The problem of identifying differentially expressed genes in designed microarray experiments is considered. Lonnstedt and Speed (2002) derived an expression for the posterior odds of differential expression in a replicated two-color experiment using a simple hierarchical parametric model. The purpose of this paper is to develop the hierarchical model of Lonnstedt and Speed (2002) into a practical approach for general microarray experiments with arbitrary numbers of treatments and RNA samples. The model is reset in the context of general linear models with arbitrary coefficients and contrasts of interest. The approach applies equally well to both single channel and two color microarray experiments. Consistent, closed form estimators are derived for the hyperparameters in the model. The estimators proposed have robust behavior even for small numbers of arrays and allow for incomplete data arising from spot filtering or spot quality weights. The posterior odds statistic is reformulated in terms of a moderated t-statistic in which posterior residual standard deviations are used in place of ordinary standard deviations. The empirical Bayes approach is equivalent to shrinkage of the estimated sample variances towards a pooled estimate, resulting in far more stable inference when the number of arrays is small. The use of moderated t-statistics has the advantage over the posterior odds that the number of hyperparameters which need to estimated is reduced; in particular, knowledge of the non-null prior for the fold changes are not required. The moderated t-statistic is shown to follow a t-distribution with augmented degrees of freedom. The moderated t inferential approach extends to accommodate tests of composite null hypotheses through the use of moderated F-statistics. The performance of the methods is demonstrated in a simulation study. Results are presented for two publicly available data sets.

/pdf/linear-models-and-empirical-bayes-methods-for-assessing-2yc9s2cjo3.pdf

Linear Models and Empirical Bayes Methods for Assessing Differential Expression in Microarray Experiments

Motivation: When running experiments that involve multiple high density oligonucleotide arrays, it is important to remove sources of variation between arrays of non-biological origin. Normalization is a process for reducing this variation. It is common to see non-linear relations between arrays and the standard normalization provided by Affymetrix does not perform well in these situations. Results: We present three methods of performing normalization at the probe intensity level. These methods are called complete data methods because they make use of data from all arrays in an experiment to form the normalizing relation. These algorithms are compared to two methods that make use of a baseline array: a one number scaling based algorithm and a method that uses a non-linear normalizing relation by comparing the variability and bias of an expression measure. Two publicly available datasets are used to carry out the comparisons. The simplest and quickest complete data method is found to perform favorably. Availabilty: Software implementing all three of the complete data normalization methods is available as part of the R package Affy, which is a part of the Bioconductor project http://www.bioconductor.org. Contact: bolstad@stat.berkeley.edu Supplementary information: Additional figures may be found at http://www.stat.berkeley.edu/∼bolstad/normalize/ index.html

http://bmbolstad.com/misc/normalize/bolstad_norm_paper.pdf

A comparison of normalization methods for high density oligonucleotide array data based on variance and bias

SUMMARY Non-biological experimental variation or “batch effects” are commonly observed across multiple batches of microarray experiments, often rendering the task of combining data from these batches difficult. The ability to combine microarray data sets is advantageous to researchers to increase statistical power to detect biological phenomena from studies where logistical considerations restrict sample size or in studies that require the sequential hybridization of arrays. In general, it is inappropriate to combine data sets without adjusting for batch effects. Methods have been proposed to filter batch effects from data, but these are often complicated and require large batch sizes (>25) to implement. Because the majority of microarray studies are conducted using much smaller sample sizes, existing methods are not sufficient. We propose parametric and non-parametric empirical Bayes frameworks for adjusting data for batch effects that is robust to outliers in small sample sizes and performs comparable to existing methods for large samples. We illustrate our methods using two example data sets and show that our methods are justifiable, easy to apply, and useful in practice. Software for our method is freely available at: http://biosun1.harvard.edu/complab/batch/.

/pdf/adjusting-batch-effects-in-microarray-expression-data-using-2pgy7nrfs2.pdf

Adjusting batch effects in microarray expression data using empirical Bayes methods

Gene set enrichment (GSE) analysis is a popular framework for condensing information from gene expression profiles into a pathway or signature summary. The strengths of this approach over single gene analysis include noise and dimension reduction, as well as greater biological interpretability. As molecular profiling experiments move beyond simple case-control studies, robust and flexible GSE methodologies are needed that can model pathway activity within highly heterogeneous data sets. To address this challenge, we introduce Gene Set Variation Analysis (GSVA), a GSE method that estimates variation of pathway activity over a sample population in an unsupervised manner. We demonstrate the robustness of GSVA in a comparison with current state of the art sample-wise enrichment methods. Further, we provide examples of its utility in differential pathway activity and survival analysis. Lastly, we show how GSVA works analogously with data from both microarray and RNA-seq experiments. GSVA provides increased power to detect subtle pathway activity changes over a sample population in comparison to corresponding methods. While GSE methods are generally regarded as end points of a bioinformatic analysis, GSVA constitutes a starting point to build pathway-centric models of biology. Moreover, GSVA contributes to the current need of GSE methods for RNA-seq data. GSVA is an open source software package for R which forms part of the Bioconductor project and can be downloaded at http://www.bioconductor.org
 .

/pdf/gsva-gene-set-variation-analysis-for-microarray-and-rna-seq-1bwfkmry7e.pdf

GSVA: gene set variation analysis for microarray and RNA-seq data.

The fine detail provided by sequencing-based transcriptome surveys suggests that RNA-seq is likely to become the platform of choice for interrogating steady state RNA. In order to discover biologically important changes in expression, we show that normalization continues to be an essential step in the analysis. We outline a simple and effective method for performing normalization and show dramatically improved results for inferring differential expression in simulated and publicly available data sets.

/pdf/a-scaling-normalization-method-for-differential-expression-4h3ageh1le.pdf

A scaling normalization method for differential expression analysis of RNA-seq data

SUMMARY In this paper we report exploratory analyses of high-density oligonucleotide array data from the Affymetrix GeneChip R � system with the objective of improving upon currently used measures of gene expression. Our analyses make use of three data sets: a small experimental study consisting of five MGU74A mouse GeneChip R � arrays, part of the data from an extensive spike-in study conducted by Gene Logic and Wyeth’s Genetics Institute involving 95 HG-U95A human GeneChip R � arrays; and part of a dilution study conducted by Gene Logic involving 75 HG-U95A GeneChip R � arrays. We display some familiar features of the perfect match and mismatch probe ( PM and MM )v alues of these data, and examine the variance–mean relationship with probe-level data from probes believed to be defective, and so delivering noise only. We explain why we need to normalize the arrays to one another using probe level intensities. We then examine the behavior of the PM and MM using spike-in data and assess three commonly used summary measures: Affymetrix’s (i) average difference (AvDiff) and (ii) MAS 5.0 signal, and (iii) the Li and Wong multiplicative model-based expression index (MBEI). The exploratory data analyses of the probe level data motivate a new summary measure that is a robust multiarray average (RMA) of background-adjusted, normalized, and log-transformed PM values. We evaluate the four expression summary measures using the dilution study data, assessing their behavior in terms of bias, variance and (for MBEI and RMA) model fit. Finally, we evaluate the algorithms in terms of their ability to detect known levels of differential expression using the spike-in data. We conclude that there is no obvious downside to using RMA and attaching a standard error (SE) to this quantity using a linear model which removes probe-specific affinities. ∗ To whom correspondence should be addressed

/pdf/exploration-normalization-and-summaries-of-high-density-2pbmlxjfbv.pdf

Exploration, normalization, and summaries of high density oligonucleotide array probe level data

High density oligonucleotide array technology is widely used in many areas of biomedical research for quantitative and highly parallel measurements of gene expression. Affymetrix GeneChip arrays are the most popular. In this technology each gene is typically represented by a set of 11–20 pairs of probes. In order to obtain expression measures it is necessary to summarize the probe level data. Using two extensive spike-in studies and a dilution study, we developed a set of tools for assessing the effectiveness of expression measures. We found that the performance of the current version of the default expression measure provided by Affymetrix Microarray Suite can be significantly improved by the use of probe level summaries derived from empirically motivated statistical models. In particular, improvements in the ability to detect differentially expressed genes are demonstrated.

/pdf/summaries-of-affymetrix-genechip-probe-level-data-5c0qex947v.pdf

Summaries of Affymetrix GeneChip probe level data

PURPOSE. To generate a profile of genes expressed in the retina, RPE, and choroid after laser treatment and to identify genes that may contribute to the beneficial effects of laser photocoagulation in the treatment of angiogenic retinal diseases. METHODS. Argon laser irradiation was delivered to the left eye of normal C57BL/6J mice (n = 30), with the right eye serving as the control in each animal. Three days after laser treatment, mice were culled, eyes enucleated, and the retinas dissected and pooled into respective groups. The total RNA of replicate samples was extracted, and expression profiles were obtained by microarray analysis. Data comparisons between control and treated samples were performed and statistically analyzed. RESULTS. Data revealed that the expression of 265 known genes and expressed sequence tags (ESTs) changed after laser treatment. Of those, 25 were found to be upregulated. These genes represented a number of biological processes, including photoreceptor metabolism, synaptic function, structural proteins, and adhesion molecules. Thus angiotensin II type 2 receptor (Agtr2), a potential candidate in the inhibition of VEGF-induced angiogenesis, was upregulated, whereas potential modulators of endothelial cell function, permeability factors, and VEGF inducers, such as FGF-14, FGF-16, IL-1β, calcitonin receptor-like receptor (CRLR), and plasminogen activator inhibitor-2 (PAI2), were downregulated. CONCLUSIONS. In this study, genes were identified that both explain and contribute to the beneficial effects of laser photocoagulation in the treatment of angiogenic retinal diseases. The molecular insights into the therapeutic effects of laser photocoagulation may provide a basis for future therapeutic strategies.

Argon laser photocoagulation-induced modification of gene expression in the retina.

The microarray is a revolutionary technology combining molecular biology and computer technology in the high throughput, simultaneous analysis of global gene expression. It is emerging as a powerful and valuable research tool that holds great promise in elucidating the molecular mechanisms involved in complex diseases. The information gained may provide direction toward identifying appropriate targets for therapeutic intervention. Despite the enormous potential of this technology, however, a number of issues exist that complicate gene expression analysis and require further resolution. This paper reviews these issues as well as the conceptual, practical and statistical aspects of microarray technology, including its current use in research and clinical applications. Furthermore, the advantages and potential benefits of this technology in ophthalmic research are discussed, with particular attention to retinal diseases, and its possible application in the identification of genes involved in ocular disease progression that may serve as clinical markers or potential therapeutic targets.

Bridget G. Hobbs

Papers

Exploration, normalization, and summaries of high density oligonucleotide array probe level data

Summaries of Affymetrix GeneChip probe level data

Argon laser photocoagulation-induced modification of gene expression in the retina.

The microarray: potential applications for ophthalmic research