Robust estimation of a two-way semilinear model with applications to microarray data normalization and analysis

Microarray technology allows the monitoring of expression values of thousands of genes simultaneously on a large scale and has been widely used in functional genomics. A basic question in analyzing cDNA microarray data is normalization. The purpose of normalization is to remove systematic bias in the observed expression values by establishing a normalization curve across the whole dynamic range. A proper normalization procedure ensures that the normalized intensity ratios provide meaningful measures of relative expression levels. We propose a robust estimation method in a two-way semilinear model (TW-SLM) for normalization and analysis of cDNA microarray data. This method does not make the usual assumptions underlying some of the existing methods. For example, it does not assume that: (i) a small percentage of genes are differentially expressed; or (ii) the up-regulated genes and the down-regulated genes are distributed symmetrically. The TW-SLM also naturally incorporates uncertainties due to normalization into significant analysis of microarrays. We use Huber's and Tukey's robust estimation procedures in the estimation of the TW-SLM. We conduct simulation studies to evaluate the TW-SLM method and apply it to two microarray data sets as illustrations. Simulation results show that the proposed TW-SLM has smaller mean square errors and bias in terms of estimating gene expression levels than the Lowess normalization method. It also has higher sensitivity and specificity in detecting differentially expressed genes than the Lowess normalization method. The proposed method is implemented in an R statistical computing package.