Bivariate microarray analysis: statistical interpretation of two-channel functional genomics data

Conventional statistical methods for interpreting microarray data require large numbers of replicates in order to provide sufficient levels of sensitivity. We recently described a method for identifying differentially-expressed genes in one-channel microarray data 1. Based on the idea that the variance structure of microarray data can itself be a reliable measure of noise, this method allows statistically sound interpretation of as few as two replicates per treatment condition. Unlike the one-channel array, the two-channel platform simultaneously compares gene expression in two RNA samples. This leads to covariation of the measured signals. Hence, by accounting for covariation in the variance model, we can significantly increase the power of the statistical test. We believe that this approach has the potential to overcome limitations of existing methods. We present here a novel approach for the analysis of microarray data that involves modeling the variance structure of paired expression data in the context of a Bayesian framework. We also describe a novel statistical test that can be used to identify differentially-expressed genes. This method, bivariate microarray analysis (BMA), demonstrates dramatically improved sensitivity over existing approaches. We show that with only two array replicates, it is possible to detect gene expression changes that are at best detected with six array replicates by other methods. Further, we show that combining results from BMA with Gene Ontology annotation yields biologically significant results in a ligand-treated macrophage cell system.     

Differential gene expression detection and sample classification using penalized linear regression models

Differential gene expression detection and sample classification using microarray data have received much research interest recently. Owing to the large number of genes p and small number of samples n (p > n), microarray data analysis poses big challenges for statistical analysis. An obvious problem owing to the 'large p small n' is over-fitting. Just by chance, we are likely to find some non-differentially expressed genes that can classify the samples very well. The idea of shrinkage is to regularize the model parameters to reduce the effects of noise and produce reliable inferences. Shrinkage has been successfully applied in the microarray data analysis. The SAM statistics proposed by Tusher et al. and the 'nearest shrunken centroid' proposed by Tibshirani et al. are ad hoc shrinkage methods. Both methods are simple, intuitive and prove to be useful in empirical studies. Recently Wu proposed the penalized t/F-statistics with shrinkage by formally using the (1) penalized linear regression models for two-class microarray data, showing good performance. In this paper we systematically discussed the use of penalized regression models for analyzing microarray data. We generalize the two-class penalized t/F-statistics proposed by Wu to multi-class microarray data. We formally derive the ad hoc shrunken centroid used by Tibshirani et al. using the (1) penalized regression models. And we show that the penalized linear regression models provide a rigorous and unified statistical framework for sample classification and differential gene expression detection.     

Comparative analysis of algorithms for signal quantitation from oligonucleotide microarrays

MOTIVATION: Recent years' exponential increase in DNA microarrays experiments has motivated the development of many signal quantitation (SQ) algorithms. These algorithms perform various transformations on the actual measurements aimed to enable researchers to compare readings of different genes quantitatively within one experiment and across separate experiments. However, it is relatively unclear whether there is a 'best' algorithm to quantitate microarray data. The ability to compare and assess such algorithms is crucial for any downstream analysis. In this work, we suggest a methodology for comparing different signal quantitation algorithms for gene expression data. Our aim is to enable researchers to compare the effect of different SQ algorithms on the specific dataset they are dealing with. We combine two kinds of tests to assess the effect of an SQ algorithm in terms of signal to noise ratio. To assess noise, we exploit redundancy within the experimental dataset to test the variability of a given SQ algorithm output. For the effect of the SQ on the signal we evaluate the overabundance of differentially expressed genes using various statistical significance tests. RESULTS: We demonstrate our analysis approach with three SQ algorithms for oligonucleotide microarrays. We compare the results of using the dChip software and the RMAExpress software to the ones obtained by using the standard Affymetrix MAS5 on a dataset containing pairs of repeated hybridizations. Our analysis suggests that dChip is more robust and stable than the MAS5 tools for about 60% of the genes while RMAExpress is able to achieve an even greater improvement in terms of signal to noise, for more than 95% of the genes.     

Interactively optimizing signal-to-noise ratios in expression profiling: project-specific algorithm selection and detection p-value weighting in Affymetrix microarrays

MOTIVATION: The most commonly utilized microarrays for mRNA profiling (Affymetrix) include 'probe sets' of a series of perfect match and mismatch probes (typically 22 oligonucleotides per probe set). There are an increasing number of reported 'probe set algorithms' that differ in their interpretation of a probe set to derive a single normalized 'signal' representative of expression of each mRNA. These algorithms are known to differ in accuracy and sensitivity, and optimization has been done using a small set of standardized control microarray data. We hypothesized that different mRNA profiling projects have varying sources and degrees of confounding noise, and that these should alter the choice of a specific probe set algorithm. Also, we hypothesized that use of the Microarray Suite (MAS) 5.0 probe set detection p-value as a weighting function would improve the performance of all probe set algorithms. RESULTS: We built an interactive visual analysis software tool (HCE2W) to test and define parameters in Affymetrix analyses that optimize the ratio of signal (desired biological variable) versus noise (confounding uncontrolled variables). Five probe set algorithms were studied with and without statistical weighting of probe sets using the MAS 5.0 probe set detection p-values. The signal-to-noise ratio optimization method was tested in two large novel microarray datasets with different levels of confounding noise, a 105 sample U133A human muscle biopsy dataset (11 groups: mutation-defined, extensive noise), and a 40 sample U74A inbred mouse lung dataset (8 groups: little noise). Performance was measured by the ability of the specific probe set algorithm, with and without detection p-value weighting, to cluster samples into the appropriate biological groups (unsupervised agglomerative clustering with F-measure values). Of the total random sampling analyses, 50% showed a highly statistically significant difference between probe set algorithms by ANOVA [F(4,10) > 14, p < 0.0001], with weighting by MAS 5.0 detection p-value showing significance in the mouse data by ANOVA [F(1,10) > 9, p < 0.013] and paired t-test [t(9) = -3.675, p = 0.005]. Probe set detection p-value weighting had the greatest positive effect on performance of dChip difference model, ProbeProfiler and RMA algorithms. Importantly, probe set algorithms did indeed perform differently depending on the specific project, most probably due to the degree of confounding noise. Our data indicate that significantly improved data analysis of mRNA profile projects can be achieved by optimizing the choice of probe set algorithm with the noise levels intrinsic to a project, with dChip difference model with MAS 5.0 detection p-value continuous weighting showing the best overall performance in both projects. Furthermore, both existing and newly developed probe set algorithms should incorporate a detection p-value weighting to improve performance. AVAILABILITY: The Hierarchical Clustering Explorer 2.0 is available at http://www.cs.umd.edu/hcil/hce/ Murine arrays (40 samples) are publicly available at the PEPR resource (http://microarray.cnmcresearch.org/pgadatatable.asp http://pepr.cnmcresearch.org Chen et al., 2004).     

Using ANOVA to analyze microarray data

ANOVA provides a general approach to the analysis of single and multiple factor experiments on both one- and two-color microarray platforms. Mixed model ANOVA is important because in many microarray experiments there are multiple sources of variation that must be taken into consideration when constructing tests for differential expression of a gene. The genome is large, and the signals of expression change can be small, so we must rely on rigorous statistical methods to distinguish signal from noise. We apply statistical tests to ensure that we are not just making up stories based on seeing patterns where there may be none.     

Clustering gene expression data based on predicted differential effects of GV interaction

Microarray has become a popular biotechnology in biological and medical research. However, systematic and stochastic variabilities in microarray data are expected and unavoidable, resulting in the problem that the raw measurements have inherent “noise” within microarray experiments. Currently, logarithmic ratios are usually analyzed by various clustering methods directly, which may introduce bias interpretation in identifying groups of genes or samples. In this paper, a statistical method based on mixed model approaches was proposed for microarray data cluster analysis. The underlying rationale of this method is to partition the observed total gene expression level into various variations caused by different factors using an ANOVA model, and to predict the differential effects of GV （gene by variety） interaction using the adjusted unbiased prediction （AUP） method. The predicted GV interaction effects can then be used as the inputs of cluster analysis. We illustrated the application of our method with a gene expression dataset and elucidated the utility of our approach using an external validation.     

Some statistical issues in microarray gene expression data

In this paper we discuss some of the statistical issues that should be considered when conducting experiments involving microarray gene expression data. We discuss statistical issues related to preprocessing the data as well as the analysis of the data. Analysis of the data is discussed in three contexts: class comparison, class prediction and class discovery. We also review the methods used in two studies that are using microarray gene expression to assess the effect of exposure to radiofrequency (RF) fields on gene expression. Our intent is to provide a guide for radiation researchers when conducting studies involving microarray gene expression data.     

Microarray standard data set and figures of merit for comparing data processing methods and experiment designs

MOTIVATION: There is a very large and growing level of effort toward improving the platforms, experiment designs, and data analysis methods for microarray expression profiling. Along with a growing richness in the approaches there is a growing confusion among most scientists as to how to make objective comparisons and choices between them for different applications. There is a need for a standard framework for the microarray community to compare and improve analytical and statistical methods. RESULTS: We report on a microarray data set comprising 204 in-situ synthesized oligonucleotide arrays, each hybridized with two-color cDNA samples derived from 20 different human tissues and cell lines. Design of the approximately 24 000 60mer oligonucleotides that report approximately 2500 known genes on the arrays, and design of the hybridization experiments, were carried out in a way that supports the performance assessment of alternative data processing approaches and of alternative experiment and array designs. We also propose standard figures of merit for success in detecting individual differential expression changes or expression levels, and for detecting similarities and differences in expression patterns across genes and experiments. We expect this data set and the proposed figures of merit will provide a standard framework for much of the microarray community to compare and improve many analytical and statistical methods relevant to microarray data analysis, including image processing, normalization, error modeling, combining of multiple reporters per gene, use of replicate experiments, and sample referencing schemes in measurements based on expression change. AVAILABILITY/SUPPLEMENTARY INFORMATION: Expression data and supplementary information are available at http://www.rii.com/publications/2003/HE_SDS.htm     

Biological assessment of robust noise models in microarray data analysis

MOTIVATION: Although several recently proposed analysis packages for microarray data can cope with heavy-tailed noise, many applications rely on Gaussian assumptions. Gaussian noise models foster computational efficiency. This comes, however, at the expense of increased sensitivity to outlying observations. Assessing potential insufficiencies of Gaussian noise in microarray data analysis is thus important and of general interest. RESULTS: We propose to this end assessing different noise models on a large number of microarray experiments. The goodness of fit of noise models is quantified by a hierarchical Bayesian analysis of variance model, which predicts normalized expression values as a mixture of a Gaussian density and t-distributions with adjustable degrees of freedom. Inference of differentially expressed genes is taken into consideration at a second mixing level. For attaining far reaching validity, our investigations cover a wide range of analysis platforms and experimental settings. As the most striking result, we find irrespective of the chosen preprocessing and normalization method in all experiments that a heavy-tailed noise model is a better fit than a simple Gaussian. Further investigations revealed that an appropriate choice of noise model has a considerable influence on biological interpretations drawn at the level of inferred genes and gene ontology terms. We conclude from our investigation that neglecting the over dispersed noise in microarray data can mislead scientific discovery and suggest that the convenience of Gaussian-based modelling should be replaced by non-parametric approaches or other methods that account for heavy-tailed noise.     

Microarray learning with ABC

Standard clustering algorithms when applied to DNA microarray data often tend to produce erroneous clusters. A major contributor to this divergence is the feature characteristic of microarray data sets that the number of predictors (genes) in such data far exceeds the number of samples by many orders of magnitude, with only a small percentage of predictors being truly informative with regards to the clustering while the rest merely add noise. An additional complication is that the predictors exhibit an unknown complex correlational configuration embedded in a small subspace of the entire predictor space. Under these conditions, standard clustering algorithms fail to find the true clusters even when applied in tandem with some sort of gene filtering or dimension reduction to reduce the number of predictors. We propose, as an alternative, a novel method for unsupervised classification of DNA microarray data. The method, which is based on the idea of aggregating results obtained from an ensemble of randomly resampled data (where both samples and genes are resampled), introduces a way of tilting the procedure so that the ensemble includes minimal representation from less important areas of the gene predictor space. The method produces a measure of dissimilarity between each pair of samples that can be used in conjunction with (a) a method like Ward's procedure to generate a cluster analysis and (b) multidimensional scaling to generate useful visualizations of the data. We call the dissimilarity measures ABC dissimilarities since they are obtained by aggregating bundles of clusters. An extensive comparison of several clustering methods using actual DNA microarray data convincingly demonstrates that classification using ABC dissimilarities offers significantly superior performance.     

Reconstructing the temporal ordering of biological samples using microarray data

MOTIVATION: Accurate time series for biological processes are difficult to estimate due to problems of synchronization, temporal sampling and rate heterogeneity. Methods are needed that can utilize multi-dimensional data, such as those resulting from DNA microarray experiments, in order to reconstruct time series from unordered or poorly ordered sets of observations. RESULTS: We present a set of algorithms for estimating temporal orderings from unordered sets of sample elements. The techniques we describe are based on modifications of a minimum-spanning tree calculated from a weighted, undirected graph. We demonstrate the efficacy of our approach by applying these techniques to an artificial data set as well as several gene expression data sets derived from DNA microarray experiments. In addition to estimating orderings, the techniques we describe also provide useful heuristics for assessing relevant properties of sample datasets such as noise and sampling intensity, and we show how a data structure called a PQ-tree can be used to represent uncertainty in a reconstructed ordering. AVAILABILITY: Academic implementations of the ordering algorithms are available as source code (in the programming language Python) on our web site, along with documentation on their use. The artificial 'jelly roll' data set upon which the algorithm was tested is also available from this web site. The publicly available gene expression data may be found at http://genome-www.stanford.edu/cellcycle/ and http://caulobacter.stanford.edu/CellCycle/.     

Universal external RNA controls for microbial gene expression analysis using microarray and qRT-PCR

Gene expression analysis provides significant insight to understand regulatory mechanisms of biology, yet acquisition and reproduction of quality data, as well as data confirmation and verification remain challenging due to a lack of proper quality controls across different assay platforms. We present a set of six universal external RNA quality controls for microbial mRNA expression analysis that can be applied to both DNA oligo microarray and real-time qRT-PCR including using SYBR Green and TaqMan probe-based chemistry. This set of controls was applied for Saccharomyces cerevisiae and Pseudomonas fluorescens Pf-5 microarray assays and qRT-PCR for yeast gene expression analysis. Highly fitted linear relationships between detected signal intensity and mRNA input were described. Valid mRNA detection range, from 10 to 7000 pg and from 100 fg to 1000 pg were defined for microarray and qRT-PCR assay, respectively. Quantitative estimation of mRNA abundance was tested using randomly selected yeast ORF including function unknown genes using the same source of samples by the two assay platforms. Estimates of mRNA abundance by the two methods were similar and highly correlated in an overlapping detection range from 10 to 1000 pg. The universal external RNA controls provide a means to compare microbial gene expression data derived from different experiments and different platforms for verification and confirmation. Such quality controls ensure reliability and reproducibility of gene expression data, and provide unbiased normalization reference for validation, quantification, and estimate of variation of gene expression experiments. Application of these controls also improves efficiency and facilitates high throughput applications of gene expression analysis using the qRT-PCR assay.     

Assessment method for a power analysis to identify differentially expressed pathways

Gene expression data can provide a very rich source of information for elucidating the biological function on the pathway level if the experimental design considers the needs of the statistical analysis methods. The purpose of this paper is to provide a comparative analysis of statistical methods for detecting the differentially expression of pathways (DEP). In contrast to many other studies conducted so far, we use three novel simulation types, producing a more realistic correlation structure than previous simulation methods. This includes also the generation of surrogate data from two large-scale microarray experiments from prostate cancer and ALL. As a result from our comprehensive analysis of 41,004 parameter configurations, we find that each method should only be applied if certain conditions of the data from a pathway are met. Further, we provide method-specific estimates for the optimal sample size for microarray experiments aiming to identify DEP in order to avoid an underpowered design. Our study highlights the sensitivity of the studied methods on the parameters of the system.     

Large scale data mining approach for gene-specific standardization of microarray gene expression data

MOTIVATION: The identification of the change of gene expression in multifactorial diseases, such as breast cancer is a major goal of DNA microarray experiments. Here we present a new data mining strategy to better analyze the marginal difference in gene expression between microarray samples. The idea is based on the notion that the consideration of gene's behavior in a wide variety of experiments can improve the statistical reliability on identifying genes with moderate changes between samples. RESULTS: The availability of a large collection of array samples sharing the same platform in public databases, such as NCBI GEO, enabled us to re-standardize the expression intensity of a gene using its mean and variation in the wide variety of experimental conditions. This approach was evaluated via the re-identification of breast cancer-specific gene expression. It successfully prioritized several genes associated with breast tumor, for which the expression difference between normal and breast cancer cells was marginal and thus would have been difficult to recognize using conventional analysis methods. Maximizing the utility of microarray data in the public database, it provides a valuable tool particularly for the identification of previously unrecognized disease-related genes. AVAILABILITY: A user friendly web-interface (http://compbio.sookmyung.ac.kr/~lage/) was constructed to provide the present large-scale approach for the analysis of GEO microarray data (GS-LAGE server).     

Statistical methods for microarray assays

The paper shortly reviews statistical methods used in the area of DNA microarray studies. All stages of the experiment are taken into account: planning, data collection, data preprocessing, analysis and validation. Among the methods of data analysis, the algorithms for estimating differential expression, multivariate approaches, clustering methods, as well as classification and discrimination are reviewed. The need is stressed for routine statistical data processing protocols and for the search of links of microarray data analysis with quantitative genetic models.     

Assessing reliability of gene clusters from gene expression data

The rapid development of microarray technologies has raised many challenging problems in experiment design and data analysis. Although many numerical algorithms have been successfully applied to analyze gene expression data, the effects of variations and uncertainties in measured gene expression levels across samples and experiments have been largely ignored in the literature. In this article, in the context of hierarchical clustering algorithms, we introduce a statistical resampling method to assess the reliability of gene clusters identified from any hierarchical clustering method. Using the clustering trees constructed from the resampled data, we can evaluate the confidence value for each node in the observed clustering tree. A majority-rule consensus tree can be obtained, showing clusters that only occur in a majority of the resampled trees. We illustrate our proposed methods with applications to two published data sets. Although the methods are discussed in the context of hierarchical clustering methods, they can be applied with other cluster-identification methods for gene expression data to assess the reliability of any gene cluster of interest. Electronic Publication     

Importance of randomization in microarray experimental designs with Illumina platforms

Measurements of gene expression from microarray experiments are highly dependent on experimental design. Systematic noise can be introduced into the data at numerous steps. On Illumina BeadChips, multiple samples are assayed in an ordered series of arrays. Two experiments were performed using the same samples but different hybridization designs. An experiment confounding genotype with BeadChip and treatment with array position was compared to another experiment in which these factors were randomized to BeadChip and array position. An ordinal effect of array position on intensity values was observed in both experiments. We demonstrate that there is increased rate of false-positive results in the confounded design and that attempts to correct for confounded effects by statistical modeling reduce power of detection for true differential expression. Simple analysis models without post hoc corrections provide the best results possible for a given experimental design. Normalization improved differential expression testing in both experiments but randomization was the most important factor for establishing accurate results. We conclude that lack of randomization cannot be corrected by normalization or by analytical methods. Proper randomization is essential for successful microarray experiments.