The investigator studies generalized additive partially linear models (GAPLM) with the aim of developing efficient and flexible estimation and inference methods, variable selection procedures,model specification tests, and model structure checks, and studies applications of these methods for biomedical research. Specifically speaking, he (a) is developing a genuine method that is able to select important parametric and nonparametric components that are numerically stable , even when the numbers of the nonparametric and parametric components diverge; (b) is developing model specification tests for GAPLM; (c) studies model structure determination for GAPLM; (d) studies marginal GAPLM for correlated data; and (e) applies the advanced models and proposed methods to analyze gene data for study of the relationship between certain diseases and genes, including the identification of signature gene expression profiles of cancer cells in response to different drug treatments, the prediction of genetic risks through integrating knowledge from genetic variations in the genome and genomic markers, and validation of epigenetic codes from data collected through next generation sequencing platforms.
The proposed models and methods are motivated by the investigator's study of gene and other potentially useful biomarkers in cancer clinical trials. The results of this project can help identify important gene expression profiles and cancer cells and trace the disease progression in cancer research. The theoretic results contribute to the advancement of the statistical theory on variable selections and semi-parametric inference with high-dimensional covariates.
