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Microarray technology, a fairly recent yet already well-established and extensively dissected method, allows for the simultaneous quantification of expression levels of entire genomes or subsets thereof [

Because the objective of such experiments is generally to assess gene expression differences between one or more biological samples, separating

An initial attempt to address nonuniform “background intensity” was incorporated directly in the design of the GeneChip platform: for each “perfect match” (PM) probe, there is a corresponding “mismatch” (MM) probe which features a single different base [

In order to make data from multiple arrays directly comparable, normalization methods such as locally weighted scatterplot smoothing (LOWESS or loess) [

It has been noted that the choice of background correction methodology has a significant impact on downstream analysis accuracy [

The currently advocated standard operating procedure with respect to the well-known issue of spatial bias in

We posit that

Using notation inspired by [_{2}-transformed HSI of probe

In justifying the use of spike-in and dilution datasets for assessing accuracy, Cope et al. assert that “to estimate bias in measurements, we need truth, in an absolute or relative form, or at least a different, more accurate measurement of the same samples” [

Although a given probe residual merely quantifies one HSI’s deviation from an estimate and thus contains contributions from many probe-specific biases (e.g., binding efficiency and specificity) and random noise, a sufficiently large pool of probe residuals with similar locations on the array provides a summary of the average bias induced by such a location. Noting that residuals (and accordingly means of residuals) share units and scale with HSIs, we thus simply propose to subtract this estimate of location-induced bias from each HSI to obtain corrected signals:

It is of theoretical interest to note that, as

The optimal choice of

In this paper, three typical Affymetrix Human Genome U133A datasets are used to evaluate the proposed algorithm: two datasets obtained from the public microarray repository GEO [

An implementation of the proposed spatial correction procedure is provided as part of an R package (“

The procedure runs for approximately one second per array (Intel Core 2 Duo 3.33 GHz) and accepts any valid

In this paper, “CPP” and “LPE” refer to the two algorithms proposed by Arteaga-Salas et al. in [

For each probe on each array in a batch, a value similar to our residual is computed, relating the deviation of the probe’s intensity from its median intensity across all arrays. A “code” is then computed for each probe, which identifies the array where this value is the largest and whether it is positive or negative. Then, to determine whether a given location in a batch of arrays is affected by spatial bias, PM and MM probes in a 5

Residuals are computed for each probe on each array as in LPE, but the authors require in this case for all arrays to be replicates of one another. Each PM intensity is corrected by subtracting its MM counterpart’s residual and vice versa. Residuals are scaled before subtraction to address differences in PM and MM distributions.

From each intensity at a given location on an array, the smallest intensity found in a (

Figure

Empirical distributions of probe residuals R, as defined in the text, with one curve associated with each of the 66 arrays found in the three datasets. In each case, the mean residual is almost zero

Under the assumption that probes are randomly located on the array, these residuals are expected to be randomly spatially distributed across the array; thus, any spatial patterns must be ascribable to some form of technical error. In practice, we frequently observe various manifestations of such patterns. Figure

Empirical spatial distribution of probe residuals in original and corrected data. Mapping probe residuals back to their originating physical locations and displaying them as a heat map reveals a variety of spatial artefacts in (a) original data: horizontal stripes (all arrays), a large region of positive residuals (GSE2189, left), and a small region of negative residuals (spike-in, bottom right); (b) after correction (

The spatial patterns identified in Figure

Figure

This “spatial dependence” can be defined quantitatively as

Quantitative effects of correction on spatial autocorrelation. Reimers-Weinstein spatial autocorrelation metric computed in data corrected by various methods (

As effective correction of array-specific spatial biases should result in greater reproducibility, we evaluated the impact of each spatial correction method on variance across replicate arrays. Figure

Effect of correction on reproducibility across replicate arrays. Standard deviation of log expression index of probe sets across replicate arrays as a function of mean log expression, as computed in data obtained with RMA (all default parameters) after pretreatment with each of the spatial correction methods (or none).

In order to assess the impact of the spatial correction methods on more tangible, biological results, we used the

Effect of correction on DEG detection power. Receiver operating characteristic (ROC) curves generated by the R/bioconductor package

Finally, we assessed the effect of parameter

Effect of

Systematic, nonbiological variations have been long known to obscure microarray data. In the case of spotted arrays, array- and print-tip-dependent biases were the first to be considered. Array bias could trivially be visualized by inspecting box plots of a batch of arrays or using more sophisticated approaches such as RLE and NUSE plots [

This strategy of addressing known sources of bias individually has been somewhat abandoned in the case of

We posit, as initially asserted by Dudoit et al. in 2002, that correcting for known biases using

We have shown that this method reduces spatial autocorrelation in HSIs, reduces variance in gene expression measures across replicate arrays, improves DEG detection power, and performs better than previously published methods in terms of replicate variance reduction and DEG detection power increase. As for spatial autocorrelation reduction, we conclude that Upton-Lloyd removes “too much” due to its working directly on HSIs as opposed to

Our analysis of parameter

An assessment based on a spike-in benchmark dataset indicated that DEG detection power is increased for low- and medium-concentration genes and is insignificantly affected for high-concentration genes. However, it should be noted that, by its very design, this central

Although the “random” spatial distribution of probes on the array surface was presented in this paper as a necessary assumption, this is an oversimplification and, thus, not strictly correct. In reality, the underlying assumption is that probe locations are independent of their targets, or—in more practical terms—of the locations of probes in the same probe set, such that any correlation between locations and residuals is always considered undesirable noise or bias; this can also be expressed as the assumption that probes are randomly spatially distributed on the array surface

Finally, the framework established herein provides opportunity for implementing further types of microarray data pretreatments: correction of a specific source of bias which can be expressed as the presence of undesirable mutual information shared by “neighbouring” probes in some given coordinate space (e.g., physical location on the array) or based on some given distance metric, as opposed to expected, desirable mutual information shared by some other sets of probes (e.g., Affymetrix “probe sets”). This approach (which we dub

Oligonucleotide array data is invariably biased by a number of confounding factors, some of which can be effectively quantified and eliminated. We have proposed a method for correcting bias arising from a known source and show the efficacy of one case, namely, spatial bias in Affymetrix GeneChip data. An implementation is provided as a convenient R package, released under the BSD license, available at

The authors thank Dr. Jose Manuel Arteaga-Salas for providing implementations of CPP and LPE. This work was supported by the Canadian Institutes of Health Research (CTP-79843). IRIC is supported in part by the Canadian Centre of Excellence in Commercialization and Research; the Canada Foundation for Innovation; and the Fonds de Recherche en Santé du Québec.