Multi-Way Semilinear Methods with Applications to Microarray Data

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This research focuses on developing statistical models, methods, and theory for normalization and significance analysis of microarray data and similar applications. Microarray technology has become an important tool for quantitatively monitoring gene expression patterns and has been widely used in functional genomics. The investigator and his collaborators have proposed and developed a two-way semilinear model for normalization and analysis of cDNA microarray data. The purpose of this research is to extend and further develop this methodology and investigate its theoretical justifications. The project covers a wide range of specific problems including multi-way semilinear models, normalization and analysis of high-density oligonucleotide arrays, incorporation of control/spike genes and biological pathway information, location-scale normalization, estimation of noise level, incorporation of data quality measurements, invertibility of information operator, asymptotic equivalence to ideal/oracle estimators of gene effects, and more.The multi-way semilinear model is an extension of widely used analysis of variance and semilinear regression models. Its applications to microarray experiments present challenging methodological and theoretical problems with high-dimensional complex datasets. These datasets have the following features: large number of unknown parameters for gene effects and small number of samples, many nonparametric components, co-linearity between bases for the estimations of nonparametric and parametric components, stochastically dependent covariates with spatially inhomogeneous distributions, interactions between observed gene expressions and possibly unobservable gene clusters and biological pathways, inhomogeneous noise level, and more. This research is motivated and will be directly applicable to functional genomic studies using microarray and similar technologies. It will also be directly applicable to high-throughput screening of chemical compounds in drug discovery experiments. This research will have significant educational impact.