure can, in particular, be applied for higher-order kernel estimators, classes of modern h4 bias kernel type estimators, superkernel estimators, the sinc kernel estimator, the k-NN estimator, orthogonal expansion estimators, and for various recently developed semi-parametric density estimators.

We present a new approach to regression function estimation in which a non-parametric regression estimator is guided by a parametric pilot estimate with the aim of reducing the bias. New classes of parametrically guided kernel weighted local polynomial estimators are introduced and formulae for asymptotic expectation and variance, hence approximated mean squared error and mean integrated squared error, are derived. It is shown that the new classes of estimators have the very same large sample variance as the estimators in the standard non-parametric setting, while there is substantial room for reducing the bias if the chosen parametric pilot function belongs to a wide neighbourhood around the true regression line. Bias reduction is discussed in light of examples and simulations.

Classical smoothers have limited usefulness in image processing, because sharp “edges” tend to be blurred. There is a literature on edge-preserving smoothers, but these all require moderately large “smooth stretches.” Here we discuss an approach to this problem called “sigma filtering” and propose an improvement based on running M estimation. Both computational and theoretical aspects are developed. For image processing, the methods have a niche between standard filtering approaches and Bayes–Markov random-field analysis.

Asymptotic properties of a semiparametric regression estimator proposed in Glad (1996) are derived, without conditioning on the predictor variables. The leading terms of unconditional asymptotic bias and variance are equal to those in the expressions obtained conditioned on the design in Glad (1996), while the unconditional approximations derived in this paper are of higher accuracy.

The study of chromatin 3D structure has recently gained much focus owing to novel techniques for detecting genome-wide chromatin contacts using next-generation sequencing. A deeper understanding of the architecture of the DNA inside the nucleus is crucial for gaining insight into fundamental processes such as transcriptional regulation, genome dynamics and genome stability. Chromatin conformation capture-based methods, such as Hi-C and ChIA-PET, are now paving the way for routine genome-wide studies of chromatin 3D structure in a range of organisms and tissues. However, appropriate methods for analyzing such data are lacking. Here, we propose a hypothesis test and an enrichment score of 3D co-localization of genomic elements that handles intra- or interchromosomal interactions, both separately and jointly, and that adjusts for biases caused by structural dependencies in the 3D data. We show that maintaining structural properties during resampling is essential to obtain valid estimation of P-values. We apply the method on chromatin states and a set of mutated regions in leukemia cells, and find significant co-localization of these elements, with varying enrichment scores, supporting the role of chromatin 3D structure in shaping the landscape of somatic mutations in cancer.

The immense increase in availability of genomic scale datasets, such as those provided by the ENCODE and Roadmap Epigenomics projects, presents unprecedented opportunities for individual researchers to pose novel falsifiable biological questions. With this opportunity, however, researchers are faced with the challenge of how to best analyze and interpret their genome-scale datasets. A powerful way of representing genome-scale data is as feature-specific coordinates relative to reference genome assemblies, i.e. as genomic tracks. The Genomic HyperBrowser (http://hyperbrowser.uio.no) is an open-ended web server for the analysis of genomic track data. Through the provision of several highly customizable components for processing and statistical analysis of genomic tracks, the HyperBrowser opens for a range of genomic investigations, related to, e.g., gene regulation, disease association or epigenetic modifications of the genome. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

We consider the problems of variable selection and estimation in nonparametric additive regression models for high-dimensional data. In recent years, several methods have been proposed to model nonlinear relationships when the number of covariates exceeds the number of observations by using spline basis functions and group penalties. Nonlinear {\it monotone} effects on the response play a central role in many situations, in particular in medicine and biology. We construct the monotone splines lasso (MS-lasso) to select variables and estimate effects using monotone spline (I-splines). The additive components in the model are represented by their I-spline basis function expansion and the component selection becomes that of selecting the groups of coefficients in the I-spline basis function expansion. We use a recent procedure, called cooperative lasso, to select sign-coherent groups, that is selecting the groups with either exclusively non-negative or non-positive coefficients. This leads to the selection of important covariates that have nonlinear monotone increasing or decreasing effect on the response. We also introduce an adaptive version of the MS-lasso which reduces both the bias and the number of false positive selections considerably. We compare the MS-lasso and the adaptive MS-lasso with other existing methods for variable selection in high dimensions by simulation and illustrate the method on two relevant genomic data sets. Results indicate that the (adaptive) MS-lasso has excellent properties compared to the other methods both by means of estimation and selection, and can be recommended for high-dimensional monotone regression., Comment: 19 pages, 4 figures and 7 tables

SUMMARY Synthetic magnetic resonance imaging involves the estimation, based on a set of measured images with noise, of three basic physical quantities that are nonlinearly related to the observations. The methods currently available for this ill-conditoned inverse problem either do not provide sufficiently accurate estimates or require time-consuming data collection. We formulate this nonlinear problem in a Bayesian framework, taking into account knowledge about the physics of the magnetic resonance imaging experiment, statistical properties of the experimental noise, and prior information about the underlying physical quantities, modelled by a suitable Markov random field. A new multilayer Markov random field is proposed. Inference is drawn by means of Markov chain Monte Carlo methods or iterated conditional modes. Some examples are included to demonstrate how synthetic magnetic resonance imaging by this approach can be performed in an accurate and reliable way.

The lasso is one of the most commonly used methods for high-dimensional regression, but can be unstable and lacks satisfactory asymptotic properties for variable selection. We propose to use weighted lasso with integrated relevant external information on the covariates to guide the selection towards more stable results. Weighting the penalties with external information gives each regression coefficient a covariate specific amount of penalization and can improve upon standard methods that do not use such information by borrowing knowledge from the external material. The method is applied to two cancer data sets, with gene expressions as covariates. We find interesting gene signatures, which we are able to validate. We discuss various ideas on how the weights should be defined and illustrate how different types of investigations can utilize our method exploiting different sources of external data. Through simulations, we show that our method outperforms the lasso and the adaptive lasso when the external information is from relevant to partly relevant, in terms of both variable selection and prediction.

Understanding genetic information to code and interpret disease phenotypes represents one major goal in modern biology. The challenge of integrating separate scientific vocabularies and insight is daunting because of the vastness and rapid evolution of the disciplines. New models and tools are needed to allow scientists to bridge knowledges, integrate concepts and information, and enable complex analysis. In this contribution we show two examples of datasets from Gene Therapy and Tubercolosis to highlight how integration between biostatistics and bioinformatics allows to gain information from the extremely large biogical databases produced with the new biotechnologies, such as Next Generation Sequencing (NGS) data.

Background Transcription factors in disease-relevant pathways represent potential drug targets, by impacting a distinct set of pathways that may be modulated through gene regulation. The influence of transcription factors is typically studied on a per disease basis, and no current resources provide a global overview of the relations between transcription factors and disease. Furthermore, existing pipelines for related large-scale analysis are tailored for particular sources of input data, and there is a need for generic methodology for integrating complementary sources of genomic information. Results We here present a large-scale analysis of multiple diseases versus multiple transcription factors, with a global map of over-and under-representation of 446 transcription factors in 1010 diseases. This map, referred to as the differential disease regulome, provides a first global statistical overview of the complex interrelationships between diseases, genes and controlling elements. The map is visualized using the Google map engine, due to its very large size, and provides a range of detailed information in a dynamic presentation format. The analysis is achieved through a novel methodology that performs a pairwise, genome-wide comparison on the cartesian product of two distinct sets of annotation tracks, e.g. all combinations of one disease and one TF. The methodology was also used to extend with maps using alternative data sets related to transcription and disease, as well as data sets related to Gene Ontology classification and histone modifications. We provide a web-based interface that allows users to generate other custom maps, which could be based on precisely specified subsets of transcription factors and diseases, or, in general, on any categorical genome annotation tracks as they are improved or become available. Conclusion We have created a first resource that provides a global overview of the complex relations between transcription factors and disease. As the accuracy of the disease regulome depends mainly on the quality of the input data, forthcoming ChIP-seq based binding data for many TFs will provide improved maps. We further believe our approach to genome analysis could allow an advance from the current typical situation of one-time integrative efforts to reproducible and upgradable integrative analysis. The differential disease regulome and its associated methodology is available at http://hyperbrowser.uio.no.

Integration of retroviral vectors in the human genome follows non random patterns that favor insertional deregulation of gene expression and may cause risks of insertional mutagenesis when used in clinical gene therapy. Understanding how viral vectors integrate into the human genome is a key issue in predicting these risks. We provide a new statistical method to compare retroviral integration patterns. We identified the positions where vectors derived from the Human Immunodeficiency Virus (HIV) and the Moloney Murine Leukemia Virus (MLV) show different integration behaviors in human hematopoietic progenitor cells. Non-parametric density estimation was used to identify candidate comparative hotspots, which were then tested and ranked. We found 100 significative comparative hotspots, distributed throughout the chromosomes. HIV hotspots were wider and contained more genes than MLV ones. A Gene Ontology analysis of HIV targets showed enrichment of genes involved in antigen processing and presentation, reflecting the high HIV integration frequency observed at the MHC locus on chromosome 6. Four histone modifications/variants had a different mean density in comparative hotspots (H2AZ, H3K4me1, H3K4me3, H3K9me1), while gene expression within the comparative hotspots did not differ from background. These findings suggest the existence of epigenetic or nuclear three-dimensional topology contexts guiding retroviral integration to specific chromosome areas., Author Summary Understanding how retroviral vectors integrate in the human genome is a major safety issue in gene therapy, since a concrete risk of developing tumors associated with the integration process has been observed in several clinical trials. Statistical analyses confirmed the non randomness of the integration. Where and why do virus-specific integrations tend to accumulate in the genome? We compared integration preferences of two retroviral vectors derived from HIV and MLV, which are used in most gene therapy trials for hematological disorders, in their actual clinical targets, i.e., human hematopoietic stem/progenitor cells. We developed a new statistical method to find areas of the genome, called comparative hotspots, where integration preferences are significantly different. We modeled the integration process as a stochastic process, so that integration sites are seen as samples from an unknown virus-specific probability density function. Thus, the problem became to identify areas where two empirical density functions differ significantly. The comparison of nonparametric variability bands around the estimated integration densities allowed identifying and ranking candidate comparative hotspots. Results indicated clear differential patterns of integration between HIV and MLV, leading to new hypotheses on the mechanisms governing retroviral integration.

The immense increase in the generation of genomic scale data poses an unmet analytical challenge, due to a lack of established methodology with the required flexibility and power. We propose a first principled approach to statistical analysis of sequence-level genomic information. We provide a growing collection of generic biological investigations that query pairwise relations between tracks, represented as mathematical objects, along the genome. The Genomic HyperBrowser implements the approach and is available at http://hyperbrowser.uio.no.

It is shown that ocean-wave spectrum parameters obtained from spectra of time series measured with heave, pitch, and roll data buoys are maximum-likelihood (ML) estimators under certain assumptions about the wave field. A modified set of ML estimators where the linear wave-theory dispersion relation is strictly enforced is shown to have only marginally better performance.

Background Oligoarrays have become an accessible technique for exploring the transcriptome, but it is presently unclear how absolute transcript data from this technique compare to the data achieved with tag-based quantitative techniques, such as massively parallel signature sequencing (MPSS) and serial analysis of gene expression (SAGE). By use of the TransCount method we calculated absolute transcript concentrations from spotted oligoarray intensities, enabling direct comparisons with tag counts obtained with MPSS and SAGE. The tag counts were converted to number of transcripts per cell by assuming that the sum of all transcripts in a single cell was 5·105. Our aim was to investigate whether the less resource demanding and more widespread oligoarray technique could provide data that were correlated to and had the same absolute scale as those obtained with MPSS and SAGE. Results A number of 1,777 unique transcripts were detected in common for the three technologies and served as the basis for our analyses. The correlations involving the oligoarray data were not weaker than, but, similar to the correlation between the MPSS and SAGE data, both when the entire concentration range was considered and at high concentrations. The data sets were more strongly correlated at high transcript concentrations than at low concentrations. On an absolute scale, the number of transcripts per cell and gene was generally higher based on oligoarrays than on MPSS and SAGE, and ranged from 1.6 to 9,705 for the 1,777 overlapping genes. The MPSS data were on same scale as the SAGE data, ranging from 0.5 to 3,180 (MPSS) and 9 to1,268 (SAGE) transcripts per cell and gene. The sum of all transcripts per cell for these genes was 3.8·105 (oligoarrays), 1.1·105 (MPSS) and 7.6·104 (SAGE), whereas the corresponding sum for all detected transcripts was 1.1·106 (oligoarrays), 2.8·105 (MPSS) and 3.8·105 (SAGE). Conclusion The oligoarrays and TransCount provide quantitative transcript concentrations that are correlated to MPSS and SAGE data, but, the absolute scale of the measurements differs across the technologies. The discrepancy questions whether the sum of all transcripts within a single cell might be higher than the number of 5·105 suggested in the literature and used to convert tag counts to transcripts per cell. If so, this may explain the apparent higher transcript detection efficiency of the oligoarrays, and has to be clarified before absolute transcript concentrations can be interchanged across the technologies. The ability to obtain transcript concentrations from oligoarrays opens up the possibility of efficient generation of universal transcript databases with low resource demands.

Motivation: Missing values are problematic for the analysis of microarray data. Imputation methods have been compared in terms of the similarity between imputed and true values in simulation experiments and not of their influence on the final analysis. The focus has been on missing at random, while entries are missing also not at random. Results: We investigate the influence of imputation on the detection of differentially expressed genes from cDNA microarray data. We apply ANOVA for microarrays and SAM and look to the differentially expressed genes that are lost because of imputation. We show that this new measure provides useful information that the traditional root mean squared error cannot capture. We also show that the type of missingness matters: imputing 5% missing not at random has the same effect as imputing 10--30% missing at random. We propose a new method for imputation (LinImp), fitting a simple linear model for each channel separately, and compare it with the widely used KNNimpute method. For 10% missing at random, KNNimpute leads to twice as many lost differentially expressed genes as LinImp. Availability: The R package for LinImp is available at http://folk.uio.no/idasch/imp Contact: idasch@math.uio.no Supplementary information: http://folk.uio.no/idasch/imp

A method providing absolute transcript concentrations from spotted microarray intensity data is presented. Number of transcripts per microg total RNA, mRNA or per cell, are obtained for each gene, enabling comparisons of transcript levels within and between tissues. The method is based on Bayesian statistical modelling incorporating available information about the experiment from target preparation to image analysis, leading to realistically large confidence intervals for estimated concentrations. The method was validated in experiments using transcripts at known concentrations, showing accuracy and reproducibility of estimated concentrations, which were also in excellent agreement with results from quantitative real-time PCR. We determined the concentration for 10,157 genes in cervix cancers and a pool of cancer cell lines and found values in the range of 10(5)-10(10) transcripts per microg total RNA. The precision of our estimates was sufficiently high to detect significant concentration differences between two tumours and between different genes within the same tumour, comparisons that are not possible with standard intensity ratios. Our method can be used to explore the regulation of pathways and to develop individualized therapies, based on absolute transcript concentrations. It can be applied broadly, facilitating the construction of the transcriptome, continuously updating it by integrating future data.

Summary: CGH-Explorer is a program for visualization and statistical analysis of microarray-based comparative genomic hybridization (array-CGH) data. The program has preprocessing facilities, tools for graphical exploration of individual arrays or groups of arrays, and tools for statistical identification of regions of amplification and deletion. Availability: The program is available as Java class files that runs on any platform with the Java 2 runtime environment (J2SE JRE) installed, and as a Windows executable. Java source files are also available. See http://www.ifi.uio.no/bioinf/Papers/CGH/ Contact: ole@ifi.uio.no

The traditional kernel density estimator of an unknown density is by construction completely nonparametric in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of semiparametric methods that are designed to work better than the kernel estimator in a broad nonparametric neighbourhood of a given parametric class of densities, for example, the normal, while not losing much in precision when the true density is far from the parametric class. The idea is to multiply an initial parametric density estimate with a kernel-type estimate of the necessary correction factor. This works well in cases where the correction factor function is less rough than the original density itself. Extensive comparisons with the kernel estimator are carried out, including exact analysis for the class of all normal mixtures. The new method, with a normal start, wins quite often, even in many cases where the true density is far from normal. Procedures for choosing the smoothing parameter of the estimator are also discussed. The new estimator should be particularly useful in higher dimensions, where the usual nonparametric methods have problems. The idea is also spelled out for nonparametric regression.

Integrative analysis of gene dosage, expression, and ontology (GO) data was performed to discover driver genes in the carcinogenesis and chemoradioresistance of cervical cancers. Gene dosage and expression profiles of 102 locally advanced cervical cancers were generated by microarray techniques. Fifty-two of these patients were also analyzed with the Illumina expression method to confirm the gene expression results. An independent cohort of 41 patients was used for validation of gene expressions associated with clinical outcome. Statistical analysis identified 29 recurrent gains and losses and 3 losses (on 3p, 13q, 21q) associated with poor outcome after chemoradiotherapy. The intratumor heterogeneity, assessed from the gene dosage profiles, was low for these alterations, showing that they had emerged prior to many other alterations and probably were early events in carcinogenesis. Integration of the alterations with gene expression and GO data identified genes that were regulated by the alterations and revealed five biological processes that were significantly overrepresented among the affected genes: apoptosis, metabolism, macromolecule localization, translation, and transcription. Four genes on 3p (RYBP, GBE1) and 13q (FAM48A, MED4) correlated with outcome at both the gene dosage and expression level and were satisfactorily validated in the independent cohort. These integrated analyses yielded 57 candidate drivers of 24 genetic events, including novel loci responsible for chemoradioresistance. Further mapping of the connections among genetic events, drivers, and biological processes suggested that each individual event stimulates specific processes in carcinogenesis through the coordinated control of multiple genes. The present results may provide novel therapeutic opportunities of both early and advanced stage cervical cancers., Author Summary Genetic gains and losses, i.e. changes in gene dosages, are common abnormalities of human cancers. Discovering these defects and understanding the biological meaning can lead to improved therapeutic opportunities. This paper reports a large scale screening of gene dosage alterations in cervical cancer and gives a broader exploration of the expression and function of genes with gains or losses. We have focused on the most frequent gene dosage alterations and the alterations associated with survival after chemoradiotherapy, since these defects are likely to be of major importance for developing disease. The most notable finding was the discovery of a set of biological processes that are known hallmarks of cancer and were associated with gains and losses of specific genes. Moreover, novel loci associated with chemoradioresistance independent of existing clinical markers were found, and the genes involved were depicted. Our results indicated that gene dosage alterations play a causative role in the carcinogenesis and chemoradioresistance of cervical cancer and pinpointed candidate biomarkers of the disease.