Mike West

Bayesian Density Estimation and Inference Using Mixtures

Abstract We describe and illustrate Bayesian inference in models for density estimation using mixtures of Dirichlet processes. These models provide natural settings for density estimation and are exemplified by special cases where data are modeled as a sample from mixtures of normal distributions. Efficient simulation methods are used to approximate various prior, posterior, and predictive distributions. This allows for direct inference on a variety of practical issues, including problems of local versus global smoothing, uncertainty about density estimates, assessment of modality, and the inference on the numbers of components. Also, convergence results are established for a general class of normal mixture models.

Oncogenic pathway signatures in human cancers as a guide to targeted therapies

The development of an oncogenic state is a complex process involving the accumulation of multiple independent mutations that lead to deregulation of cell signalling pathways central to the control of cell growth and cell fate. The ability to define cancer subtypes, recurrence of disease and response to specific therapies using DNA microarray-based gene expression signatures has been demonstrated in multiple studies. Various studies have also demonstrated the potential for using gene expression profiles for the analysis of oncogenic pathways. Here we show that gene expression signatures can be identified that reflect the activation status of several oncogenic pathways. When evaluated in several large collections of human cancers, these gene expression signatures identify patterns of pathway deregulation in tumours and clinically relevant associations with disease outcomes. Combining signature-based predictions across several pathways identifies coordinated patterns of pathway deregulation that distinguish between specific cancers and tumour subtypes. Clustering tumours based on pathway signatures further defines prognosis in respective patient subsets, demonstrating that patterns of oncogenic pathway deregulation underlie the development of the oncogenic phenotype and reflect the biology and outcome of specific cancers. Predictions of pathway deregulation in cancer cell lines are also shown to predict the sensitivity to therapeutic agents that target components of the pathway. Linking pathway deregulation with sensitivity to therapeutics that target components of the pathway provides an opportunity to make use of these oncogenic pathway signatures to guide the use of targeted therapeutics.

Predicting the clinical status of human breast cancer by using gene expression profiles

Prognostic and predictive factors are indispensable tools in the treatment of patients with neoplastic disease. For the most part, such factors rely on a few specific cell surface, histological, or gross pathologic features. Gene expression assays have the potential to supplement what were previously a few distinct features with many thousands of features. We have developed Bayesian regression models that provide predictive capability based on gene expression data derived from DNA microarray analysis of a series of primary breast cancer samples. These patterns have the capacity to discriminate breast tumors on the basis of estrogen receptor status and also on the categorized lymph node status. Importantly, we assess the utility and validity of such models in predicting the status of tumors in crossvalidation determinations. The practical value of such approaches relies on the ability not only to assess relative probabilities of clinical outcomes for future samples but also to provide an honest assessment of the uncertainties associated with such predictive classifications on the basis of the selection of gene subsets for each validation analysis. This latter point is of critical importance in the ability to apply these methodologies to clinical assessment of tumor phenotype.

Gene expression predictors of breast cancer outcomes

BACKGROUND Correlation of risk factors with genomic data promises to provide specific treatment for individual patients, and needs interpretation of complex, multivariate patterns in gene expression data, as well as assessment of their ability to improve clinical predictions. We aimed to predict nodal metastatic states and relapse for breast cancer patients. METHODS We analysed DNA microarray data from samples of primary breast tumours, using non-linear statistical analyses to assess multiple patterns of interactions of groups of genes that have predictive value for the individual patient, with respect to lymph node metastasis and cancer recurrence. FINDINGS We identified aggregate patterns of gene expression (metagenes) that associate with lymph node status and recurrence, and that are capable of predicting outcomes in individual patients with about 90% accuracy. The metagenes defined distinct groups of genes, suggesting different biological processes underlying these two characteristics of breast cancer. Initial external validation came from similarly accurate predictions of nodal status of a small sample in a distinct population. INTERPRETATION Multiple aggregate measures of profiles of gene expression define valuable predictive associations with lymph node metastasis and disease recurrence for individual patients. Gene expression data have the potential to aid accurate, individualised, prognosis. Importantly, these data are assessed in terms of precise numerical predictions, with ranges of probabilities of outcome. Precise and statistically valid assessments of risks specific for patients, will ultimately be of most value to clinicians faced with treatment decisions.

Combined Parameter and State Estimation in Simulation-Based Filtering

Much of the recent and current interest in simulation-based methods of sequential Bayesian analysis of dynamic models has been focused on improved methods of filtering for time-varying state vectors. We now have quite effective algorithms for time-varying states, as represented throughout this volume. Variants of the auxiliary particle filtering algorithm (Pitt and Shephard 1999b), in particular, are of proven applied efficacy in quite elaborate models. However, the need for more general algorithms that deal simultaneously with both fixed model parameters and state variables is especially pressing. We simply do not have access to efficient and effective methods of treating this problem, especially in models with realistically large numbers of fixed model parameters. It is a very challenging problem.

Role for E2F in Control of Both DNA Replication and Mitotic Functions as Revealed from DNA Microarray Analysis

ABSTRACT We have used high-density DNA microarrays to provide an analysis of gene regulation during the mammalian cell cycle and the role of E2F in this process. Cell cycle analysis was facilitated by a combined examination of gene control in serum-stimulated fibroblasts and cells synchronized at G1/S by hydroxyurea block that were then released to proceed through the cell cycle. The latter approach (G1/S synchronization) is critical for rigorously maintaining cell synchrony for unambiguous analysis of gene regulation in later stages of the cell cycle. Analysis of these samples identified seven distinct clusters of genes that exhibit unique patterns of expression. Genes tend to cluster within these groups based on common function and the time during the cell cycle that the activity is required. Placed in this context, the analysis of genes induced by E2F proteins identified genes or expressed sequence tags not previously described as regulated by E2F proteins; surprisingly, many of these encode proteins known to function during mitosis. A comparison of the E2F-induced genes with the patterns of cell growth-regulated gene expression revealed that virtually all of the E2F-induced genes are found in only two of the cell cycle clusters; one group was regulated at G1/S, and the second group, which included the mitotic activities, was regulated at G2. The activation of the G2 genes suggests a broader role for E2F in the control of both DNA replication and mitotic activities.

Monte Carlo Smoothing for Nonlinear Time Series

We develop methods for performing smoothing computations in general state-space models. The methods rely on a particle representation of the filtering distributions, and their evolution through time using sequential importance sampling and resampling ideas. In particular, novel techniques are presented for generation of sample realizations of historical state sequences. This is carried out in a forward-filtering backward-smoothing procedure that can be viewed as the nonlinear, non-Gaussian counterpart of standard Kalman filter-based simulation smoothers in the linear Gaussian case. Convergence in the mean squared error sense of the smoothed trajectories is proved, showing the validity of our proposed method. The methods are tested in a substantial application for the processing of speech signals represented by a time-varying autoregression and parameterized in terms of time-varying partial correlation coefficients, comparing the results of our algorithm with those from a simple smoother based on the filtered trajectories.

Dynamic Generalized Linear Models and Bayesian Forecasting

Abstract Dynamic Bayesian models are developed for application in nonlinear, non-normal time series and regression problems, providing dynamic extensions of standard generalized linear models. A key feature of the analysis is the use of conjugate prior and posterior distributions for the exponential family parameters. This leads to the calculation of closed, standard-form predictive distributions for forecasting and model criticism. The structure of the models depends on the time evolution of underlying state variables, and the feedback of observational information to these variables is achieved using linear Bayesian prediction methods. Data analytic aspects of the models concerning scale parameters and outliers are discussed, and some applications are provided. Dynamic Bayesian models are developed for application in nonlinear, non-normal time series and regression problems, providing dynamic extensions of standard generalized linear models. A key feature of the analysis is the use of conjugate prior and...

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.

Bayesian Dynamic Factor Models and Portfolio Allocation

We discuss the development of dynamic factor models for multivariate financial time series, and the incorporation of stochastic volatility components for latent factor processes. Bayesian inference and computation is developed and explored in a study of the dynamic factor structure of daily spot exchange rates for a selection of international currencies. The models are direct generalizations of univariate stochastic volatility models and represent specific varieties of models recently discussed in the growing multivariate stochastic volatility literature. We discuss model fitting based on retrospective data and sequential analysis for forward filtering and short-term forecasting. Analyses are compared with results from the much simpler method of dynamic variance-matrix discounting that, for over a decade, has been a standard approach in applied financial econometrics. We study these models in analysis, forecasting, and sequential portfolio allocation for a selected set of international exchange-rate-return time series. Our goals are to understand a range of modeling questions arising in using these factor models and to explore empirical performance in portfolio construction relative to discount approaches. We report on our experiences and conclude with comments about the practical utility of structured factor models and on future potential model extensions.