Empirical Bayes models for multiple probe type microarrays at the probe level

Background  

When analyzing microarray data a primary objective is often to find differentially expressed genes. With empirical Bayes and penalized t-tests the sample variances are adjusted towards a global estimate, producing more stable results compared to ordinary t-tests. However, for Affymetrix type data a clear dependency between variability and intensity-level generally exists, even for logged intensities, most clearly for data at the probe level but also for probe-set summarizes such as the MAS5 expression index. As a consequence, adjustment towards a global estimate results in an intensity-level dependent false positive rate.     

Application of Bayesian decomposition for analysing microarray data

MOTIVATION: Microarray and gene chip technology provide high throughput tools for measuring gene expression levels in a variety of circumstances, including cellular response to drug treatment, cellular growth and development, tumorigenesis, among many other processes. In order to interpret the large data sets generated in experiments, data analysis techniques that consider biological knowledge during analysis will be extremely useful. We present here results showing the application of such a tool to expression data from yeast cell cycle experiments. RESULTS: Originally developed for spectroscopic analysis, Bayesian Decomposition (BD) includes two features which make it useful for microarray data analysis: the ability to assign genes to multiple coexpression groups and the ability to encode biological knowledge into the system. Here we demonstrate the ability of the algorithm to provide insight into the yeast cell cycle, including identification of five temporal patterns tied to cell cycle phases as well as the identification of a pattern tied to an approximately 40 min cell cycle oscillator. The genes are simultaneously assigned to the patterns, including partial assignment to multiple patterns when this is required to explain the expression profile. AVAILABILITY: The application is available free to academic users under a material transfer agreement. Go to http://bioinformatics.fccc.edu/ for more details.     

A Bayesian method for analysing spotted microarray data

In the decade since their invention, spotted microarrays have been undergoing technical advances that have increased the utility, scope and precision of their ability to measure gene expression. At the same time, more researchers are taking advantage of the fundamentally quantitative nature of these tools with refined experimental designs and sophisticated statistical analyses. These new approaches utilise the power of microarrays to estimate differences in gene expression levels, rather than just categorising genes as up- or down-regulated, and allow the comparison of expression data across multiple samples. In this review, some of the technical aspects of spotted microarrays that can affect statistical inference are highlighted, and a discussion is provided of how several methods for estimating gene expression level across multiple samples deal with these challenges. The focus is on a Bayesian analysis method, BAGEL, which is easy to implement and produces easily interpreted results.     

A rapid computer technique for analysing molecular interactions

A rapid method for analysing enzyme — substrate interactionsusing a discriminant analysis program is described. This technqueidentifies the structural features of substrate molecules whichare important in determining metabolic activity. Two model systems,nucleoside diphosphatase activity of Golgi membranes and theinteraction of yeast hexokinase with a range of D-sugars, areused as illustrations of the technique. The conclusions fromboth models are consistent with those previously obtained fromanalytical techniques. Received on January 21, 1986; accepted on April 1, 1986     

Modern computational approaches for analysing molecular genetic variation data

An explosive growth is occurring in the quantity, quality and complexity of molecular variation data that are being collected. Historically, such data have been analysed by using model-based methods. Models are useful for sharpening intuition, for explanation and for prediction: they add to our understanding of how the data were formed, and they can provide quantitative answers to questions of interest. We outline some of these model-based approaches, including the coalescent, and discuss the applicability of the computational methods that are necessary given the highly complex nature of current and future data sets.     

Mixture models for detecting differentially expressed genes in microarrays

An important and common problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. As this problem concerns the selection of significant genes from a large pool of candidate genes, it needs to be carried out within the framework of multiple hypothesis testing. In this paper, we focus on the use of mixture models to handle the multiplicity issue. With this approach, a measure of the local FDR (false discovery rate) is provided for each gene. An attractive feature of the mixture model approach is that it provides a framework for the estimation of the prior probability that a gene is not differentially expressed, and this probability can subsequently be used in forming a decision rule. The rule can also be formed to take the false negative rate into account. We apply this approach to a well-known publicly available data set on breast cancer, and discuss our findings with reference to other approaches.     

Bayesian graphical models for genomewide association studies

As the extent of human genetic variation becomes more fully characterized, the research community is faced with the challenging task of using this information to dissect the heritable components of complex traits. Genomewide association studies offer great promise in this respect, but their analysis poses formidable difficulties. In this article, we describe a computationally efficient approach to mining genotype-phenotype associations that scales to the size of the data sets currently being collected in such studies. We use discrete graphical models as a data-mining tool, searching for single- or multilocus patterns of association around a causative site. The approach is fully Bayesian, allowing us to incorporate prior knowledge on the spatial dependencies around each marker due to linkage disequilibrium, which reduces considerably the number of possible graphical structures. A Markov chain-Monte Carlo scheme is developed that yields samples from the posterior distribution of graphs conditional on the data from which probabilistic statements about the strength of any genotype-phenotype association can be made. Using data simulated under scenarios that vary in marker density, genotype relative risk of a causative allele, and mode of inheritance, we show that the proposed approach has better localization properties and leads to lower false-positive rates than do single-locus analyses. Finally, we present an application of our method to a quasi-synthetic data set in which data from the CYP2D6 region are embedded within simulated data on 100K single-nucleotide polymorphisms. Analysis is quick (<5 min), and we are able to localize the causative site to a very short interval.     

Bayesian multimodel inference for geostatistical regression models

The problem of simultaneous covariate selection and parameter inference for spatial regression models is considered. Previous research has shown that failure to take spatial correlation into account can influence the outcome of standard model selection methods. A Markov chain Monte Carlo (MCMC) method is investigated for the calculation of parameter estimates and posterior model probabilities for spatial regression models. The method can accommodate normal and non-normal response data and a large number of covariates. Thus the method is very flexible and can be used to fit spatial linear models, spatial linear mixed models, and spatial generalized linear mixed models (GLMMs). The Bayesian MCMC method also allows a priori unequal weighting of covariates, which is not possible with many model selection methods such as Akaike's information criterion (AIC). The proposed method is demonstrated on two data sets. The first is the whiptail lizard data set which has been previously analyzed by other researchers investigating model selection methods. Our results confirmed the previous analysis suggesting that sandy soil and ant abundance were strongly associated with lizard abundance. The second data set concerned pollution tolerant fish abundance in relation to several environmental factors. Results indicate that abundance is positively related to Strahler stream order and a habitat quality index. Abundance is negatively related to percent watershed disturbance.     

Tissue microarrays enabling high-throughput molecular pathology

The tissue microarray has enabled high-throughput pathology. Rather than the laborious review of individual slides and issues of assay reproducibility across large series of specimens, tissue microarrays allow the review of a single stain on a single slide containing tens to hundreds of samples. This is a paradigm shift in pathology, away from histomorphology and toward molecular characterization by immunohistochemistry. This platform allows large retrospective clinical studies of biomarkers for correlation with outcome and can equally well be applied toward high-throughput analysis of cell lines and xenografts. Tissue microarrays encourage novel approaches to assaying tissue with retained histomorphology and have enabled image analysis in pathology. The reduction of tissue to an analyte for high-throughput analysis has highlighted the importance of a high quality tissue and the impact of tissue handling and processing in the quality of data that can be obtained from analysis of tissue.     

Bayesian latent variable models for mixed discrete outcomes

In studies of complex health conditions, mixtures of discrete outcomes (event time, count, binary, ordered categorical) are commonly collected. For example, studies of skin tumorigenesis record latency time prior to the first tumor, increases in the number of tumors at each week, and the occurrence of internal tumors at the time of death. Motivated by this application, we propose a general underlying Poisson variable framework for mixed discrete outcomes, accommodating dependency through an additive gamma frailty model for the Poisson means. The model has log-linear, complementary log-log, and proportional hazards forms for count, binary and discrete event time outcomes, respectively. Simple closed form expressions can be derived for the marginal expectations, variances, and correlations. Following a Bayesian approach to inference, conditionally-conjugate prior distributions are chosen that facilitate posterior computation via an MCMC algorithm. The methods are illustrated using data from a Tg.AC mouse bioassay study.     

Conjugate Gibbs sampling for Bayesian phylogenetic models.

We propose a new Markov Chain Monte Carlo (MCMC) sampling mechanism for Bayesian phylogenetic inference. This method, which we call conjugate Gibbs, relies on analytical conjugacy properties, and is based on an alternation between data augmentation and Gibbs sampling. The data augmentation step consists in sampling a detailed substitution history for each site, and across the whole tree, given the current value of the model parameters. Provided convenient priors are used, the parameters of the model can then be directly updated by a Gibbs sampling procedure, conditional on the current substitution history. Alternating between these two sampling steps yields a MCMC device whose equilibrium distribution is the posterior probability density of interest. We show, on real examples, that this conjugate Gibbs method leads to a significant improvement of the mixing behavior of the MCMC. In all cases, the decorrelation times of the resulting chains are smaller than those obtained by standard Metropolis Hastings procedures by at least one order of magnitude. The method is particularly well suited to heterogeneous models, i.e. assuming site-specific random variables. In particular, the conjugate Gibbs formalism allows one to propose efficient implementations of complex models, for instance assuming site-specific substitution processes, that would not be accessible to standard MCMC methods.     

Empirical evaluation of a prior for Bayesian phylogenetic inference

The Bayesian method of phylogenetic inference often produces high posterior probabilities (PPs) for trees or clades, even when the trees are clearly incorrect. The problem appears to be mainly due to large sizes of molecular datasets and to the large-sample properties of Bayesian model selection and its sensitivity to the prior when several of the models under comparison are nearly equally correct (or nearly equally wrong) and are of the same dimension. A previous suggestion to alleviate the problem is to let the internal branch lengths in the tree become increasingly small in the prior with the increase in the data size so that the bifurcating trees are increasingly star-like. In particular, if the internal branch lengths are assigned the exponential prior, the prior mean mu0 should approach zero faster than 1/square root n but more slowly than 1/n, where n is the sequence length. This paper examines the usefulness of this data size-dependent prior using a dataset of the mitochondrial protein-coding genes from the baleen whales, with the prior mean fixed at mu0=0.1n(-2/3). In this dataset, phylogeny reconstruction is sensitive to the assumed evolutionary model, species sampling and the type of data (DNA or protein sequences), but Bayesian inference using the default prior attaches high PPs for conflicting phylogenetic relationships. The data size-dependent prior alleviates the problem to some extent, giving weaker support for unstable relationships. This prior may be useful in reducing apparent conflicts in the results of Bayesian analysis or in making the method less sensitive to model violations.     

A multidisciplinary approach for molecular diagnostics based on biosensors and microarrays

The present review describes the multidisciplinary approach followed by the Chemistry and Nanobiotechnology group of INL since ten years, to develop a complete technological platform dedicated to molecular diagnosis using biochips and biosensors. This work, replaced in an international context, illustrates the importance to identify the various pitfalls inherent to molecular analysis throughout an elaboration and analysis line: choice of solid support, surface physicochemistry, immobilisation of biomolecules, biomolecular recognition, microfluidics and detection.