A probe-treatment-reference (PTR) model for the analysis of oligonucleotide expression microarrays

Background: Microarray pre-processing usually consists of normalization and summarization. Normalization aims to remove non-biological variations across different arrays. The normalization algorithms generally require the specification of reference and target arrays. The issue of reference selection has not been fully addressed. Summarization aims to estimate the transcript abundance from normalized intensities. In this paper, we consider normalization and summarization jointly by a new strategy of reference selection. Results: We propose a Probe-Treatment-Reference ( PTR) model to streamline normalization and summarization by allowing multiple references. We estimate parameters in the model by the Least Absolute Deviations ( LAD) approach and implement the computation by median polishing. We show that the LAD estimator is robust in the sense that it has bounded influence in the three-factor PTR model. This model fitting, implicitly, defines an "optimal reference" for each probe-set. We evaluate the effectiveness of the PTR method by two Affymetrix spike- in data sets. Our method reduces the variations of non-differentially expressed genes and thereby increases the detection power of differentially expressed genes. Conclusion: Our results indicate that the reference effect is important and should be considered in microarray pre-processing. The proposed PTR method is a general framework to deal with the issue of reference selection and can readily be applied to existing normalization algorithms such as theinvariant- set, sub-array and quantile method.