This proposal reflects our continuing interest in solving problems of measurement error, incomplete data nd/or functional (curve) data in general regression settings. The proposed research topics have arisen aturally from various important studies. These studies include (i) a colon cancer tumorigenesis project, vhich consists of a series of experiments to study .colon cancer tumorigenesis at the cellular level, (ii) artially degraded mRNA fecal microarray experiments, in which the investigators intend to recover genetic nformation from exfoliated colonocytes in the fecal stream as the initial step in building a non-invasive colon .ancer detection tool, and (iii) a spectroscopic oblique incidence reflectometry skin-lesion diagnostic study, vhich aims to use a newly developed bioengineering device to identify physiological features that reflect the athology of skin lesions. """"""""he statistical methods we investigate can be divided into five primary research goals: . To develop and evaluate marginal estimation methods under general nonparametric and semiparametric egression models with flexible data collection designs. 2. To develop and evaluate semiparametric methods when a major covariate is a latent variable in a secondary mixed model. 3. To develop and evaluate efficient semiparametric methods to accommodate incomplete data using estimating equation and imputation-maximization approaches. 4. To develop and evaluate nonparametric and semiparametric generalized linear model approaches for;orrelated data with functional covariates and a scalar response. 5. To develop and evaluate semiparametric standardization procedures for microarray data with a large proportion of outlying observations. The major focus of this proposal is the development of intuitive, efficient and computationally feasible methods without imposing unnecessary parametric assumptions. We expect our effort on these interesting biological studies to have significant impact on advancements in cancer research.
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