Estimation of transformation parameters for microarray data

MOTIVATION AND RESULTS: Durbin et al. (2002), Huber et al. (2002) and Munson (2001) independently introduced a family of transformations (the generalized-log family) which stabilizes the variance of microarray data up to the first order. We introduce a method for estimating the transformation parameter in tandem with a linear model based on the procedure outlined in Box and Cox (1964). We also discuss means of finding transformations within the generalized-log family which are optimal under other criteria, such as minimum residual skewness and minimum mean-variance dependency. AVAILABILITY: R and Matlab code and test data are available from the authors on request.     

Model-based variance-stabilizing transformation for Illumina microarray data

Variance stabilization is a step in the preprocessing of microarray data that can greatly benefit the performance of subsequent statistical modeling and inference. Due to the often limited number of technical replicates for Affymetrix and cDNA arrays, achieving variance stabilization can be difficult. Although the Illumina microarray platform provides a larger number of technical replicates on each array (usually over 30 randomly distributed beads per probe), these replicates have not been leveraged in the current log2 data transformation process. We devised a variance-stabilizing transformation (VST) method that takes advantage of the technical replicates available on an Illumina microarray. We have compared VST with log2 and Variance-stabilizing normalization (VSN) by using the Kruglyak bead-level data (2006) and Barnes titration data (2005). The results of the Kruglyak data suggest that VST stabilizes variances of bead-replicates within an array. The results of the Barnes data show that VST can improve the detection of differentially expressed genes and reduce false-positive identifications. We conclude that although both VST and VSN are built upon the same model of measurement noise, VST stabilizes the variance better and more efficiently for the Illumina platform by leveraging the availability of a larger number of within-array replicates. The algorithms and Supplementary Data are included in the lumi package of Bioconductor, available at: www.bioconductor.org.     

lumi: a pipeline for processing Illumina microarray

Illumina microarray is becoming a popular microarray platform. The BeadArray technology from Illumina makes its preprocessing and quality control different from other microarray technologies. Unfortunately, most other analyses have not taken advantage of the unique properties of the BeadArray system, and have just incorporated preprocessing methods originally designed for Affymetrix microarrays. lumi is a Bioconductor package especially designed to process the Illumina microarray data. It includes data input, quality control, variance stabilization, normalization and gene annotation portions. In specific, the lumi package includes a variance-stabilizing transformation (VST) algorithm that takes advantage of the technical replicates available on every Illumina microarray. Different normalization method options and multiple quality control plots are provided in the package. To better annotate the Illumina data, a vendor independent nucleotide universal identifier (nuID) was devised to identify the probes of Illumina microarray. The nuID annotation packages and output of lumi processed results can be easily integrated with other Bioconductor packages to construct a statistical data analysis pipeline for Illumina data. Availability: The lumi Bioconductor package, www.bioconductor.org     

A generalized likelihood ratio test to identify differentially expressed genes from microarray data

MOTIVATION: Microarray technology emerges as a powerful tool in life science. One major application of microarray technology is to identify differentially expressed genes under various conditions. Currently, the statistical methods to analyze microarray data are generally unsatisfactory, mainly due to the lack of understanding of the distribution and error structure of microarray data. RESULTS: We develop a generalized likelihood ratio (GLR) test based on the two-component model proposed by Rocke and Durbin to identify differentially expressed genes from microarray data. Simulation studies show that the GLR test is more powerful than commonly used methods, like the fold-change method and the two-sample t-test. When applied to microarray data, the GLR test identifies more differentially expressed genes than the t-test, has a lower false discovery rate and shows more consistency over independently repeated experiments. AVAILABILITY: The approach is implemented in software called GLR, which is freely available for downloading at http://www.cc.utah.edu/~jw27c60     

An overview of image-processing methods for Affymetrix GeneChips

We present an overview of image-processing methods for Affymetrix GeneChips. All GeneChips are affected to some extent by spatially coherent defects and image processing has a number of potential impacts on the downstream analysis of GeneChip data. Fortunately, there are now a number of robust and accurate algorithms, which identify the most disabling defects. One group of algorithms concentrate on the transformation from the original hybridisation DAT image to the representative CEL file. Another set uses dedicated pattern recognition routines to detect different types of hybridisation defect in replicates. A third type exploits the information provided by public repositories of GeneChips (such as GEO). The use of these algorithms improves the sensitivity of GeneChips, and should be a prerequisite for studies in which there are only few probes per relevant biological signal, such as exon arrays and SNP chips.     

BGX: a fully Bayesian integrated approach to the analysis of Affymetrix GeneChip data

We present Bayesian hierarchical models for the analysis of Affymetrix GeneChip data. The approach we take differs from other available approaches in two fundamental aspects. Firstly, we aim to integrate all processing steps of the raw data in a common statistically coherent framework, allowing all components and thus associated errors to be considered simultaneously. Secondly, inference is based on the full posterior distribution of gene expression indices and derived quantities, such as fold changes or ranks, rather than on single point estimates. Measures of uncertainty on these quantities are thus available. The models presented represent the first building block for integrated Bayesian Analysis of Affymetrix GeneChip data: the models take into account additive as well as multiplicative error, gene expression levels are estimated using perfect match and a fraction of mismatch probes and are modeled on the log scale. Background correction is incorporated by modeling true signal and cross-hybridization explicitly, and a need for further normalization is considerably reduced by allowing for array-specific distributions of nonspecific hybridization. When replicate arrays are available for a condition, posterior distributions of condition-specific gene expression indices are estimated directly, by a simultaneous consideration of replicate probe sets, avoiding averaging over estimates obtained from individual replicate arrays. The performance of the Bayesian model is compared to that of standard available point estimate methods on subsets of the well known GeneLogic and Affymetrix spike-in data. The Bayesian model is found to perform well and the integrated procedure presented appears to hold considerable promise for further development.     

A powerful method for detecting differentially expressed genes from GeneChip arrays that does not require replicates

Background  

Studies of differential expression that use Affymetrix GeneChip arrays are often carried out with a limited number of replicates. Reasons for this include financial considerations and limits on the available amount of RNA for sample preparation. In addition, failed hybridizations are not uncommon leading to a further reduction in the number of replicates available for analysis. Most existing methods for studying differential expression rely on the availability of replicates and the demand for alternative methods that require few or no replicates is high.     

Normalization of microarray data: single-labeled and dual-labeled arrays

DNA microarray is a powerful tool for high-throughput analysis of biological systems. Various computational tools have been created to facilitate the analysis of the large volume of data produced in DNA microarray experiments. Normalization is a critical step for obtaining data that are reliable and usable for subsequent analysis such as identification of differentially expressed genes and clustering. A variety of normalization methods have been proposed over the past few years, but no methods are still perfect. Various assumptions are often taken in the process of normalization. Therefore, the knowledge of underlying assumption and principle of normalization would be helpful for the correct analysis of microarray data. We present a review of normalization techniques from single-labeled platforms such as the Affymetrix GeneChip array to dual-labeled platforms like spotted array focusing on their principles and assumptions.     

Normality of oligonucleotide microarray data and implications for parametric statistical analyses

MOTIVATION: Experimental limitations have resulted in the popularity of parametric statistical tests as a method for identifying differentially regulated genes in microarray data sets. However, these tests assume that the data follow a normal distribution. To date, the assumption that replicate expression values for any gene are normally distributed, has not been critically addressed for Affymetrix GeneChip data. RESULTS: The normality of the expression values calculated using four different commercial and academic software packages was investigated using a data set consisting of the same target RNA applied to 59 human Affymetrix U95A GeneChips using a combination of statistical tests and visualization techniques. For the majority of probe sets obtained from each analysis suite, the expression data showed a good correlation with normality. The exception was a large number of low-expressed genes in the data set produced using Affymetrix Microarray Suite 5.0, which showed a striking non-normal distribution. In summary, our data provide strong support for the application of parametric tests to GeneChip data sets without the need for data transformation.     

A comparison of cDNA, oligonucleotide, and Affymetrix GeneChip gene expression microarray platforms.

We have conducted a study to compare the variability in measured gene expression levels associated with three types of microarray platforms. Total RNA samples were obtained from liver tissue of four male mice, two each from inbred strains A/J and C57BL/6J. The same four samples were assayed on Affymetrix Mouse Genome Expression Set 430 GeneChips (MOE430A and MOE430B), spotted cDNA microarrays, and spotted oligonucleotide microarrays using eight arrays of each type. Variances associated with measurement error were observed to be comparable across all microarray platforms. The MOE430A GeneChips and cDNA arrays had higher precision across technical replicates than the MOE430B GeneChips and oligonucleotide arrays. The Affymetrix platform showed the greatest range in the magnitude of expression levels followed by the oligonucleotide arrays. We observed good concordance in both estimated expression level and statistical significance of common genes between the Affymetrix MOE430A GeneChip and the oligonucleotide arrays. Despite their apparently high precision, cDNA arrays showed poor concordance with other platforms.     

Normalized Affymetrix expression data are biased by G-quadruplex formation

Probes with runs of four or more guanines (G-stacks) in their sequences can exhibit a level of hybridization that is unrelated to the expression levels of the mRNA that they are intended to measure. This is most likely caused by the formation of G-quadruplexes, where inter-probe guanines form Hoogsteen hydrogen bonds, which probes with G-stacks are capable of forming. We demonstrate that for a specific microarray data set using the Human HG_U133A Affymetrix GeneChip and RMA normalization there is significant bias in the expression levels, the fold change and the correlations between expression levels. These effects grow more pronounced as the number of G-stack probes in a probe set increases. Approximately 14% of the probe sets are directly affected. The analysis was repeated for a number of other normalization pipelines and two, FARMS and PLIER, minimized the bias to some extent. We estimate that ～15% of the data sets deposited in the GEO database are susceptible to the effect. The inclusion of G-stack probes in the affected data sets can bias key parameters used in the selection and clustering of genes. The elimination of these probes from any analysis in such affected data sets outweighs the increase of noise in the signal.     

Contrast normalization of oligonucleotide arrays.

Affymetrix high-density oligonucleotide array is a tool that has the capacity to simultaneously measure the abundance of thousands of mRNA sequences in biological samples. In order to allow direct array-to-array comparisons, normalization is a necessity. When deciding on an appropriate normalization procedure there are a couple questions that need to be addressed, e.g., on which level should the normalization be performed: On the level of feature intensities or on the level of expression indexes? Should all features/expression indexes be used or can we choose a subset of features likely to be unregulated? Another question is how to actually perform the normalization: normalize using the overall mean intensity or use a smooth normalization curve? Most of the currently used normalization methods are linear; e.g., the normalization method implemented in the Affymetrix software GeneChip is based on the overall mean intensity. However, along with alternative methods of summarizing feature intensities into an expression index, nonlinear methods have recently started to appear. For many of these alternative methods, the natural choice is to normalize on the level of feature intensities, either using all feature intensities or only perfect match intensities. In this report, a nonlinear normalization procedure aimed for normalizing feature intensities is proposed.     

affy--analysis of Affymetrix GeneChip data at the probe level

MOTIVATION: The processing of the Affymetrix GeneChip data has been a recent focus for data analysts. Alternatives to the original procedure have been proposed and some of these new methods are widely used. RESULTS: The affy package is an R package of functions and classes for the analysis of oligonucleotide arrays manufactured by Affymetrix. The package is currently in its second release, affy provides the user with extreme flexibility when carrying out an analysis and make it possible to access and manipulate probe intensity data. In this paper, we present the main classes and functions in the package and demonstrate how they can be used to process probe-level data. We also demonstrate the importance of probe-level analysis when using the Affymetrix GeneChip platform.     

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

In this paper we report exploratory analyses of high-density oligonucleotide array data from the Affymetrix GeneChip 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 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 arrays; and part of a dilution study conducted by Gene Logic involving 75 HG-U95A GeneChip arrays. We display some familiar features of the perfect match and mismatch probe (PM and MM) values 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 multi-array 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.