Preprocessing of gene expression data by optimally robust estimators

The preprocessing of gene expression data obtained from several platforms routinely includes the aggregation of multiple raw signal intensities to one expression value. Examples are the computation of a single expression measure based on the perfect match (PM) and mismatch (MM) probes for the Affymetrix technology, the summarization of bead level values to bead summary values for the Illumina technology or the aggregation of replicated measurements in the case of other technologies including real-time quantitative polymerase chain reaction (RT-qPCR) platforms. The summarization of technical replicates is also performed in other "-omics" disciplines like proteomics or metabolomics.Preprocessing methods like MAS 5.0, Illumina's default summarization method, RMA, or VSN show that the use of robust estimators is widely accepted in gene expression analysis. However, the selection of robust methods seems to be mainly driven by their high breakdown point and not by efficiency.

We describe how optimally robust radius-minimax (rmx) estimators, i.e. estimators that minimize an asymptotic maximum risk on shrinking neighborhoods about an ideal model, can be used for the aggregation of multiple raw signal intensities to one expression value for Affymetrix and Illumina data. With regard to the Affymetrix data, we have implemented an algorithm which is a variant of MAS 5.0.Using datasets from the literature and Monte-Carlo simulations we provide some reasoning for assuming approximate log-normal distributions of the raw signal intensities by means of the Kolmogorov distance, at least for the discussed datasets, and compare the results of our preprocessing algorithms with the results of Affymetrix's MAS 5.0 and Illumina's default method.The numerical results indicate that when using rmx estimators an accuracy improvement of about 10-20% is obtained compared to Affymetrix's MAS 5.0 and about 1-5% compared to Illumina's default method. The improvement is also visible in the analysis of technical replicates where the reproducibility of the values (in terms of Pearson and Spearman correlation) is increased for all Affymetrix and almost all Illumina examples considered. Our algorithms are implemented in the R package named RobLoxBioC which is publicly available via CRAN, The Comprehensive R Archive Network (http://cran.r-project.org/web/packages/RobLoxBioC/).

Optimally robust rmx estimators have a high breakdown point and are computationally feasible. They can lead to a considerable gain in efficiency for well-established bioinformatics procedures and thus, can increase the reproducibility and power of subsequent statistical analysis.