Estimation of Expression Indexes for Oligonucleotide Arrays Using the Singular Value Decomposition

Abstract

Multiprobe oligonucleotide arrays are a widely used type of expression microarray with the attractive feature that numerous probes are used to represent each transcript. An “expression index” is a statistic used to represent expression level for a particular gene that is estimated from the probe hybridization intensities. We show that a popular model-based expression index proposed by Li and Wong has an interpretation as a component of the singular value decomposition (SVD) of the probe intensity matrix. Following this observation, we propose a new SVD model that accounts for differing variance structure across probes. We also propose that nonlinearity in intensity response to expression can be corrected to some extent through a data transformation, which is guided by an SVD entropy measure. The methods are demonstrated with simulation and applications to two real datasets.