Shapley values for cluster importance

This paper proposes a novel approach to explain the predictions made by data-driven methods. Since such predictions rely heavily on the data used for training, explanations that convey information about how the training data affects the predictions are useful. The paper proposes a novel approach to quantify how different data-clusters of the training data affect a prediction. The quantification is based on Shapley values, a concept which originates from coalitional game theory, developed to fairly distribute the payout among a set of cooperating players. A player’s Shapley value is a measure of that player’s contribution. Shapley values are often used to quantify feature importance, ie. how features affect a prediction. This paper extends this to cluster importance, letting clusters of the training data act as players in a game where the predictions are the payouts. The novel methodology proposed in this paper lets us explore and investigate how different clusters of the training data affect the predictions made by any black-box model, allowing new aspects of the reasoning and inner workings of a prediction model to be conveyed to the users. The methodology is fundamentally different from existing explanation methods, providing insight which would not be available otherwise, and should complement existing explanation methods, including explanations based on feature importance.

Tailored graphical lasso for data integration in gene network reconstruction

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 [Formula: see text]-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, 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. 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.

Partially linear monotone methods with automatic variable selection and monotonicity direction discovery

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.

Graph Peak Caller: Calling ChIP-seq peaks on graph-based reference genomes

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.

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.

Distinct DNA methylation profiles in bone and blood of osteoporotic and healthy postmenopausal women

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.

Coordinates and intervals in graph-based reference genomes

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 .

The Genomic HyperBrowser: an analysis web server for genome-scale data

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.

Handling realistic assumptions in hypothesis testing of 3D co-localization of genomic elements

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.

Estimated comparative integration hotspots identify different behaviors of retroviral gene transfer vectors

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.

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 differential disease regulome

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.

The Genomic HyperBrowser: inferential genomics at the sequence level

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.

Validation of oligoarrays for quantitative exploration of the transcriptome

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.

The influence of missing value imputation on detection of differentially expressed genes from microarray data

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.

Genome-wide estimation of transcript concentrations from spotted cDNA microarray data

A method providing absolute transcript concentrations from spotted microarray intensity data is presented. Number of transcripts per µg 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 10⁵–10¹⁰ transcripts per µg 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.

CGH-Explorer: a program for analysis of array-CGH 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.