Resolving conflicts between statistical methods by probability combination: Application to empirical Bayes analyses of genomic data
David R. Bickel
发表信息：
D. R. Bickel, Game-theoretic probability combination with applications to resolving conflicts between statistical methods, International Journal of Approximate Reasoning 53, 880-891 (2012)
In the typical analysis of a data set, a single method is selected for statistical reporting even when equally applicable methods yield very different results. Examples of equally applicable methods can correspond to those of different ancillary statistics in frequentist inference and of different prior distributions in Bayesian inference. More broadly, choices are made between parametric and nonparametric methods and between frequentist and Bayesian methods.
Rather than choosing a single method, it can be safer, in a game-theoretic sense, to combine those that are equally appropriate in light of the available information. Since methods of combining subjectively assessed probability distributions are not objective enough for that purpose, this paper introduces a method of distribution combination that does not require any assignment of distribution weights. It does so by formalizing a hedging strategy in terms of a game between three players: nature, a statistician combining distributions, and a statistician refusing to combine distributions. The optimal move of the first statistician reduces to the solution of a simpler problem of selecting an estimating distribution that minimizes the Kullback-Leibler loss maximized over the plausible distributions to be combined. The resulting combined distribution is a linear combination of the most extreme of the distributions to be combined that are scientifically plausible. The optimal weights are close enough to each other that no extreme distribution dominates the others.
The new methodology is illustrated by combining conflicting empirical Bayes methodologies in the context of gene expression data analysis.
Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional independence has been studied using sparse Gaussian graphical models for continuous data and sparse Ising models for discrete data. However, there are two clear situations when these approaches are inadequate. The first occurs when the data are continuous but display non-normal marginal behavior such as heavy tails or skewness, rendering an assumption of norma…
Recent breakthroughs in cancer research have come via the up-and-coming field of pathway analysis. By applying statistical methods to prior known gene and protein regulatory information, pathway analysis provides a meaningful way to interpret genomic data. While many gene/protein regulatory relationships have been studied, never before has such a significant amount data been made available in organized forms of gene/protein regulatory networks and pathways. However, pathway analysis research is still in its infancy, especially when applying it to solve practical problems. In this paper we prop…
Rapid advancements in collection and dissemination of multi-platform molecular and genomics data has resulted in enormous opportunities to aggregate such data in order to understand, prevent, and treat human diseases. While significant improvements have been made in multi-omic data integration methods to discover biological markers and mechanisms underlying both prognosis and treatment, the precise cellular functions governing these complex mechanisms still need detailed and data-driven de-novo evaluations. We propose a framework called Functional Integrative Bayesian Analysis of High-dimensio…
Significant advances in biotechnology have allowed for simultaneous measurement of molecular data points across multiple genomic and transcriptomic levels from a single tumor/cancer sample. This has motivated systematic approaches to integrate multi-dimensional structured datasets since cancer development and progression is driven by numerous co-ordinated molecular alterations and the interactions between them. We propose a novel two-step Bayesian approach that combines a variable selection framework with integrative structure learning between multiple sources of data. The structure learning i…
Integrative network modeling of data arising from multiple genomic platforms provides insight into the holistic picture of the interactive system, as well as the flow of information across many disease domains including cancer. The basic data structure consists of a sequence of hierarchically ordered datasets for each individual subject, which facilitates integration of diverse inputs, such as genomic, transcriptomic, and proteomic data. A primary analytical task in such contexts is to model the layered architecture of networks where the vertices can be naturally partitioned into ordered layer…
Simultaneous analysis of gene expression data and genetic variants is highly of interest, especially when the number of gene expressions and genetic variants are both greater than the sample size. Association of both causal genes and effective SNPs makes the use of sparse modeling of such genetic data sets, highly important. The high-dimensional sparse instrumental variables models are one of such useful association models, which models the simultaneous relation of the gene expressions and genetic variants with complex traits. From a Bayesian viewpoint, the sparsity can be favored using sparsi…
Motivated by the genomic application of expression quantitative trait loci (eQTL) mapping, we propose a new procedure to perform simultaneous testing of multiple hypotheses using Bayes factors as input test statistics. One of the most significant features of this method is its robustness in controlling the targeted false discovery rate (FDR) even under misspecifications of parametric alternative models. Moreover, the proposed procedure is highly computationally efficient, which is ideal for treating both complex system and big data in genomic applications. We discuss the theoretical properties…
Seemingly unrelated regression is a natural framework for regressing multiple correlated responses on multiple predictors. The model is very flexible, with multiple linear regression and covariance selection models being special cases. However, its practical deployment in genomic data analysis under a Bayesian framework is limited due to both statistical and computational challenges. The statistical challenge is that one needs to infer both the mean vector and the inverse covariance matrix, a problem inherently more complex than separately estimating each. The computational challenge is due to…
We introduce a sparse high-dimensional regression approach that can incorporate prior information on the regression parameters and can borrow information across a set of similar datasets. Prior information may for instance come from previous studies or genomic databases, and information borrowed across a set of genes or genomic networks. The approach is based on prior modelling of the regression parameters using the horseshoe prior, with a prior on the sparsity index that depends on external information. Multiple datasets are integrated by applying an empirical Bayes strategy on hyperparameter…
Modern cancer genomics datasets involve widely varying sizes and scales, measurement variables, and correlation structures. A fundamental analytical goal in these high-throughput studies is the development of general statistical techniques that can cleanly sift the signal from noise in identifying disease-specific genomic signatures across a set of experimental or biological conditions. We propose BayesDiff, a nonparametric Bayesian approach based on a novel class of first order mixture models, called the Sticky Poisson-Dirichlet process or multicuisine restaurant franchise. The BayesDiff meth…
It is well known that the integration among different data-sources is reliable because of its potential of unveiling new functionalities of the genomic expressions which might be dormant in a single source analysis. Moreover, different studies have justified the more powerful analyses of multi-platform data. Toward this, in this study, we consider the circadian genes' omics profile such as copy number changes and RNA sequence data along with their survival response. We develop a Bayesian structural equation modeling coupled with linear regressions and log normal accelerated failure time regres…
The analysis of large-scale datasets, especially in biomedical contexts, frequently involves a principled screening of multiple hypotheses. The celebrated two-group model jointly models the distribution of the test statistics with mixtures of two competing densities, the null and the alternative distributions. We investigate the use of weighted densities and, in particular, non-local densities as working alternative distributions, to enforce separation from the null and thus refine the screening procedure. We show how these weighted alternatives improve various operating characteristics, such …
Rapid technological advances have allowed for molecular profiling across multiple omics domains from a single sample for clinical decision making in many diseases, especially cancer. As tumor development and progression are dynamic biological processes involving composite genomic aberrations, key challenges are to effectively assimilate information from these domains to identify genomic signatures and biological entities that are druggable, develop accurate risk prediction profiles for future patients, and identify novel patient subgroups for tailored therapy and monitoring. We propose integra…
A major goal in genomics is to properly capture the complex dynamical behaviors of gene regulatory networks (GRNs). This includes inferring the complex interactions between genes, which can be used for a wide range of genomics analyses, including diagnosis or prognosis of diseases and finding effective treatments for chronic diseases such as cancer. Boolean networks have emerged as a successful class of models for capturing the behavior of GRNs. In most practical settings, inference of GRNs should be achieved through limited and temporally sparse genomics data. A large number of genes in GRNs …
We propose small-variance asymptotic approximations for the inference of tumor heterogeneity (TH) using next-generation sequencing data. Understanding TH is an important and open research problem in biology. The lack of appropriate statistical inference is a critical gap in existing methods that the proposed approach aims to fill. We build on a hierarchical model with an exponential family likelihood and a feature allocation prior. The proposed approach generalizes similar small-variance approximations proposed by Kulis and Jordan (2012) and Broderick et.al (2012) for inference with Dirichlet …
High-dimensional data often arise from clinical genomics research to infer relevant predictors of a particular trait. A way to improve the predictive performance is to include information on the predictors derived from prior knowledge or previous studies. Such information is also referred to as ``co-data''. To this aim, we develop a novel Bayesian model for including co-data in a high-dimensional regression framework, called Informative Horseshoe regression (infHS). The proposed approach regresses the prior variances of the regression parameters on the co-data variables, improving variable sel…
Recent technological advancements have enabled detailed investigation of associations between the molecular architecture and tumor heterogeneity, through multi-source integration of radiological imaging and genomic (radiogenomic) data. In this paper, we integrate and harness radiogenomic data in patients with lower grade gliomas (LGG), a type of brain cancer, in order to develop a regression framework called RADIOHEAD (RADIOgenomic analysis incorporating tumor HEterogeneity in imAging through Densities) to identify radiogenomic associations. Imaging data is represented through voxel intensity …
Variable selection is crucial in high-dimensional omics-based analyses, since it is biologically reasonable to assume only a subset of non-noisy features contributes to the data structures. However, the task is particularly hard in an unsupervised setting, and a priori ad hoc variable selection is still a very frequent approach, despite the evident drawbacks and lack of reproducibility. We propose a Bayesian variable selection approach for rank-based unsupervised transcriptomic analysis. Making use of data rankings instead of the actual continuous measurements increases the robustness of concl…
