A generalized additive model for microarray gene expression data analysis

Microarray technology allows the measurement of expression levels of a large number of genes simultaneously. There are inherent biases in microarray data generated from an experiment. Various statistical methods have been proposed for data normalization and data analysis. This paper proposes a generalized additive model for the analysis of gene expression data. This model consists of two sub-models: a non-linear model and a linear model. We propose a two-step normalization algorithm to fit the two sub-models sequentially. The first step involves a non-parametric regression using lowess fits to adjust for non-linear systematic biases. The second step uses a linear ANOVA model to estimate the remaining effects including the interaction effect of genes and treatments, the effect of interest in a study. The proposed model is a generalization of the ANOVA model for microarray data analysis. We show correspondences between the lowess fit and the ANOVA model methods. The normalization procedure does not assume the majority of genes do not change their expression levels, and neither does it assume two channel intensities from the same spot are independent. The procedure can be applied to either one channel or two channel data from the experiments with multiple treatments or multiple nuisance factors. Two toxicogenomic experiment data sets and a simulated data set are used to contrast the proposed method with the commonly known lowess fit and ANOVA methods.