Use of signal quality measurements to gain efficiency in the analysis of cDNA microarray datacDNA microarray data

This research provides a new way to measure error in microarray data in order to improve gene expression analysis. Microarray data contains many sources of error. In order to glean information about mRNA expression levels, the true signal must first be segregated from noise. This research focuses on the variation that can be captured at the spot level in cDNA microarray images. Variation at other levels, due to differences at the array, dye, and block levels, can be corrected for by a variety of existing normalization procedures. Two signal quality estimates that capture the reliability of each spot printed on a microarray are described. A parametric estimate of within-spot variance, referred to here as σ²_spot, assumes that pixels follow a normal distribution and are spatially correlated. A non-parametric estimate of error, called the mean square prediction error (MSPE), assumes that spots of high quality possess pixels that are similar to their neighbors. This paper will provide a framework to use either spot quality measure in downstream analysis, specifically as weights in regression models. Using these spot quality estimates as weights can result in greater efficiency, in a statistical sense, when modeling microarray data.     

Use of signal quality measurements to gain efficiency in the analysis of cDNA microarray data

This research provides a new way to measure error in microarray data in order to improve gene expression analysis.Microarray data contains many sources of error.In order to glean information about mRNA expression levels,the true signal must first be segregated from noise.This research focuses on the variation that can be captured at the spot level in cDNA microarray images.Variation at other levels,due to differences at the array,dye,and block levels,can be corrected for by a variety of existing normalizati...     

Weighted analysis of microarray gene expression using maximum-likelihood

MOTIVATION: The numerical values of gene expression measured using microarrays are usually presented to the biological end-user as summary statistics of spot pixel data, such as the spot mean, median and mode. Much of the subsequent data analysis reported in the literature, however, uses only one of these spot statistics. This results in sub-optimal estimates of gene expression levels and a need for improvement in quantitative spot variation surveillance. RESULTS: This paper develops a maximum-likelihood method for estimating gene expression using spot mean, variance and pixel number values available from typical microarray scanners. It employs a hierarchical model of variation between and within microarray spots. The hierarchical maximum-likelihood estimate (MLE) is shown to be a more efficient estimator of the mean than the 'conventional' estimate using solely the spot mean values (i.e. without spot variance data). Furthermore, under the assumptions of our model, the spot mean and spot variance are shown to be sufficient statistics that do not require the use of all pixel data.The hierarchical MLE method is applied to data from both Monte Carlo (MC) simulations and a two-channel dye-swapped spotted microarray experiment. The MC simulations show that the hierarchical MLE method leads to improved detection of differential gene expression particularly when 'outlier' spots are present on the arrays. Compared with the conventional method, the MLE method applied to data from the microarray experiment leads to an increase in the number of differentially expressed genes detected for low cut-off P-values of interest.     

Analysis of variance for gene expression microarray data.

Spotted cDNA microarrays are emerging as a powerful and cost-effective tool for large-scale analysis of gene expression. Microarrays can be used to measure the relative quantities of specific mRNAs in two or more tissue samples for thousands of genes simultaneously. While the power of this technology has been recognized, many open questions remain about appropriate analysis of microarray data. One question is how to make valid estimates of the relative expression for genes that are not biased by ancillary sources of variation. Recognizing that there is inherent "noise" in microarray data, how does one estimate the error variation associated with an estimated change in expression, i.e., how does one construct the error bars? We demonstrate that ANOVA methods can be used to normalize microarray data and provide estimates of changes in gene expression that are corrected for potential confounding effects. This approach establishes a framework for the general analysis and interpretation of microarray data.     

A novel strategy for microarray quality control using Bayesian networks

MOTIVATION: High-throughput microarray technologies enable measurements of the expression levels of thousands of genes in parallel. However, microarray printing, hybridization and washing may create substantial variability in the quality of the data. As erroneous measurements may have a drastic impact on the results by disturbing the normalization schemes and by introducing expression patterns that lead to incorrect conclusions, it is crucial to discard low quality observations in the early phases of a microarray experiment. A typical microarray experiment consists of tens of thousands of spots on a microarray, making manual extraction of poor quality spots impossible. Thus, there is a need for a reliable and general microarray spot quality control strategy. RESULTS: We suggest a novel strategy for spot quality control by using Bayesian networks, which contain many appealing properties in the spot quality control context. We illustrate how a non-linear least squares based Gaussian fitting procedure can be used in order to extract features for a spot on a microarray. The features we used in this study are: spot intensity, size of the spot, roundness of the spot, alignment error, background intensity, background noise, and bleeding. We conclude that Bayesian networks are a reliable and useful model for microarray spot quality assessment. SUPPLEMENTARY INFORMATION: http://sigwww.cs.tut.fi/TICSP/SpotQuality/.     

Improved background correction for spotted DNA microarrays.

Most microarray scanning software for glass spotted arrays provides estimates for the intensity for the "foreground" and "background" of two channels for every spot. The common approach in further analyzing such data is to first subtract the background from the foreground for each channel and to use the ratio of these two results as the estimate of the expression level. The resulting ratios are, after possible averaging over replicates, the usual inputs for further data analysis, such as clustering. If, with this background correction procedure, the foreground intensity was smaller than the background intensity for a channel, that spot (on that array) yields no usable data. In this paper it is argued that this preprocessing leads to estimates of the expression that have a much larger variance than needed when the expression levels are low.     

Microarray image analysis: background estimation using quantile and morphological filters

Background  

In a microarray experiment the difference in expression between genes on the same slide is up to 10³ fold or more. At low expression, even a small error in the estimate will have great influence on the final test and reference ratios. In addition to the true spot intensity the scanned signal consists of different kinds of noise referred to as background. In order to assess the true spot intensity background must be subtracted. The standard approach to estimate background intensities is to assume they are equal to the intensity levels between spots. In the literature, morphological opening is suggested to be one of the best methods for estimating background this way.     

Improving gene quantification by adjustable spot-image restoration

MOTIVATION: One of the major factors that complicate the task of microarray image analysis is that microarray images are distorted by various types of noise. In this study a robust framework is proposed, designed to take into account the effect of noise in microarray images in order to assist the demanding task of microarray image analysis. The proposed framework, incorporates in the microarray image processing pipeline a novel combination of spot adjustable image analysis and processing techniques and consists of the following stages: (1) gridding for facilitating spot identification, (2) clustering (unsupervised discrimination between spot and background pixels) applied to spot image for automatic local noise assessment, (3) modeling of local image restoration process for spot image conditioning (adjustable wiener restoration using an empirically determined degradation function), (4) automatic spot segmentation employing seeded-region-growing, (5) intensity extraction and (6) assessment of the reproducibility (real data) and the validity (simulated data) of the extracted gene expression levels. RESULTS: Both simulated and real microarray images were employed in order to assess the performance of the proposed framework against well-established methods implemented in publicly available software packages (Scanalyze and SPOT). Regarding simulated images, the novel combination of techniques, introduced in the proposed framework, rendered the detection of spot areas and the extraction of spot intensities more accurate. Furthermore, on real images the proposed framework proved of better stability across replicates. Results indicate that the proposed framework improves spots' segmentation and, consequently, quantification of gene expression levels. AVAILABILITY: All algorithms were implemented in Matlab (The Mathworks, Inc., Natick, MA, USA) environment. The codes that implement microarray gridding, adaptive spot restoration and segmentation/intensity extraction are available upon request. Supplementary results and the simulated microarray images used in this study are available for download from: ftp://users:bioinformatics@mipa.med.upatras.gr. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Statistical adjustment of signal censoring in gene expression experiments

MOTIVATION: Numerical output of spotted microarrays displays censoring of pixel intensities at some software dependent threshold. This reduces the quality of gene expression data, because it seriously violates the linearity of expression with respect to signal intensity. Statistical methods based on typically available spot summaries together with some parametric assumptions can suggest ways to correct for this defect. RESULTS: A maximum likelihood approach is suggested together with a sensible approximation to the joint density of the mean, median and variance-which are typically available to the biological end-user. The method 'corrects' the gene expression values for pixel censoring. A by-product of our approach is a comparison between several two-parameter models for pixel intensity values. It suggests that pixels separated by one or two other pixels can be considered independent draws from a Lognormal or a Gamma distribution. AVAILABILITY: The R/S-Plus code is available at http://www.stats.gla.ac.uk/~microarray/software.     

On differential variability of expression ratios: improving statistical inference about gene expression changes from microarray data.

We consider the problem of inferring fold changes in gene expression from cDNA microarray data. Standard procedures focus on the ratio of measured fluorescent intensities at each spot on the microarray, but to do so is to ignore the fact that the variation of such ratios is not constant. Estimates of gene expression changes are derived within a simple hierarchical model that accounts for measurement error and fluctuations in absolute gene expression levels. Significant gene expression changes are identified by deriving the posterior odds of change within a similar model. The methods are tested via simulation and are applied to a panel of Escherichia coli microarrays.     

Characterization and simulation of cDNA microarray spots using a novel mathematical model

Background  

The quality of cDNA microarray data is crucial for expanding its application to other research areas, such as the study of gene regulatory networks. Despite the fact that a number of algorithms have been suggested to increase the accuracy of microarray gene expression data, it is necessary to obtain reliable microarray images by improving wet-lab experiments. As the first step of a cDNA microarray experiment, spotting cDNA probes is critical to determining the quality of spot images.     

A stepwise framework for the normalization of array CGH data

Background  

In two-channel competitive genomic hybridization microarray experiments, the ratio of the two fluorescent signal intensities at each spot on the microarray is commonly used to infer the relative amounts of the test and reference sample DNA levels. This ratio may be influenced by systematic measurement effects from non-biological sources that can introduce biases in the estimated ratios. These biases should be removed before drawing conclusions about the relative levels of DNA. The performance of existing gene expression microarray normalization strategies has not been evaluated for removing systematic biases encountered in array-based comparative genomic hybridization (CGH), which aims to detect single copy gains and losses typically in samples with heterogeneous cell populations resulting in only slight shifts in signal ratios. The purpose of this work is to establish a framework for correcting the systematic sources of variation in high density CGH array images, while maintaining the true biological variations.     

Weighted quality estimates in machine learning

MOTIVATION: Machine learning methods such as neural networks, support vector machines, and other classification and regression methods rely on iterative optimization of the model quality in the space of the parameters of the method. Model quality measures (accuracies, correlations, etc.) are frequently overly optimistic because the training sets are dominated by particular families and subfamilies. To overcome the bias, the dataset is usually reduced by filtering out closely related objects. However, such filtering uses fixed similarity thresholds and ignores a part of the training information. RESULTS: We suggested a novel approach to calculate prediction model quality based on assigning to each data point inverse density weights derived from the postulated distance metric. We demonstrated that our new weighted measures estimate the model generalization better and are consistent with the machine learning theory. The Vapnik-Chervonenkis theorem was reformulated and applied to derive the space-uniform error estimates. Two examples were used to illustrate the advantages of the inverse density weighting. First, we demonstrated on a set with a built-in bias that the unweighted cross-validation procedure leads to an overly optimistic quality estimate, while the density-weighted quality estimates are more realistic. Second, an analytical equation for weighted quality estimates was used to derive an SVM model for signal peptide prediction using a full set of known signal peptides, instead of the usual filtered subset.     

Identifying differentially expressed genes in cDNA microarray experiments.

A major goal of microarray experiments is to determine which genes are differentially expressed between samples. Differential expression has been assessed by taking ratios of expression levels of different samples at a spot on the array and flagging spots (genes) where the magnitude of the fold difference exceeds some threshold. More recent work has attempted to incorporate the fact that the variability of these ratios is not constant. Most methods are variants of Student's t-test. These variants standardize the ratios by dividing by an estimate of the standard deviation of that ratio; spots with large standardized values are flagged. Estimating these standard deviations requires replication of the measurements, either within a slide or between slides, or the use of a model describing what the standard deviation should be. Starting from considerations of the kinetics driving microarray hybridization, we derive models for the intensity of a replicated spot, when replication is performed within and between arrays. Replication within slides leads to a beta-binomial model, and replication between slides leads to a gamma-Poisson model. These models predict how the variance of a log ratio changes with the total intensity of the signal at the spot, independent of the identity of the gene. Ratios for genes with a small amount of total signal are highly variable, whereas ratios for genes with a large amount of total signal are fairly stable. Log ratios are scaled by the standard deviations given by these functions, giving model-based versions of Studentization. An example is given.     

Pooling mRNA in microarray experiments and its effect on power

MOTIVATION: Microarrays can simultaneously measure the expression levels of many genes and are widely applied to study complex biological problems at the genetic level. To contain costs, instead of obtaining a microarray on each individual, mRNA from several subjects can be first pooled and then measured with a single array. mRNA pooling is also necessary when there is not enough mRNA from each subject. Several studies have investigated the impact of pooling mRNA on inferences about gene expression, but have typically modeled the process of pooling as if it occurred in some transformed scale. This assumption is unrealistic. RESULTS: We propose modeling the gene expression levels in a pool as a weighted average of mRNA expression of all individuals in the pool on the original measurement scale, where the weights correspond to individual sample contributions to the pool. Based on these improved statistical models, we develop the appropriate F statistics to test for differentially expressed genes. We present formulae to calculate the power of various statistical tests under different strategies for pooling mRNA and compare resulting power estimates to those that would be obtained by following the approach proposed by Kendziorski et al. (2003). We find that the Kendziorski estimate tends to exceed true power and that the estimate we propose, while somewhat conservative, is less biased. We argue that it is possible to design a study that includes mRNA pooling at a significantly reduced cost but with little loss of information.     

Estimation and control of multiple testing error rates for microarray studies

The analysis of microarray data often involves performing a large number of statistical tests, usually at least one test per queried gene. Each test has a certain probability of reaching an incorrect inference; therefore, it is crucial to estimate or control error rates that measure the occurrence of erroneous conclusions in reporting and interpreting the results of a microarray study. In recent years, many innovative statistical methods have been developed to estimate or control various error rates for microarray studies. Researchers need guidance choosing the appropriate statistical methods for analysing these types of data sets. This review describes a family of methods that use a set of P-values to estimate or control the false discovery rate and similar error rates. Finally, these methods are classified in a manner that suggests the appropriate method for specific applications and diagnostic procedures that can identify problems in the analysis are described.     

Quantitative quality control in microarray image processing and data acquisition

A new integrated image analysis package with quantitative quality control schemes is described for cDNA microarray technology. The package employs an iterative algorithm that utilizes both intensity characteristics and spatial information of the spots on a microarray image for signal–background segmentation and defines five quality scores for each spot to record irregularities in spot intensity, size and background noise levels. A composite score q_com is defined based on these individual scores to give an overall assessment of spot quality. Using q_com we demonstrate that the inherent variability in intensity ratio measurements is closely correlated with spot quality, namely spots with higher quality give less variable measurements and vice versa. In addition, gauging data by q_com can improve data reliability dramatically and efficiently. We further show that the variability in ratio measurements drops exponentially with increasing q_com and, for the majority of spots at the high quality end, this improvement is mainly due to an improvement in correlation between the two dyes. Based on these studies, we discuss the potential of quantitative quality control for microarray data and the possibility of filtering and normalizing microarray data using a quality metrics-dependent scheme.     

A comprehensive sensitivity analysis of microarray breast cancer classification under feature variability

Background  

Large discrepancies in signature composition and outcome concordance have been observed between different microarray breast cancer expression profiling studies. This is often ascribed to differences in array platform as well as biological variability. We conjecture that other reasons for the observed discrepancies are the measurement error associated with each feature and the choice of preprocessing method. Microarray data are known to be subject to technical variation and the confidence intervals around individual point estimates of expression levels can be wide. Furthermore, the estimated expression values also vary depending on the selected preprocessing scheme. In microarray breast cancer classification studies, however, these two forms of feature variability are almost always ignored and hence their exact role is unclear.     

Microarray optimizations: increasing spot accuracy and automated identification of true microarray signals

In this paper, fluorescent microarray images and various analysis techniques are described to improve the microarray data acquisition processes. Signal intensities produced by rarely expressed genes are initially correctly detected, but they are often lost in corrections for background, log or ratio. Our analyses indicate that a simple correlation between the mean and median signal intensities may be the best way to eliminate inaccurate microarray signals. Unlike traditional quality control methods, the low intensity signals are retained and inaccurate signals are eliminated in this mean and median correlation. With larger amounts of microarray data being generated, it becomes increasingly more difficult to analyze data on a visual basis. Our method allows for the automatic quantitative determination of accurate and reliable signals, which can then be used for normalization. We found that a mean to median correlation of 85% or higher not only retains more data than current methods, but the retained data is more accurate than traditional thresholds or common spot flagging algorithms. We have also found that by using pin microtapping and microvibrations, we can control spot quality independent from initial PCR volume.