Identify Estimable Components in a Large Two-way ANOVA Model from Normalization of Microarray Data

Abstract

Motivated by normalization in cDNA microarray data to correct for intensity effect, we consider the problem of identify estimable components in a N?—G two- way additive ANOVA model where N is large, G is much larger than N, and the number of observations falling in each column is I. Here I is often to be small. As a comparison to the lowess normalization method, this method uses a piecewise constant to approximate the normalized curve. However, the utility of lowess normalization method depends critically on whether the percentage of differentially expressed genes is small or whether there is symmetry in the expression levels of up-regulated and down-regulated genes. In order to remove this constraint, Fan et al. (2005, JASA) and Huang et al. (2005, JASA) consider the normalization method which utilizes the replications (I) within each array or several arrays (I) simultaneously. As in those two papers, we consider how the variance of resulting estimate of intensity effect depends on I under general design conditions. An algorithm is proposed to identify estimable intensity effects. Moreover, a condition relating G, N, and I to ensure consistent estimate of intensity effects is given. This result will give a guideline on the design stage to determine the number of replications within each and the total number of arrays. This result is augmented by simulation studies and illustrated by a published microarray dataset. Joint work with Huey-Fan Ni.