Correlated and high-dimensional data arise frequently in health sciences research, especially in cancer research. Correlated data arise in longitudinal studies and familial studies, while high-dimensional data have emerged in recent years as a consequence of the rapid advance of genomic and proteomic research. We propose in this application to develop nonparametric and semiparametric regression methods for clustered/longitudinal data and high-dimensional genomic and proteomic data. Specifically, we propose to develop (1) the kernel (spline) profile EM method for generalized semiparametric mixed models for clustered/longitudinal data;(2) nonparametric and semiparametric regression models for longitudinal data with dropouts;(3) the mixed model kernel machine method for generalized semiparametric regression models and semiparametric Cox models for the analysis of gene expression pathways and tag single nucleotide polymorphisms (SNPs) within a candidate gene, and the sparse kernel machine (SKM) method for selecting genes and tag SNPs from a large pool of genes or tag SNPs;(4) the joint modeling method using functional wavelet models and generalized semiparametric models for mass spectrometry proteomic data and disease outcomes. Asymptotic properties of the proposed methods will be investigated and simulation studies will be conducted to evaluate their finite sample performance. Efficient numerical algorithms and user-friendly statistical software will be developed, with the goal of disseminating these models and methods to health sciences researchers. In collaboration with biomedical investigators, we will apply the proposed models and methods to several motivating data sets on cancer research and other fields of research.
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