Joseph E. Lucas

High-Dimensional Sparse Factor Modeling: Applications in Gene Expression Genomics

We describe studies in molecular profiling and biological pathway analysis that use sparse latent factor and regression models for microarray gene expression data. We discuss breast cancer applications and key aspects of the modeling and computational methodology. Our case studies aim to investigate and characterize heterogeneity of structure related to specific oncogenic pathways, as well as links between aggregate patterns in gene expression profiles and clinical biomarkers. Based on the metaphor of statistically derived “factors” as representing biological “subpathway” structure, we explore the decomposition of fitted sparse factor models into pathway subcomponents and investigate how these components overlay multiple aspects of known biological activity. Our methodology is based on sparsity modeling of multivariate regression, ANOVA, and latent factor models, as well as a class of models that combines all components. Hierarchical sparsity priors address questions of dimension reduction and multiple comparisons, as well as scalability of the methodology. The models include practically relevant non-Gaussian/nonparametric components for latent structure, underlying often quite complex non-Gaussianity in multivariate expression patterns. Model search and fitting are addressed through stochastic simulation and evolutionary stochastic search methods that are exemplified in the oncogenic pathway studies. Supplementary supporting material provides more details of the applications, as well as examples of the use of freely available software tools for implementing the methodology.

A pathway-based classification of human breast cancer

The hallmark of human cancer is heterogeneity, reflecting the complexity and variability of the vast array of somatic mutations acquired during oncogenesis. An ability to dissect this heterogeneity, to identify subgroups that represent common mechanisms of disease, will be critical to understanding the complexities of genetic alterations and to provide a framework to develop rational therapeutic strategies. Here, we describe a classification scheme for human breast cancer making use of patterns of pathway activity to build on previous subtype characterizations using intrinsic gene expression signatures, to provide a functional interpretation of the gene expression data that can be linked to therapeutic options. We show that the identified subgroups provide a robust mechanism for classifying independent samples, identifying tumors that share patterns of pathway activity and exhibit similar clinical and biological properties, including distinct patterns of chromosomal alterations that were not evident in the heterogeneous total population of tumors. We propose that this classification scheme provides a basis for understanding the complex mechanisms of oncogenesis that give rise to these tumors and to identify rational opportunities for combination therapies.

The Genomic Analysis of Lactic Acidosis and Acidosis Response in Human Cancers

The tumor microenvironment has a significant impact on tumor development. Two important determinants in this environment are hypoxia and lactic acidosis. Although lactic acidosis has long been recognized as an important factor in cancer, relatively little is known about how cells respond to lactic acidosis and how that response relates to cancer phenotypes. We develop genome-scale gene expression studies to dissect transcriptional responses of primary human mammary epithelial cells to lactic acidosis and hypoxia in vitro and to explore how they are linked to clinical tumor phenotypes in vivo. The resulting experimental signatures of responses to lactic acidosis and hypoxia are evaluated in a heterogeneous set of breast cancer datasets. A strong lactic acidosis response signature identifies a subgroup of low-risk breast cancer patients having distinct metabolic profiles suggestive of a preference for aerobic respiration. The association of lactic acidosis response with good survival outcomes may relate to the role of lactic acidosis in directing energy generation toward aerobic respiration and utilization of other energy sources via inhibition of glycolysis. This “inhibition of glycolysis” phenotype in tumors is likely caused by the repression of glycolysis gene expression and Akt inhibition. Our study presents a genomic evaluation of the prognostic information of a lactic acidosis response independent of the hypoxic response. Our results identify causal roles of lactic acidosis in metabolic reprogramming, and the direct functional consequence of lactic acidosis pathway activity on cellular responses and tumor development. The study also demonstrates the utility of genomic analysis that maps expression-based findings from in vitro experiments to human samples to assess links to in vivo clinical phenotypes.

A Genomic Strategy to Elucidate Modules of Oncogenic Pathway Signaling Networks

Recent studies have emphasized the importance of pathway-specific interpretations for understanding the functional relevance of gene alterations in human cancers. Although signaling activities are often conceptualized as linear events, in reality, they reflect the activity of complex functional networks assembled from modules that each respond to input signals. To acquire a deeper understanding of this network structure, we developed an approach to deconstruct pathways into modules represented by gene expression signatures. Our studies confirm that they represent units of underlying biological activity linked to known biochemical pathway structures. Importantly, we show that these signaling modules provide tools to dissect the complexity of oncogenic states that define disease outcomes as well as response to pathway-specific therapeutics. We propose that this model of pathway structure constitutes a framework to study the processes by which information propogates through cellular networks and to elucidate the relationships of fundamental modules to cellular and clinical phenotypes.

A host transcriptional signature for presymptomatic detection of infection in humans exposed to influenza H1N1 or H3N2.

There is great potential for host-based gene expression analysis to impact the early diagnosis of infectious diseases. In particular, the influenza pandemic of 2009 highlighted the challenges and limitations of traditional pathogen-based testing for suspected upper respiratory viral infection. We inoculated human volunteers with either influenza A (A/Brisbane/59/2007 (H1N1) or A/Wisconsin/67/2005 (H3N2)), and assayed the peripheral blood transcriptome every 8 hours for 7 days. Of 41 inoculated volunteers, 18 (44%) developed symptomatic infection. Using unbiased sparse latent factor regression analysis, we generated a gene signature (or factor) for symptomatic influenza capable of detecting 94% of infected cases. This gene signature is detectable as early as 29 hours post-exposure and achieves maximal accuracy on average 43 hours (p = 0.003, H1N1) and 38 hours (p-value = 0.005, H3N2) before peak clinical symptoms. In order to test the relevance of these findings in naturally acquired disease, a composite influenza A signature built from these challenge studies was applied to Emergency Department patients where it discriminates between swine-origin influenza A/H1N1 (2009) infected and non-infected individuals with 92% accuracy. The host genomic response to Influenza infection is robust and may provide the means for detection before typical clinical symptoms are apparent.

Functional Interaction between Responses to Lactic Acidosis and Hypoxia Regulates Genomic Transcriptional Outputs

Within solid tumor microenvironments, lactic acidosis, and hypoxia each have powerful effects on cancer pathophysiology. However, the influence that these processes exert on each other is unknown. Here, we report that a significant portion of the transcriptional response to hypoxia elicited in cancer cells is abolished by simultaneous exposure to lactic acidosis. In particular, lactic acidosis abolished stabilization of HIF-1α protein which occurs normally under hypoxic conditions. In contrast, lactic acidosis strongly synergized with hypoxia to activate the unfolded protein response (UPR) and an inflammatory response, displaying a strong similarity to ATF4-driven amino acid deprivation responses (AAR). In certain breast tumors and breast tumor cells examined, an integrative analysis of gene expression and array CGH data revealed DNA copy number alterations at the ATF4 locus, an important activator of the UPR/AAR pathway. In this setting, varying ATF4 levels influenced the survival of cells after exposure to hypoxia and lactic acidosis. Our findings reveal that the condition of lactic acidosis present in solid tumors inhibits canonical hypoxia responses and activates UPR and inflammation responses. Furthermore, these data suggest that ATF4 status may be a critical determinant of the ability of cancer cells to adapt to oxygen and acidity fluctuations in the tumor microenvironment, perhaps linking short-term transcriptional responses to long-term selection for copy number alterations in cancer cells.

Bayesian Gaussian Copula Factor Models for Mixed Data

Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables or through generalized latent trait models accommodating measurements in the exponential family. However, when generalizing to non-Gaussian measured variables, the latent variables typically influence both the dependence structure and the form of the marginal distributions, complicating interpretation and introducing artifacts. To address this problem, we propose a novel class of Bayesian Gaussian copula factor models that decouple the latent factors from the marginal distributions. A semiparametric specification for the marginals based on the extended rank likelihood yields straightforward implementation and substantial computational gains. We provide new theoretical and empirical justifications for using this likelihood in Bayesian inference. We propose new default priors for the factor loadings and develop efficient parameter-expanded Gibbs sampling for posterior computation. The methods are evaluated through simulations and applied to a dataset in political science. The models in this article are implemented in the R package bfa (available from http://stat.duke.edu/jsm38/software/bfa). Supplementary materials for this article are available online.

Bayesian joint analysis of heterogeneous genomics data

SUMMARY A non-parametric Bayesian factor model is proposed for joint analysis of multi-platform genomics data. The approach is based on factorizing the latent space (feature space) into a shared component and a data-specific component with the dimensionality of these components (spaces) inferred via a beta-Bernoulli process. The proposed approach is demonstrated by jointly analyzing gene expression/copy number variations and gene expression/methylation data for ovarian cancer patients, showing that the proposed model can potentially uncover key drivers related to cancer. AVAILABILITY AND IMPLEMENTATION The source code for this model is written in MATLAB and has been made publicly available at https://sites.google.com/site/jointgenomics/. CONTACT catherine.ll.zheng@gmail.com SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.

High predictive accuracy of an unbiased proteomic profile for sustained virologic response in chronic hepatitis C patients

Chronic hepatitis C (CHC) infection is a leading cause of endstage liver disease. Current standard‐of‐care (SOC) interferon‐based therapy results in sustained virological response (SVR) in only one‐half of patients, and is associated with significant side effects. Accurate host predictors of virologic response are needed to individualize treatment regimens. We applied a label‐free liquid chromatography mass spectrometry (LC‐MS)‐based proteomics discovery platform to pretreatment sera from a well‐characterized and matched training cohort of 55 CHC patients, and an independent validation set of 41 CHC genotype 1 patients with characterized IL28B genotype. Accurate mass and retention time methods aligned samples to generate quantitative peptide data, with predictive modeling using Bayesian sparse latent factor regression. We identified 105 proteins of interest with two or more peptides, and a total of 3,768 peptides. Regression modeling selected three identified metaproteins, vitamin D binding protein, alpha 2 HS glycoprotein, and Complement C5, with a high predictive area under the receiver operator characteristic curve (AUROC) of 0.90 for SVR in the training cohort. A model averaging approach for identified peptides resulted in an AUROC of 0.86 in the validation cohort, and correctly identified virologic response in 71% of patients without the favorable IL28B “responder” genotype. Conclusion: Our preliminary data indicate that a serum‐based protein signature can accurately predict treatment response to current SOC in most CHC patients. (HEPATOLOGY 2011)

Latent Factor Analysis to Discover Pathway-Associated Putative Segmental Aneuploidies in Human Cancers

Tumor microenvironmental stresses, such as hypoxia and lactic acidosis, play important roles in tumor progression. Although gene signatures reflecting the influence of these stresses are powerful approaches to link expression with phenotypes, they do not fully reflect the complexity of human cancers. Here, we describe the use of latent factor models to further dissect the stress gene signatures in a breast cancer expression dataset. The genes in these latent factors are coordinately expressed in tumors and depict distinct, interacting components of the biological processes. The genes in several latent factors are highly enriched in chromosomal locations. When these factors are analyzed in independent datasets with gene expression and array CGH data, the expression values of these factors are highly correlated with copy number alterations (CNAs) of the corresponding BAC clones in both the cell lines and tumors. Therefore, variation in the expression of these pathway-associated factors is at least partially caused by variation in gene dosage and CNAs among breast cancers. We have also found the expression of two latent factors without any chromosomal enrichment is highly associated with 12q CNA, likely an instance of “trans”-variations in which CNA leads to the variations in gene expression outside of the CNA region. In addition, we have found that factor 26 (1q CNA) is negatively correlated with HIF-1α protein and hypoxia pathways in breast tumors and cell lines. This agrees with, and for the first time links, known good prognosis associated with both a low hypoxia signature and the presence of CNA in this region. Taken together, these results suggest the possibility that tumor segmental aneuploidy makes significant contributions to variation in the lactic acidosis/hypoxia gene signatures in human cancers and demonstrate that latent factor analysis is a powerful means to uncover such a linkage.