The computation of a similarity measure for genomic data is a standard tool in computational genetics. The principal components of such matrices are routinely used to correct for biases due to confounding by population stratification, for instance in linear regressions. However, the calculation of both a similarity matrix and its singular value decomposition (SVD) are computationally intensive. The contribution of this article is threefold. First, we demonstrate that the calculation of three matrices (called the covariance matrix, the weighted Jaccard matrix, and the genomic relationship matrix) can be reformulated in a unified way which allows for the application of a randomized SVD algorithm, which is faster than the traditional computation. The fast SVD algorithm we present is adapted from an existing randomized SVD algorithm and ensures that all computations are carried out in sparse matrix algebra. The algorithm only assumes that row-wise and column-wise subtraction and multiplication of a vector with a sparse matrix is available, an operation that is efficiently implemented in common sparse matrix packages. An exception is the so-called Jaccard matrix, which does not have a structure applicable for the fast SVD algorithm. Second, an approximate Jaccard matrix is introduced to which the fast SVD computation is applicable. Third, we establish guaranteed theoretical bounds on the accuracy (in [Formula: see text] norm and angle) between the principal components of the Jaccard matrix and the ones of our proposed approximation, thus putting the proposed Jaccard approximation on a solid mathematical foundation, and derive the theoretical runtime of our algorithm. We illustrate that the approximation error is low in practice and empirically verify the theoretical runtime scalings on both simulated data and data of the 1000 Genome Project.

Chronic obstructive pulmonary disease (COPD) is a complex disease influenced by well-established environmental exposures (most notably, cigarette smoking) and incompletely defined genetic factors. The chromosome 4q region harbors multiple genetic risk loci for COPD, including signals near HHIP, FAM13A, GSTCD, TET2, and BTC. Leveraging RNA-Seq data from lung tissue in COPD cases and controls, we estimated the co-expression network for genes in the 4q region bounded by HHIP and BTC (~70MB), through partial correlations informed by protein-protein interactions. We identified several co-expressed gene pairs based on partial correlations, including NPNT-HHIP, BTC-NPNT and FAM13A-TET2, which were replicated in independent lung tissue cohorts. Upon clustering the co-expression network, we observed that four genes previously associated to COPD: BTC, HHIP, NPNT and PPM1K appeared in the same network community. Finally, we discovered a sub-network of genes differentially co-expressed between COPD vs controls (including FAM13A, PPA2, PPM1K and TET2). Many of these genes were previously implicated in cell-based knock-out experiments, including the knocking out of SPP1 which belongs to the same genomic region and could be a potential local key regulatory gene. These analyses identify chromosome 4q as a region enriched for COPD genetic susceptibility and differential co-expression.

As of June 2022, the GISAID database contains more than 11 million SARS-CoV-2 genomes, including several thousand nucleotide sequences for the most common variants such as delta or omicron. These SARS-CoV-2 strains have been collected from patients around the world since the beginning of the pandemic. We start by assessing the similarity of all pairs of nucleotide sequences using the Jaccard index and principal component analysis. As shown previously in the literature, an unsupervised cluster analysis applied to the SARS-CoV-2 genomes results in clusters of sequences according to certain characteristics such as their strain or their clade. Importantly, we observe that nucleotide sequences of common variants are often outliers in clusters of sequences stemming from variants identified earlier on during the pandemic. Motivated by this finding, we are interested in applying outlier detection to nucleotide sequences. We demonstrate that nucleotide sequences of common variants (such as alpha, delta, or omicron) can be identified solely based on a statistical outlier criterion. We argue that outlier detection might be a useful surveillance tool to identify emerging variants in real time as the pandemic progresses.

MOTIVATION: Analysis of rare variants in family-based studies remains a challenge. Transmission-based approaches provide robustness against population stratification, but the evaluation of the significance of test statistics based on asymptotic theory can be imprecise. Also, power will depend heavily on the choice of the test statistic and on the underlying genetic architecture of the locus, which will be generally unknown. RESULTS: In our proposed framework, we utilize the FBAT haplotype algorithm to obtain the conditional offspring genotype distribution under the null hypothesis given the sufficient statistic. Based on this conditional offspring genotype distribution, the significance of virtually any association test statistic can be evaluated based on simulations or exact computations, without the need for asymptotic approximations. Besides standard linear burden-type statistics, this enables our approach to also evaluate other test statistics such as variance components statistics, higher criticism approaches, and maximum-single-variant-statistics, where asymptotic theory might be involved or does not provide accurate approximations for rare variant data. Based on these P-values, combined test statistics such as the aggregated Cauchy association test (ACAT) can also be utilized. In simulation studies, we show that our framework outperforms existing approaches for family-based studies in several scenarios. We also applied our methodology to a TOPMed whole-genome sequencing dataset with 897 asthmatic trios from Costa Rica. AVAILABILITY AND IMPLEMENTATION: FBAT software is available at https://sites.google.com/view/fbatwebpage. Simulation code is available at https://github.com/julianhecker/FBAT_rare_variant_test_simulations. Whole-genome sequencing data for 'NHLBI TOPMed: The Genetic Epidemiology of Asthma in Costa Rica' is available at https://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?study_id=phs000988.v4.p1. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Most predictive models based on gene expression data do not leverage information related to gene splicing, despite the fact that splicing is a fundamental feature of eukaryotic gene expression. Cigarette smoking is an important environmental risk factor for many diseases, and it has profound effects on gene expression. Using smoking status as a prediction target, we developed deep neural network predictive models using gene, exon, and isoform level quantifications from RNA sequencing data in 2,557 subjects in the COPDGene Study. We observed that models using exon and isoform quantifications clearly outperformed gene-level models when using data from 5 genes from a previously published prediction model. Whereas the test set performance of the previously published model was 0.82 in the original publication, our exon-based models including an exon-to-isoform mapping layer achieved a test set AUC (area under the receiver operating characteristic) of 0.88, which improved to an AUC of 0.94 using exon quantifications from a larger set of genes. Isoform variability is an important source of latent information in RNA-seq data that can be used to improve clinical prediction models.

Crowdclustering is a practical way to incorporate domain knowledge into clustering, by combining opinions from multiple domain experts. Existing crowdclustering methods analyze binary pairwise similarity labels. However, in some applications, experts might provide partition labels. If we convert partition labels into pairwise similarity, then it would be difficult to understand the relationships between clustering solutions from different experts. In this paper, we propose a crowdclustering model that directly analyzes partition labels. The proposed model adopts a novel approach based on a modified multinomial logistic regression model, which simultaneously learns the number of clusters and determines hyper-planes that partition samples into clusters. The proposed model also learns a mapping between the latent clusters and expert labels, revealing the agreements and disagreements between experts. Experiments on benchmark data demonstrate that the proposed model simultaneously learns the number of clusters and discovers the clustering structure. An experiment on disease subtyping problem illustrates that the proposed model helps us understand the agreement and disagreement between experts.

Utilizing expert input often improves clustering performance. However in a knowledge discovery problem, ground truth is unknown even to an expert. Thus, instead of one expert, we solicit the opinion from multiple experts. The key question motivating this work is: which experts should be assigned higher weights when there is disagreement on whether to put a pair of samples in the same group? To model the uncertainty in constraints from different experts, we build a probabilistic model for pairwise constraints through jointly modeling each expert’s accuracy and the mapping from features to latent cluster assignments. After learning our probabilistic discriminative clustering model and accuracies of different experts, 1) samples that were not annotated by any expert can be clustered using the discriminative clustering model; and 2) experts with higher accuracies are automatically assigned higher weights in determining the latent cluster assignments. Experimental results on UCI benchmark datasets and a real-world disease subtyping dataset demonstrate that our proposed approach outperforms competing alternatives, including semi-crowdsourced clustering, semi-supervised clustering with constraints from majority voting, and consensus clustering.

Expert input can improve clustering performance. In today’s collaborative environment, the availability of crowdsourced multiple expert input is becoming common. Given multiple experts’ inputs, most existing approaches can only discover one clustering structure. However, data is multi-faced by nature and can be clustered in different ways (also known as views). In an exploratory analysis problem where ground truth is not known, different experts may have diverse views on how to cluster data. In this paper, we address the problem on how to automatically discover multiple ways to cluster data given potentially diverse inputs from multiple uncertain experts. We propose a novel Bayesian probabilistic model that automatically learns the multiple expert views and the clustering structure associated with each view. The benefits of learning the experts’ views include 1) enabling the discovery of multiple diverse clustering structures, and 2) improving the quality of clustering solution in each view by assigning higher weights to experts with higher confidence. In our approach, the expert views, multiple clustering structures and expert confidences are jointly learned via variational inference. Experimental results on synthetic datasets, benchmark datasets and a real-world disease subtyping problem show that our proposed approach outperforms competing baselines, including meta clustering, semi-supervised clustering, semi-crowdsourced clustering and consensus clustering.

Clustering is a challenging problem because given the same data set, it can be grouped in multiple different ways. Which of these clustering solutions is interesting depends on its domain application. Thus, incorporating domain expert input often improves clustering performance. However, most existing semi-supervised clustering techniques can only incorporate instance-level constraints (a few labels or must-link/cannot-link constraints), which domain experts may not be comfortable providing in knowledge discovery problems because categories are not known. Fortunately, domain experts often have an idea regarding properties that clustering solutions should have in order to be useful in domain application based on domain relevant scores. In this paper, we provide a framework for jointly optimizing the usefulness and quality of a clustering solution. Experiments on a synthetic data, a benchmark data, and a real-world disease subtyping problem demonstrate the usefulness of our proposed approach.

We introduce a novel Bayesian nonparametric model that uses the concept of disease trajectories for disease subtype identification. Although our model is general, we demonstrate that by treating fractions of tissue patterns derived from medical images as compositional data, our model can be applied to study distinct progression trends between population subgroups. Specifically, we apply our algorithm to quantitative emphysema measurements obtained from chest CT scans in the COPDGene Study and show several distinct progression patterns. As emphysema is one of the major components of chronic obstructive pulmonary disease (COPD), the third leading cause of death in the United States [1], an improved definition of emphysema and COPD subtypes is of great interest. We investigate several models with our algorithm, and show that one with age , pack years (a measure of cigarette exposure), and smoking status as predictors gives the best compromise between estimated predictive performance and model complexity. This model identified nine subtypes which showed significant associations to seven single nucleotide polymorphisms (SNPs) known to associate with COPD. Additionally, this model gives better predictive accuracy than multiple, multivariate ordinary least squares regression as demonstrated in a five-fold cross validation analysis. We view our subtyping algorithm as a contribution that can be applied to bridge the gap between CT-level assessment of tissue composition to population-level analysis of compositional trends that vary between disease subtypes.

Clustering is a technique that is usually applied as a tool for exploratory data analysis. Because of the exploratory nature of this task, it would be beneficial if a clustering method generates interpretable results, and allows incorporating domain knowledge. This motivates us to develop a probabilistic discriminative model that learns a rectangular decision rule for each cluster, we call Discriminative Rectangle Mixture (DReaM) model. DReaM gives interpretable clustering results, because the rectangular decision rules discovered explicitly illustrate how one cluster is defined and differs from other clusters. It also facilitates us to take advantage of existing rules because we can choose informative prior distributions for the rectangular rules. Moreover, DReaM allows that the features for generating rules do not have to be the same as the features for discovering cluster structure. We approximate the distribution for the rules discovered via variational inference. Experimental results demonstrate that DReaM gives more interpretable clustering results, and yet its performance is comparable to existing clustering methods when solving traditional clustering. Furthermore, in real applications, DReaM is able to effectively take advantage of domain knowledge, and to generate reasonable clustering results.

Chronic obstructive pulmonary disease (COPD) is a lung disease characterized by airflow limitation usually associated with an inflammatory response to noxious particles, such as cigarette smoke. COPD is currently the third leading cause of death in the United States and is the only leading cause of death that is increasing in prevalence. It also represents an enormous financial burden to society, costing tens of billions of dollars annually in the U.S. It is widely accepted by the medical community that COPD is a heterogeneous disease, with substantial evidence indicating that genetic variation contributes to varying levels of disease susceptibility. This heterogeneity makes it difficult to predict health decline and develop targeted treatments for better patient care. Although researchers have made several attempts to discover disease subtypes, results have been inconclusive, in part because standard clustering methods have not properly dealt with disease manifestations that may worsen with increased exposure. In this paper we introduce a transformative way of looking at the COPD subtyping task. Specifically, we model the relationship between risk factors (such as age and smoke exposure) and manifestations of disease severity using Gaussian Processes, which allow us to represent so-called "disease trajectories". We also posit that individuals can be associated with multiple disease types (latent clusters), which we assume are influenced by genetics. Furthermore, we predict that only subsets of the numerous disease-related quantitative features are useful for describing each latent subtype. We model these associations using two separate beta process priors, and we describe a variational inference approach to discover the most probable latent cluster assignments. Results are validated with associations to genetic markers.

MOTIVATION: For samples of unrelated individuals, we propose a general analysis framework in which hundred thousands of genetic loci can be tested simultaneously for association with complex phenotypes. The approach is built on spatial-clustering methodology, assuming that genetic loci that are associated with the target phenotype cluster in certain genomic regions. In contrast to standard methodology for multilocus analysis, which has focused on the dimension reduction of the data, our multilocus association-clustering test profits from the availability of large numbers of genetic loci by detecting clusters of loci that are associated with the phenotype. RESULTS: The approach is computationally fast and powerful, enabling the simultaneous association testing of large genomic regions. Even the entire genome or certain chromosomes can be tested simultaneously. Using simulation studies, the properties of the approach are evaluated. In an application to a genome-wide association study for chronic obstructive pulmonary disease, we illustrate the practical relevance of the proposed method by simultaneously testing all genotyped loci of the genome-wide association study and by testing each chromosome individually. Our findings suggest that statistical methodology that incorporates spatial-clustering information will be especially useful in whole-genome sequencing studies in which millions or billions of base pairs are recorded and grouped by genomic regions or genes, and are tested jointly for association. AVAILABILITY AND IMPLEMENTATION: Implementation of the approach is available upon request.