Biostatistics Advance Access first published online on December 12, 2006
This version published online on May 18, 2007
Biostatistics, doi:10.1093/biostatistics/kxl041
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When should one subtract background fluorescence in 2-color microarrays?
Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD, USA rscharpf{at}jhsph.edu
Departments of Pathology and Oncology, The Sol Goldman Pancreatic Cancer Research Center, Johns Hopkins University School of Medicine, Baltimore, MD, USA
Department of Biochemistry, Stanford University School of Medicine, Stanford, CA, USA
Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health Baltimore, MD, USA and Department of Oncology, Johns Hopkins University School of Medicine, Baltimore, MD, USA
* To whom correspondence should be addressed.
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SUMMARY |
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 TOP SUMMARY 1. INTRODUCTION2. METHODS3. RESULTS4. DISCUSSIONREFERENCES |
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Two-color microarrays are a powerful tool for genomic analysis, but have noise components that make inferences regarding gene expression inefficient and potentially misleading. Background fluorescence, whether attributable to nonspecific binding or other sources, is an important component of noise. The decision to subtract fluorescence surrounding spots of hybridization from spot fluorescence has been controversial, with no clear criteria for determining circumstances that may favor, or disfavor, background subtraction. While it is generally accepted that subtracting background reduces bias but increases variance in the estimates of the ratios of interest, no formal analysis of the bias–variance trade off of background subtraction has been undertaken. In this paper, we use simulation to systematically examine the bias–variance trade off under a variety of possible experimental conditions. Our simulation is based on data obtained from 2 self versus self microarray experiments and is free of distributional assumptions. Our results identify factors that are important for determining whether to background subtract, including the correlation of foreground to background intensity ratios. Using these results, we develop recommendations for diagnostic visualizations that can help decisions about background subtraction.
Keywords: Background substraction; Microarray
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1. INTRODUCTION |
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TOPSUMMARY1. INTRODUCTION2. METHODS3. RESULTS4. DISCUSSIONREFERENCES |
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Two-color microarrays evaluate the expression of thousands of genes and expressed sequence tags (ESTs) in a single assay by quantifying the relative abundance of messenger RNA (mRNA). The discovery of differentially expressed genes using microarrays depends crucially on the choice of normalization (Simon and others, 2003
; Speed, 2003; Parmigiani and others 2003). Considerations for optimal normalization of the microarray data are platform dependent.
The focus of this paper is on noise intrinsic to fluorescent-imaging platforms. Specifically, we consider cDNA microarrays where target and reference mRNA are reverse transcribed to cDNA and tagged by green and red fluorophores. The target and reference preparations are combined and competitively hybridized to short DNA sequences (probes) spotted on a glass slide. Each probe on the array binds, in theory, to a single gene or EST. After imaging the array, statistics such as the median red and green intensity at each spot (foreground) as well as comparable statistics for the local fluorescence surrounding the spot of hybridization are usually available. We will refer to the latter measure of fluorescence as background. Estimates of background can be highly variable and are sensitive to the imaging methodology used (Brown and others, 2001). Background is often subtracted from foreground prior to normalization. Ideally, the added variability would be compensated by a reduction in bias. See Schena (2000), Hardiman (2002), and Southern (2001) for a more complete description of cDNA microarray technology.
Background can arise from a number of sources, including incomplete washing after hybridization, features of the slide that bind dye or RNA, and imprecision in spot localization (segmentation) during image acquisition. See Schuchhardt and others (2000) for a comprehensive list of sources of variability in cDNA microarrays. Background subtraction (BS) is an imperfect solution for reducing bias due, in part, to imprecision of the imaging measure of background, as well as heterogeneity of background near the spot of hybridization Brown and others (2001). BS introduces another layer of variability to the gene expression measure.
The decision to implement BS plays an important role in identifying differentially expressed genes. See Chen and others (1997), Baggerly and others (2001), and Quackenbush (2002) for considerations when inferring differential expression by ratios of signal intensity. Subtracting background from low abundance genes results in overdispersion of log intensity ratios. Also problematic with low abundance genes is the potential for estimates of background to be greater than foreground. We and others believe that subtracting local estimates of background from foreground is less than ideal (Brown and others, 2001), (, Qin2004), (, Martinez2003). More sophisticated normalization methods have been implemented to deal with this problem (Kooperberg and others, 2002), (, Brown2001). Nevertheless, the decision of whether to perform BS has been largely a matter of personal preference with few guidelines for determining when BS is appropriate. One barrier to a more formal analysis of the bias–variance trade off has been the absence of a suitable model for simulating the variability in microarray experiments.
Factors influencing the bias and variability in microarray data are not limited to the abundance of cDNA in the hybridized samples. Implicitly, BS assumes that the background is homogeneous across spotted and nonspotted portions of the array. However, this assumption is often not valid. Foreground fluorescence arising from cross hybridization (whether specific or nonspecific) and location-specific binding are common and each contributes to unmeasured background heterogeneity. BS is inappropriate if such location-specific biases exist (Martinez and others, 2003), (, Brown2001). Location-dependent normalization procedures such as loess (see Section 2) may only partially correct for this problem. Diagnostics for visualizing when such biases are likely to exist are needed.
Through simulation, we consider multiple factors that are likely to influence the decision to perform BS, including the abundance of hybridized transcript. We use 2 self versus self (SVS) microarray experiments (see Section 2) for the simulation to ensure that our results are not biased to the technological variability in one experiment. Advantages of using SVS experimental data include that the true differential expression is known to be absent, variability in the gene expression is from actual data, and thousands of genes can be simulated, rather than one at a time. Because we compare the bias, variance, and mean squared error (MSE) with and without BS, these results provide guidance on whether to subtract estimates of background from foreground in 2-color microarrays.
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2. METHODS |
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TOPSUMMARY1. INTRODUCTION2. METHODS3. RESULTS4. DISCUSSIONREFERENCES |
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R (Ihaka and Gentleman, 1996
) and Bioconductor (http://www.bioconductor.org) (Gentleman, 2003) were used for all statistical analyses. Our simulation uses data from 2 SVS hybridizations (one array per hybridization). Briefly, SVS hybridization refers to labeling one aliquot of cDNA with red fluorophores and a separate aliquot from the same sample with green fluorophores. Equal mass amounts of red- and green-labeled cDNA are then competitively hybridized to the microarray. In truth, no differential expression should occur.
A SVS hybridization of amplified Stratagene universal reference RNA was obtained from the Stanford Microarray Database (http://genome-www.stanford.edu/microarray) (Gollub and others, 2003
). Stratagene human universal reference RNA contains RNA from 10 pooled human cell lines. Universal reference RNA is commonly used as the reference sample in microarray platforms that use competitive hybridization to quantify relative mRNA abundance since most arrayed genes in the pooled sample are detectable above background noise (Yang and others, 2002). The microarray for this experiment was spotted with 43 104 clones. Background fluorescence was computed as the median pixel intensity from several locations adjacent to the spot of hybridization. Similarly, spot fluorescence was computed as the median pixel intensity from several locations within the target region for hybridization. Segmentation and image analysis were performed using GenePix Pro 3.0.6.86
[EC]
(Axon Instruments, Inc.). See Fielden and others (2002) for more information on GenePix. These data are publicly available at the Stanford Microarray Database.
A second SVS hybridization of breast cancer cell line MCF7 was downloaded from Supplementary Material available at www.biostatistics.oxfordjournals.org (Berger and others, 2004
). The microarray was scanned with an Agilent laser confocal scanner and gridded using the DEARRAY software (Chen and others, 2002). Spot and background fluorescence were calculated as average intensities within the target area, after trimming the top and bottom 5%. The cDNA microarray was printed with 11 520 clones from Incyte Genomics and 1136 clones from Research Genetics library for a total of 13 440 spots. See Berger and others (2004) for more detailed information regarding this experiment. We hereafter refer to arrays 1 and 2 as "Stratagene" and "MCF7", respectively.
Negative spot intensities after BS are not sensible and methods that use BS typically exclude such spots. To facilitate comparison of BS to no background subtraction (NBS), we excluded spots where background was measured greater than foreground (though this is typically not necessary for NBS). Of 43 104 spots, 28 837 and of 13 440 spots, 6933 had foreground greater than background in both channels for the Stratagene and MCF7 experiments, respectively. Because pixel level data within a spot have been shown to be a useful indicator of spot quality (Brown and others, 2001), additional filtering criteria were applied to the Stratagene array to obtain a smaller subset of 16 908 spots. The additional filtering required a correlation greater than 0.6 of red and green pixels within a spot, no flags generated from the GenePix imaging software, and median foreground 1.5-fold greater than median background for both the red and the green intensities. The simulation was performed with minimal filtering of the data (28 837 and 6933 spots for Stratagene and MCF7, respectively), as well as with the more filtered Stratagene subset (16 908 spots).
The spot statistics used for normalizing the microarrays are the log2 abundance (A) and the log2 ratio (M) of median red (R) and green (G) foreground. Hence, A,M,R, and G are spot statistics computed without subtracting background. Ms and As are the corresponding statistics for the ratio and abundance, respectively, after subtracting median red (Rb) and green (Gb) background. Explicitly,
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A-dependent normalization was performed by robust locally weighted least squares regression (loess) (Cleveland, 1979), (, Cleveland1981) using Bioconductor software (Gentleman, 2003), (, dudo:yang:2003). A-dependent normalization procedures for smoothing MA scatter plots are often preferable to global normalization due to the frequent occurrence of intensity biases (Park and others, 2003). In addition, we used loess to smooth scatter plots of background abundance (Ab) and intensity ratios (Mb), where
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Hereafter, foreground and background ratios refer to log2 ratios of intensities unless otherwise explicitly stated.
We assume an additive model stating that the true biological signal is the difference in the spot intensity and the latent background intensity. Let 
denote a 4-dimensional vector of parameters that represent the true state of nature for a single spot: = (
A, Ab, M, Mb), where X is the parameter for the statistic X. Note that the true ratio of differential expression (Ms) is known through , that is
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The assumption that background and biological signal add to equal the spot intensity needs further empirical verification.
For a given , we simulate the expression of thousands of genes that vary around this truth without relying on distributional assumptions that are difficult to verify. SVS hybridizations are a natural choice since we are able to observe variability in differential expression across a range of abundance when the true differential expression is known to be absent. The algorithm for the simulation is outlined in panels a–c of Supplementary Figure 1 (available at www.biostatistics.oxfordjournals.org), and is repeated for each specification of . Specifications of were chosen to cover a range of plausible values (see Section 3). Here, we describe the simulation for a fixed .
Quantities of interest for a gene are simulated by independent random draws of observed normalized M and Mb from a SVS experiment. Sampling with replacement of M and Mb was restricted to deciles of spot abundance determined by A (see Supplementary Figure 1a and 1b available at www.biostatistics. oxfordjournals.org). The pair (Mi,Mbi) denotes the ith observation from 2 independent draws and need not correspond to an actual spot in the SVS hybridization. That is, Mi and Mbi may correspond to the original foreground and background ratios of genes j and k, j
k. We append the subscript A to M and Mb in (2.2) and (2.3) to make their dependence on abundance explicit.
To assess the critical role of the relationship of MA to MbA, we obtain the best fit line by linear regression
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The simulation uses observed residuals directly so that it is not necessary to specify a distribution for these values. To manipulate the dependence of the foreground ratio on the background ratio, we parameterize the correlation of MA and MbA by 
and vary this correlation by scaling the observed residuals in (2.2) by a constant k such that
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The average of MA and MbA is zero. We simulate nonzero foreground ratios (M
ger) and background ratios (M
) by the following relationships:
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Hence, the simulated foreground ratio, Mger, is obtained from the adjusted residuals in (2.3) by shifting the regression line by an amount given by the true foreground ratio, M. To see this, we can rewrite (2.4) as
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To summarize, we have simulated ratios of foreground that have an abundance-dependent distribution determined by the SVS experiment and whose dependence on background is parameterized by . Calculations to obtain the simulated foreground and background intensities are straightforward:
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The bias and variance with BS and NBS for one spot are given by the following relationships:
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Estimates of the bias, variance, and MSE were obtained by averaging over 1000 simulations.
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3. RESULTS |
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TOPSUMMARY1. INTRODUCTION2. METHODS3. RESULTS4. DISCUSSIONREFERENCES |
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We suggest 2 simple diagnostic plots to explore whether BS is needed: spatial images of background (logarithm scale) and scatter plots of M versus Mb. Figure 1 shows images of background from the Stratagene (row 1) and MCF7 (row 2) experiments. For Stratagene, log2Rb (plot 1) and log2Gb (plot 2) are comparable across most locations of the array, and background is reasonably homogeneous with the notable exception of the lower right sector. The Spearman correlation coefficient for the M versus Mb scatter plot was relatively high (0.54). The high correlation of the foreground to background ratios suggests that a reduction in bias by BS may be achieved. By contrast, the spatial images of MCF7 background are more heterogeneous across channels and the Spearman correlation coefficient for the M versus Mb scatter plot is much lower (0.14).
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While background is reasonably homogeneous across the red and green channels for most regions of the MCF7 array, a region in cell 2,1 and several regions in column 2 show more heterogeneity across channels. Whether the correlation of the ratios is also small within these subregions of the array is an important question that may influence both the bias and the variability in the estimates of differential expression for a large number of genes in this region of array. We further discuss the important issue of spatially dependent correlations of the spot and background intensities in the Supplementary Materials (available at www.biostatistics.oxfordjournals.org). Whether the reduction in bias obtained by BS in the Stratagene and MCF7 experiments will offset the added variability is not clear. MA plots are useful for visualizing the added variability in the foreground ratios for low abundance genes after BS. See Supplementary Figure 2 (available at www.biostatistics.oxfordjournals.org) for illustration. More formally, we treat the decision of BS versus NBS as a trade off between bias and variance that can be addressed through simulation.
To determine when it is preferable to perform BS, we performed the simulation described in Section 2.3. The values of parameters used for the simulation were chosen to illustrate the trade off in bias and variance, as well as to reflect empirically determined values in the SVS experiments. In particular, A was chosen so that foreground ratios were sampled within deciles 1, 3, 5, and 7 of the observed A. Values for Ab were determined by the median of the first and third quartiles of Ab.
Figures 2 and 3 show the bias–variance trade off for the simulations using the Stratagene and MCF7 data, respectively. Each panel plots the difference in estimates of the bias, variance, and MSE (vertical axis) using BS and NBS across a range of Ms (horizontal axis) for a fixed A (row) and fixed Mb (column). The three 16-panel plots in Figures 2 and 3 differ with respect to the correlation of Mger to M given by . Shown here are correlations of 0.3, 0.2, and 0.1. Estimates of MSE using higher correlations (0.4) uniformly favored BS, whereas simulations using lower correlations (0.05) uniformly favored NBS (data not shown). The results shown here are for Ab equal to the median of the first quartile of Ab. However, our findings were qualitatively similar using a value of Ab in the third quartile of Ab (data not shown).
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A recurring feature in Figures 2 and 3 for
= 0.3 and 0.2 is the concavity of the line plotting the difference in MSE as a function of the true differential expression, Ms. For negative Ms, estimates of differential expression are biased if we do not subtract background. The penalty in bias is proportional to the correlation of the ratios of foreground and background intensities, with higher correlations driving more negative differences in squared bias between BS and NBS. If the correlation is small (as in the plot with = 0.1), the bias from NBS does not outweigh the cost of the added variability as reflected by a positive difference in MSE.
Comparing Figure 2 to Figure 3, we observe similar trends but BS is generally more favorable in the simulation using the MCF7 data for = 0.2 and higher, whereas in the Stratagene experiment NBS was preferable for = 0.2. However, if we filtered the Stratagene data on flags generated by the imaging software and pixel level correlations of red and green intensities, BS was also preferable for = 0.2 and higher (data not shown). While there appears to be less variability in the foreground ratios after more stringent filtering, this further reduces the number of genes considered in the analysis by 40%. Finally, note that in each of the plots, the BS decision is less critical as the ratio of A/Ab increases. For instance, in Figure 2 the largest difference in MSE for row 1 is roughly 20-fold greater than the largest difference in MSE for row 4.
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4. DISCUSSION |
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TOPSUMMARY1. INTRODUCTION2. METHODS3. RESULTS4. DISCUSSIONREFERENCES |
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Images of background fluorescence together with scatter plots of ratios of foreground and background are useful diagnostics for quality control and aiding the decision of whether to subtract estimates of local background. Through simulation, we show the bias–variance trade off of BS over a range of experimental conditions observed in practice.
Because the variability of gene expression in cDNA microarrays is known to be dependent on spot abundance (Newton and others, 2001), (, Baggerly2001), our simulation captures abundance-dependent variability from 2 SVS hybridizations where the true differential expression is known to be absent. In this way, we avoid specifying a parametric model and simulate genes having a range of possible true differential expressions with varying levels of abundance and background intensity ratios. Additionally, we simulated foreground ratios with varying degrees of correlation to background ratios. Figures 2 and 3 show that BS is less favorable in terms of MSE across a range of possible truths for differential expression when the correlation of background and foreground intensity ratios was low (0.1 and less). Conversely, high correlation (0.3 and greater) of foreground to background ratios favors BS and may indicate that background is not spot localized, or that appreciable nonsequence-based fluorescence occurs within regions of hybridization. Preprocessing procedures that do not background subtract are penalized by the large bias in these instances. If correlations of foreground and background ratios are spatially heterogeneous within an array (see Supplementary Materials available at www.biostatistics.oxfordjournals.org, Figure 3), a model that estimates background as a function of this correlation may be preferable. For instance, a Bayesian approach proposed by Kooperberg and others (2002) assumes that the observed mean foreground Xf and background Xb intensities are Gaussian with locations µt + µb and µb, respectively. Parametrization of the Gaussian distributions in this way induces a correlation of Xf and Xb, whereby posterior estimates of µb are a function of this correlation. When the correlations of foreground and background across arrays are borderline (i.e. between 0.1 and 0.3), an all- or none-approach to BS across arrays is preferable as a mixed strategy necessitates a more careful cross-array normalization.
With experiments involving multiple arrays, the decision to background subtract on a per-array basis is controversial. However, consider a simple experiment with 2 chips, each hybridizing the same RNA in the red and green channels. Assume that one chip has a large artifact that is artificially inflating both foreground and background in a particular region, while the other chip does not. The artifact induces a high foreground–background correlation in the first chip but not in the second. Are the estimates for the red/green ratio more comparable across chips if we use different BS strategies? If the artifact is strong enough, of the 3 subtraction options (subtract in both arrays, subtract in one array, and subtract in neither array) the method that subtracts background in only one array results in the lowest MSE in our simulations. Because MSE measures how close each array's ratios will be to the truth on average and subsequent cross-array normalization can adjust for overall changes in the variance of the estimated ratios from array to array, we propose that such an approach, carefully applied, may be useful for obtaining better estimates of the signal in each array. Implicit in such an approach is that the model for background changes between arrays within an experiment—a controversial procedure from a model-based perspective. Because it is difficult to assess when BS for a subset of arrays is the right choice, we prefer NBS for all arrays when the correlations are borderline.
Whether the correlation of foreground and background intensity ratios is used to assess array quality or to inform the decision to BS, the preprocessing algorithm should be followed by an appropriate normalization between arrays to remove nonbiological sources of variation that may occur during preparation and processing of the arrays. See Smyth and Speed (2003) for a recent review and available software.
Microarrays have different sources of technological variation that may arise at any step during the experiment, including RNA preparation, printing of the microarray, and imaging of the hybridized samples. Our simulation is based on 2 SVS hybridizations and as such may have noise that differs from other microarrays. That the results were qualitatively similar across 2 SVS experiments produced by different laboratories, different biological samples, and different imaging software suggests that our simulation is not overly sensitive to the specific technological variability in these 2 experiments. The findings presented here are consistent with others who have used different methods to evaluate BS. For instance, Qin and others (2004) compare BS to NBS in 4 microarray experiments with spike-in genes (genes inserted at known ratios). BS was inferior to NBS in each of the 4 microarray experiments, largely because of the variability in the log intensity ratios of the low-mid abundance genes. Additionally, while we performed our analysis with cDNA microarrays, this work is relevant and can be easily adapted to other 2-channel microarray platforms, such as Agilent (Hughes and others, 2001).
Our simulation shows the relationship of bias, variance, and MSE for intensity-dependent normalization procedures performed with and without BS across a range of simulated differential expressions. The correlation of foreground to background ratios is an important consideration before subtracting background fluorescence. A preprocessing methodology informed by these correlations may help identify differentially expressed genes, particularly at lower abundances where variation of the red/green intensity ratios is most susceptible to the BS decision.
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ACKNOWLEDGMENTS |
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We thank John Berger for making the data for the MCF7 cell line publicly available. We thank Leslie Cope for his comments and suggestions regarding this manuscript. Robert B. Scharpf was supported by the grant 5T32ES012871 from the US National Institute of Environmental Health Sciences. Giovanni Parmigiani was supported by National Cancer Institute grant P50CA88843 and National Science Foundation grants DMS034211 and NCIP30CA06973. Conflict of Interest: None declared.
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REFERENCES |
|---|
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TOPSUMMARY1. INTRODUCTION2. METHODS3. RESULTS4. DISCUSSIONREFERENCES |
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Baggerly KA, Coombes KR, Hess KR, Stivers DN, Abruzzo LV, Zhang W. Identifying differentially expressed genes in cDNA microarray experiments. Journal of Computational Biology (2001) 8:639–659.[CrossRef][Web of Science][Medline]
Berger JA, Hautaniemi S, Järvinen A-K, Edgren H, Mitra SK, Astola J. Optimized LOWESS normalization parameter selection for DNA microarray data. BMC Bioinformatics (2004) 5:194.[CrossRef][Medline]
Brown CS, Goodwin PC, Sorger PK. Image metrics in the statistical analysis of DNA microarray data. Proceedings of the National Academy of Sciences of the United States of America (2001) 98:8944–8949.
Chen Y, Dougherty E, Bittner M. Ratio-based decisions and the quantitative analysis of cDNA micro-array images. Journal of Biomedical Optics (1997) 2:364–374.[CrossRef]
Chen Y, Kamat V, Dougherty ER, Bittner ML, Meltzer PS, Trent JM. Ratio statistics of gene expression levels and applications to microarray data analysis. Bioinformatics (2002) 18:1207–1215.
Cleveland WS. Robust locally weighted regression and smoothing scatterplots. Journal of American Statistics Association (1979) 74:829–836.[CrossRef]
Cleveland WS. Lowess: a program for smoothing scatterplots by robust locally weighted regression. The American Statistician (1981) 35:54.
Dudoit S, Yang JYH. Bioconductor R packages for exploratory analysis and normalization of cDNA microarray data. In: The Analysis of Gene Expression Data: Methods and Software—Parmigiani G, Garrett ES, Irizarry RA, Zeger SL, eds. (2003) New York: Springer. 73–101.
Fielden MR, Halgren RG, Dere E, Zacharewski TR. GP3: GenePix post-processing program for automated analysis of raw microarray data. Bioinformatics (2002) 18:771–773.
Gentleman R. BioConductor: Open Source Software for Bioinformatics. (2003) http://www.bioconductor.org.
Gollub J, Ball CA, Binkley G, Demeter J, Finkelstein DB, Hebert JM, Hernandez-Boussard T, Jin H, Kaloper M, and others. The Stanford Microarray Database: data access and quality assessment tools. Nucleic Acids Research (2003) 31:94–96.
Hardiman G. Microarray technologies—an overview. Pharmacogenomics (2002) 3:293–297.[CrossRef][Medline]
Hughes TR, Mao M, Jones AR, Burchard J, Marton MJ, Shannon KW, Lefkowitz SM, Ziman M, Schelter JM, Meyer MR, and others. Expression profiling using microarrays fabricated by an ink-jet oligonucleotide synthesizer. Nature Biotechnology (2001) 19:342–347.[CrossRef][Web of Science][Medline]
Ihaka R, Gentleman R. R: a language for data analysis and graphics. Journal of Computational and Graphical Statistics (1996) 5:299–314.[CrossRef]
Kooperberg C, Fazzio TG, Delrow JJ, Tsukiyama T. Improved background correction for spotted DNA microarrays. Journal of Computational Biology (2002) 9:55–66.[CrossRef][Web of Science][Medline]
Martinez MJ, Aragon AD, Rodriguez AL, Weber JM, Timlin JA, Sinclair MB, Haaland DM, Werner-Washburne M. Identification and removal of contaminating fluorescence from commercial and in-house printed DNA microarrays. Nucleic Acids Research (2003) 31:e18.
Newton MA, Kendziorski CM, Richmond CS, Blattner FR, Tsui KW. On differential variability of expression ratios: improving statistical inference about gene expression changes from microarray data. Journal of Computational Biology (2001) 8:37–52.[CrossRef][Web of Science][Medline]
Park T, Yi S-G, Kang S-H, Lee SY, Lee Y-S, Simon R. Evaluation of normalization methods for microarray data. BMC Bioinformatics (2003) 4:33.[CrossRef][Medline]
Parmigiani G, Garrett ES, Irizarry RA, Zeger SL. The Analysis of Gene Expression Data: Methods and Software (2003) New York: Springer.
Qin L-X, Kerr KF, CONTRIBUTING MEMBERS OF THE TOXICOGENOMICS RESEARCH CONSORTIUM. Empirical evaluation of data transformations and ranking statistics for microarray analysis. Nucleic Acids Research (2004) 32:5471–5479.
Quackenbush J. Microarray data normalization and transformation. Nature Genetics (2002) 32S:496–501.[CrossRef][Web of Science][Medline]
Schena M. Microarray Biochip Technology (2000) Westborough, MA: BioTechniques Press.
Schuchhardt J, Beule D, Malik A, Wolski E, Eickhoff H, Lehrach H, Herzel H. Normalization strategies for cDNA microarrays. Nucleic Acids Res (2000) 28:e47.
Simon RM, Korn EL, McShane LM, Radmacher MD, Wright GW, Zhao Y. Design and Analyis of DNA Microarray Investigations (2003) New York: Springer.
Smyth GK, Speed T. Normalization of cDNA microarray data. Methods (2003) 31:265–273.[CrossRef][Web of Science][Medline]
Southern EM. DNA microarrays. History and overview. Methods in Molecular Biology (2001) 170:1–15.[Medline]
Speed TP, ed. Statistical Analysis of Gene Expression Microarray Data (2003) London: Chapman and Hall.
Yang YH, Dudoit S, Luu P, Lin DM, Peng V, Ngai J, Speed T. Normalization for cDNA microarray data: a robust composite method addressing single and multiple slide systematic variation. Nucleic Acids Research (2002) 30:e15.
Received July 21, 2005; revised May 19, 2006; revised September 15, 2006; revised October 27, 2006; accepted for publication December 2, 2006.
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