We describe cell type–specific significance analysis of microarrays (cssam) for analyzing differential gene expression for each cell type in a biological sample from microarray data and relative cell-type frequencies. first, we validated cssam with predesigned mixtures and then applied it to whole-blood gene expression datasets from stable post-transplant kidney transplant recipients and those experiencing acute transplant rejection, which revealed hundreds of differentially expressed genes that were otherwise undetectable.
We discuss the identification of genes that are associated with an outcome in RNA sequencing and other sequence-based comparative genomic experiments. RNA-sequencing data take the form of counts, so models based on the Gaussian distribution are unsuitable. Moreover, normalization is challenging because different sequencing experiments may generate quite different total numbers of reads. To overcome these difficulties, we use a log-linear model with a new approach to normalization. We derive a novel procedure to estimate the false discovery rate (FDR). Our method can be applied to data with quantitative, two-class, or multiple-class outcomes, and the computation is fast even for large data sets. We study the accuracy of our approaches for significance calculation and FDR estimation, and we demonstrate that our method has potential advantages over existing methods that are based on a Poisson or negative binomial model. In summary, this work provides a pipeline for the significance analysis of sequencing data.
Differential expression; FDR; Overdispersion; Poisson log-linear model; RNA-Seq; Score statistic
We suggest a method for estimating a covariance matrix on the basis of a sample of vectors drawn from a multivariate normal distribution. In particular, we penalize the likelihood with a lasso penalty on the entries of the covariance matrix. This penalty plays two important roles: it reduces the effective number of parameters, which is important even when the dimension of the vectors is smaller than the sample size since the number of parameters grows quadratically in the number of variables, and it produces an estimate which is sparse. In contrast to sparse inverse covariance estimation, our method’s close relative, the sparsity attained here is in the covariance matrix itself rather than in the inverse matrix. Zeros in the covariance matrix correspond to marginal independencies; thus, our method performs model selection while providing a positive definite estimate of the covariance. The proposed penalized maximum likelihood problem is not convex, so we use a majorize-minimize approach in which we iteratively solve convex approximations to the original nonconvex problem. We discuss tuning parameter selection and demonstrate on a flow-cytometry dataset how our method produces an interpretable graphical display of the relationship between variables. We perform simulations that suggest that simple elementwise thresholding of the empirical covariance matrix is competitive with our method for identifying the sparsity structure. Additionally, we show how our method can be used to solve a previously studied special case in which a desired sparsity pattern is prespecified.
Concave-convex procedure; Covariance graph; Covariance matrix; Generalized gradient descent; Lasso; Majorization-minimization; Regularization; Sparsity
We consider the supervised classification setting, in which the data consist of p features measured on n observations, each of which belongs to one of K classes. Linear discriminant analysis (LDA) is a classical method for this problem. However, in the high-dimensional setting where p ≫ n, LDA is not appropriate for two reasons. First, the standard estimate for the within-class covariance matrix is singular, and so the usual discriminant rule cannot be applied. Second, when p is large, it is difficult to interpret the classification rule obtained from LDA, since it involves all p features. We propose penalized LDA, a general approach for penalizing the discriminant vectors in Fisher’s discriminant problem in a way that leads to greater interpretability. The discriminant problem is not convex, so we use a minorization-maximization approach in order to efficiently optimize it when convex penalties are applied to the discriminant vectors. In particular, we consider the use of L1 and fused lasso penalties. Our proposal is equivalent to recasting Fisher’s discriminant problem as a biconvex problem. We evaluate the performances of the resulting methods on a simulation study, and on three gene expression data sets. We also survey past methods for extending LDA to the high-dimensional setting, and explore their relationships with our proposal.
classification; feature selection; high dimensional; lasso; linear discriminant analysis; supervised learning
Array-based comparative genomic hybridization (aCGH) enables the measurement of DNA copy number across thousands of locations in a genome. The main goals of analyzing aCGH data are to identify the regions of copy number variation (CNV) and to quantify the amount of CNV. Although there are many methods for analyzing single-sample aCGH data, the analysis of multi-sample aCGH data is a relatively new area of research. Further, many of the current approaches for analyzing multi-sample aCGH data do not appropriately utilize the additional information present in the multiple samples. We propose a procedure called the Fused Lasso Latent Feature Model (FLLat) that provides a statistical framework for modeling multi-sample aCGH data and identifying regions of CNV. The procedure involves modeling each sample of aCGH data as a weighted sum of a fixed number of features. Regions of CNV are then identified through an application of the fused lasso penalty to each feature. Some simulation analyses show that FLLat outperforms single-sample methods when the simulated samples share common information. We also propose a method for estimating the false discovery rate. An analysis of an aCGH data set obtained from human breast tumors, focusing on chromosomes 8 and 17, shows that FLLat and Significance Testing of Aberrant Copy number (an alternative, existing approach) identify similar regions of CNV that are consistent with previous findings. However, through the estimated features and their corresponding weights, FLLat is further able to discern specific relationships between the samples, for example, identifying 3 distinct groups of samples based on their patterns of CNV for chromosome 17.
Cancer; DNA copy number; False discovery rate; Mutation
We propose a hierarchical Bayesian model for analyzing gene expression data to identify pathways differentiating between two biological states (e.g., cancer vs. non-cancer and mutant vs. normal). Finding significant pathways can improve our understanding of biological processes. When the biological process of interest is related to a specific disease, eliciting a better understanding of the underlying pathways can lead to designing a more effective treatment. We apply our method to data obtained by interrogating the mutational status of p53 in 50 cancer cell lines (33 mutated and 17 normal). We identify several significant pathways with strong biological connections. We show that our approach provides a natural framework for incorporating prior biological information, and it has the best overall performance in terms of correctly identifying significant pathways compared to several alternative methods.
Biological pathways; Hierarchical Bayesian models; Mixture priors
Rheumatoid arthritis (RA) is a prototypical autoimmune arthritis affecting nearly 1% of the world population and is a significant cause of worldwide disability. Though prior studies have demonstrated the appearance of RA-related autoantibodies years before the onset of clinical RA, the pattern of immunologic events preceding the development of RA remains unclear. To characterize the evolution of the autoantibody response in the preclinical phase of RA, we used a novel multiplex autoantigen array to evaluate development of the anti-citrullinated protein antibodies (ACPA) and to determine if epitope spread correlates with rise in serum cytokines and imminent onset of clinical RA. To do so, we utilized a cohort of 81 patients with clinical RA for whom stored serum was available from 1–12 years prior to disease onset. We evaluated the accumulation of ACPA subtypes over time and correlated this accumulation with elevations in serum cytokines. We then used logistic regression to identify a profile of biomarkers which predicts the imminent onset of clinical RA (defined as within 2 years of testing). We observed a time-dependent expansion of ACPA specificity with the number of ACPA subtypes. At the earliest timepoints, we found autoantibodies targeting several innate immune ligands including citrullinated histones, fibrinogen, and biglycan, thus providing insights into the earliest autoantigen targets and potential mechanisms underlying the onset and development of autoimmunity in RA. Additionally, expansion of the ACPA response strongly predicted elevations in many inflammatory cytokines including TNF-α, IL-6, IL-12p70, and IFN-γ. Thus, we observe that the preclinical phase of RA is characterized by an accumulation of multiple autoantibody specificities reflecting the process of epitope spread. Epitope expansion is closely correlated with the appearance of preclinical inflammation, and we identify a biomarker profile including autoantibodies and cytokines which predicts the imminent onset of clinical arthritis.
We use the term “index predictor” to denote a score that consists of K binary rules such as “age > 60” or “blood pressure > 120 mm Hg.” The index predictor is the sum of these binary scores, yielding a value from 0 to K. Such indices as often used in clinical studies to stratify population risk: They are usually derived from subject area considerations. In this paper, we propose a fast data-driven procedure for automatically constructing such indices for linear, logistic, and Cox regression models. We also extend the procedure to create indices for detecting treatment–marker interactions. The methods are illustrated on a study with protein biomarkers as well as a large microarray gene expression study.
Degree of freedom; Index predictor; International prognostic index
Characterizing dynamic gene expression pattern and predicting patient outcome is now significant and will be of more interest in the future with large scale clinical investigation of microarrays. However, there is currently no method that has been developed for prediction of patient outcome using longitudinal gene expression, where gene expression of patients is being monitored across time. Here, we propose a novel prediction approach for patient survival time that makes use of time course structure of gene expression. This method is applied to a burn study. The genes involved in the final predictors are enriched in the inflammatory response and immune system related pathways. Moreover, our method is consistently better than prediction methods using individual time point gene expression or simply pooling gene expression from each time point.
prediction; time course; gene expression; survival
Combining tumor antigens with an immunostimulant can induce the immune system to specifically eliminate cancer cells. Generally, this combination is accomplished in an ex vivo, customized manner. In a preclinical lymphoma model, intratumoral injection of a Toll-like receptor 9 (TLR9) agonist induced systemic antitumor immunity and cured large, disseminated tumors.
Patients and Methods
We treated 15 patients with low-grade B-cell lymphoma using low-dose radiotherapy to a single tumor site and—at that same site—injected the C-G enriched, synthetic oligodeoxynucleotide (also referred to as CpG) TLR9 agonist PF-3512676. Clinical responses were assessed at distant, untreated tumor sites. Immune responses were evaluated by measuring T-cell activation after in vitro restimulation with autologous tumor cells.
This in situ vaccination maneuver was well-tolerated with only grade 1 to 2 local or systemic reactions and no treatment-limiting adverse events. One patient had a complete clinical response, three others had partial responses, and two patients had stable but continually regressing disease for periods significantly longer than that achieved with prior therapies. Vaccination induced tumor-reactive memory CD8 T cells. Some patients' tumors were able to induce a suppressive, regulatory phenotype in autologous T cells in vitro; these patients tended to have a shorter time to disease progression. One clinically responding patient received a second course of vaccination after relapse resulting in a second, more rapid clinical response.
In situ tumor vaccination with a TLR9 agonist induces systemic antilymphoma clinical responses. This maneuver is clinically feasible and does not require the production of a customized vaccine product.
We consider the problems of estimating the parameters as well as the structure of binary-valued Markov networks. For maximizing the penalized log-likelihood, we implement an approximate procedure based on the pseudo-likelihood of Besag (1975) and generalize it to a fast exact algorithm. The exact algorithm starts with the pseudo-likelihood solution and then adjusts the pseudo-likelihood criterion so that each additional iterations moves it closer to the exact solution. Our results show that this procedure is faster than the competing exact method proposed by Lee, Ganapathi, and Koller (2006a). However, we also find that the approximate pseudo-likelihood as well as the approaches of Wainwright et al. (2006), when implemented using the coordinate descent procedure of Friedman, Hastie, and Tibshirani (2008b), are much faster than the exact methods, and only slightly less accurate.
Markov networks; logistic regression; L1 penalty; model selection; Binary variables
We use convex relaxation techniques to provide a sequence of regularized low-rank solutions for large-scale matrix completion problems. Using the nuclear norm as a regularizer, we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm. Our algorithm Soft-Impute iteratively replaces the missing elements with those obtained from a soft-thresholded SVD. With warm starts this allows us to efficiently compute an entire regularization path of solutions on a grid of values of the regularization parameter. The computationally intensive part of our algorithm is in computing a low-rank SVD of a dense matrix. Exploiting the problem structure, we show that the task can be performed with a complexity linear in the matrix dimensions. Our semidefinite-programming algorithm is readily scalable to large matrices: for example it can obtain a rank-80 approximation of a 106 × 106 incomplete matrix with 105 observed entries in 2.5 hours, and can fit a rank 40 approximation to the full Netflix training set in 6.6 hours. Our methods show very good performance both in training and test error when compared to other competitive state-of-the art techniques.
CD81 is a tetraspanin cell surface protein that regulates CD19 expression in B lymphocytes and enables hepatitis C virus infection of human cells. Immunohistologic analysis in normal hematopoietic tissue showed strong staining for CD81 in normal germinal center B cells, a cell type in which its increased expression has not been previously recognized. High-dimensional flow cytometry analysis of normal hematopoietic tissue confirmed that among B and T cell subsets, germinal center B cells showed the highest level of CD81 expression. In over 800 neoplastic tissue samples, its expression was also found in a majority of non-Hodgkin lymphomas. Staining for CD81 was rarely seen in multiple myeloma, Hodgkin lymphoma, or myeloid leukemia. In hierarchical cluster analysis of diffuse large B cell lymphoma, staining for CD81 was most similar to other germinal center B cell-associated markers, particularly LMO2. By flow cytometry, CD81 was expressed in diffuse large B cell lymphoma cells independent of the presence or absence of CD10, another germinal center B cell marker. The detection of CD81 in routine biopsy samples and its differential expression in lymphoma subtypes, particularly diffuse large B cell lymphoma, warrants further study to assess CD81 expression and its role in the risk stratification of diffuse large B cell lymphoma patients.
CD81; lymphoma; tissue microarray
We consider the problem of estimating sparse graphs by a lasso penalty applied to the inverse covariance matrix. Using a coordinate descent procedure for the lasso, we develop a simple algorithm—the graphical lasso—that is remarkably fast: It solves a 1000-node problem (~500 000 parameters) in at most a minute and is 30–4000 times faster than competing methods. It also provides a conceptual link between the exact problem and the approximation suggested by Meinshausen and Bühlmann (2006). We illustrate the method on some cell-signaling data from proteomics.
Gaussian covariance; Graphical model; L1; Lasso
Diffuse large B cell lymphoma (DLBCL) is clinically and biologically heterogeneous. In most cases of DLBCL, lymphoma cells coexpress vascular endothelial growth factor (VEGF) and its receptors VEGFR1 and VEGFR2, suggesting autocrine in addition to angiogenic effects. We enumerated microvessel density and scored lymphoma cell expression of VEGF, VEGFR1, VEGFR2 and phosphorylated VEGFR2 in 162 de novo DLBCL patients treated with R-CHOP (rituximab, cyclophosphamide, vincristine, doxorubicin and prednisone)-like regimens. VEGFR2 expression correlated with shorter overall survival (OS) independent of International Prognostic Index (IPI) (p=0.0028). Phosphorylated VEGFR2 (detected in 13% of cases) correlated with shorter progression-free survival (PFS, p=0.044) and trended toward shorter OS on univariate analysis. VEGFR1 was not predictive of survival on univariate analysis, but it did correlate with better OS on multivariate analysis with VEGF, VEGFR2, and IPI (p=0.036); in patients with weak VEGFR2, lack of VEGFR1 coexpression was significantly correlated with poor OS independent of IPI (p=0.01). These results are concordant with our prior finding of an association of VEGFR1 with longer OS in DLBCL treated with chemotherapy alone. We postulate that VEGFR1 may oppose autocrine VEGFR2 signaling in DLBCL by competing for VEGF binding. In contrast to our prior results with chemotherapy alone, microvessel density was not prognostic of PFS or OS with R-CHOP-like therapy.
Non-Hodgkin lymphoma; VEGF; angiogenesis; tumour biology; prognostic factors
We consider the problem of clustering observations using a potentially large set of features. One might expect that the true underlying clusters present in the data differ only with respect to a small fraction of the features, and will be missed if one clusters the observations using the full set of features. We propose a novel framework for sparse clustering, in which one clusters the observations using an adaptively chosen subset of the features. The method uses a lasso-type penalty to select the features. We use this framework to develop simple methods for sparse K-means and sparse hierarchical clustering. A single criterion governs both the selection of the features and the resulting clusters. These approaches are demonstrated on simulated data and on genomic data sets.
Leiomyosarcoma (LMS) is a soft tissue tumor with a significant degree of morphologic and molecular heterogeneity. We employed integrative molecular profiling to discover and characterize molecular subtypes of LMS. Gene expression profiling was performed on 51 LMS samples. Unsupervised clustering demonstrated 3 reproducible LMS clusters. Array comparative genomic hybridization (aCGH) was performed on 20 LMS samples and demonstrated that the molecular subtypes defined by gene-expression showed distinct genomic changes. Tumors from the “muscle-enriched” cluster showed significantly increased copy number changes (p=0.04). Most muscle-enriched cases showed loss at 16q24 which contains FANCA, known to play an important role in DNA repair, and loss at 1p36 which contains PRDM16, whose loss promotes muscle differentiation. Immunohistochemistry was performed on LMS tissue microarrays (n=377) for five markers with high levels of mRNA in the muscle-enriched cluster (ACTG2, CASQ2, SLMAP,CFL2, MYLK) and demonstrated significantly correlated expression of the 5 proteins (all pairwise p < 0.005). Expression of the 5 markers was associated with improved disease-specific survival (DSS) in a multivariate Cox regression analysis (p < 0.04). In this analysis that combined gene expression profiling, aCGH and immunohistochemistry, we characterized distinct molecular LMS subtypes, provided insight into their pathogenesis, and identified prognostic biomarkers.
sarcoma; leiomyosarcoma; integrative genomics; gene expression profiling; array comparative genomic hybridization; tissue microarrays
We present a penalized matrix decomposition (PMD), a new framework for computing a rank-K approximation for a matrix. We approximate the matrix X as , where dk, uk, and vk minimize the squared Frobenius norm of X, subject to penalties on uk and vk. This results in a regularized version of the singular value decomposition. Of particular interest is the use of L1-penalties on uk and vk, which yields a decomposition of X using sparse vectors. We show that when the PMD is applied using an L1-penalty on vk but not on uk, a method for sparse principal components results. In fact, this yields an efficient algorithm for the “SCoTLASS” proposal (Jolliffe and others 2003) for obtaining sparse principal components. This method is demonstrated on a publicly available gene expression data set. We also establish connections between the SCoTLASS method for sparse principal component analysis and the method of Zou and others (2006). In addition, we show that when the PMD is applied to a cross-products matrix, it results in a method for penalized canonical correlation analysis (CCA). We apply this penalized CCA method to simulated data and to a genomic data set consisting of gene expression and DNA copy number measurements on the same set of samples.
Canonical correlation analysis; DNA copy number; Integrative genomic analysis; L1; Matrix decomposition; Principal component analysis; Sparse principal component analysis; SVD
In recent work, several authors have introduced methods for sparse canonical correlation analysis (sparse CCA). Suppose that two sets of measurements are available on the same set of observations. Sparse CCA is a method for identifying sparse linear combinations of the two sets of variables that are highly correlated with each other. It has been shown to be useful in the analysis of high-dimensional genomic data, when two sets of assays are available on the same set of samples. In this paper, we propose two extensions to the sparse CCA methodology. (1) Sparse CCA is an unsupervised method; that is, it does not make use of outcome measurements that may be available for each observation (e.g., survival time or cancer subtype). We propose an extension to sparse CCA, which we call sparse supervised CCA, which results in the identification of linear combinations of the two sets of variables that are correlated with each other and associated with the outcome. (2) It is becoming increasingly common for researchers to collect data on more than two assays on the same set of samples; for instance, SNP, gene expression, and DNA copy number measurements may all be available. We develop sparse multiple CCA in order to extend the sparse CCA methodology to the case of more than two data sets. We demonstrate these new methods on simulated data and on a recently published and publicly available diffuse large B-cell lymphoma data set.
Ultra-high throughput sequencing technologies provide opportunities both for discovery of novel molecular species and for detailed comparisons of gene expression patterns. Small RNA populations are particularly well suited to this analysis, as many different small RNAs can be completely sequenced in a single instrument run.
We prepared small RNA libraries from 29 tumour/normal pairs of human cervical tissue samples. Analysis of the resulting sequences (42 million in total) defined 64 new human microRNA (miRNA) genes. Both arms of the hairpin precursor were observed in twenty-three of the newly identified miRNA candidates. We tested several computational approaches for the analysis of class differences between high throughput sequencing datasets and describe a novel application of a log linear model that has provided the most effective analysis for this data. This method resulted in the identification of 67 miRNAs that were differentially-expressed between the tumour and normal samples at a false discovery rate less than 0.001.
This approach can potentially be applied to any kind of RNA sequencing data for analysing differential sequence representation between biological sample sets.
We propose a method for prediction in Cox's proportional model, when the number of features (regressors), p, exceeds the number of observations, n. The method assumes that the features are independent in each risk set, so that the partial likelihood factors into a product. As such, it is analogous to univariate thresholding in linear regression and nearest shrunken centroids in classification. We call the procedure Cox univariate shrinkage and demonstrate its usefulness on real and simulated data. The method has the attractive property of being essentially univariate in its operation: the features are entered into the model based on the size of their Cox score statistics. We illustrate the new method on real and simulated data, and compare it to other proposed methods for survival prediction with a large number of predictors.
Prostate cancer is thought to arise as a result of oxidative stresses and induction of antioxidant electrophile defense (phase 2) enzymes has been proposed as a prostate cancer prevention strategy. The isothiocyanate sulforaphane, derived from cruciferous vegetables like broccoli, potently induces surrogate markers of phase 2 enzyme activity in prostate cells in vitro and in vivo. To better understand the temporal effects of sulforaphane and broccoli sprouts on gene expression in prostate cells, we carried out comprehensive transcriptome analysis using cDNA microarrays.
Transcripts significantly modulated by sulforaphane over time were identified using StepMiner analysis. Ingenuity Pathway Analysis (IPA) analysis was used to identify biological pathways, networks and functions significantly altered by sulforaphane treatment.
StepMiner and IPA revealed significant changes in many transcripts associated with cell growth and the cell cycle, as well as a significant number associated with cellular response to oxidative damage and stress. Comparison to an existing dataset suggested that sulforaphane blocked cell growth by inducing G2/M arrest. Cell growth assays and flow cytometry analysis confirmed that sulforaphane inhibited cell growth and induced cell cycle arrest.
Our data suggests that in prostate cells sulforaphane primarily induces cellular defenses and inhibits cell growth by causing G2/M phase arrest. Furthermore, based on the striking similarities in the gene expression patterns induced across experiments in these cells, sulforaphane appears to be the primary bioactive compound present in broccoli sprouts, suggesting that broccoli sprouts can serve as a suitable source for sulforaphane in intervention trials.
Sulforaphane; microarray; gene expression; prostate cancer; cancer prevention
Gene expression microarrays are the most widely used technique for genome-wide expression profiling. However, microarrays do not perform well on formalin fixed paraffin embedded tissue (FFPET). Consequently, microarrays cannot be effectively utilized to perform gene expression profiling on the vast majority of archival tumor samples. To address this limitation of gene expression microarrays, we designed a novel procedure (3′-end sequencing for expression quantification (3SEQ)) for gene expression profiling from FFPET using next-generation sequencing. We performed gene expression profiling by 3SEQ and microarray on both frozen tissue and FFPET from two soft tissue tumors (desmoid type fibromatosis (DTF) and solitary fibrous tumor (SFT)) (total n = 23 samples, which were each profiled by at least one of the four platform-tissue preparation combinations). Analysis of 3SEQ data revealed many genes differentially expressed between the tumor types (FDR<0.01) on both the frozen tissue (∼9.6K genes) and FFPET (∼8.1K genes). Analysis of microarray data from frozen tissue revealed fewer differentially expressed genes (∼4.64K), and analysis of microarray data on FFPET revealed very few (69) differentially expressed genes. Functional gene set analysis of 3SEQ data from both frozen tissue and FFPET identified biological pathways known to be important in DTF and SFT pathogenesis and suggested several additional candidate oncogenic pathways in these tumors. These findings demonstrate that 3SEQ is an effective technique for gene expression profiling from archival tumor samples and may facilitate significant advances in translational cancer research.
In recent years, many methods have been developed for regression in high-dimensional settings. We propose covariance-regularized regression, a family of methods that use a shrunken estimate of the inverse covariance matrix of the features in order to achieve superior prediction. An estimate of the inverse covariance matrix is obtained by maximizing its log likelihood, under a multivariate normal model, subject to a constraint on its elements; this estimate is then used to estimate coefficients for the regression of the response onto the features. We show that ridge regression, the lasso, and the elastic net are special cases of covariance-regularized regression, and we demonstrate that certain previously unexplored forms of covariance-regularized regression can outperform existing methods in a range of situations. The covariance-regularized regression framework is extended to generalized linear models and linear discriminant analysis, and is used to analyze gene expression data sets with multiple class and survival outcomes.
regression; classification; n ≪ p; covariance regularization