This proposal reflects our continuing interest in solving problems of measurement error, missing data in general regression settings. The proposed research topics naturally arise from two important studies: (i) Colon Cancer Tumorigenesis Project, which consists of a series of experiments to study colon cancer tumorigenesis at the cellular level, and (ii) Prostate Cancer Outcomes Study, which is the largest multicenter observational study to investigate the link between medical practices in the uncontrolled real-world environment and health-related quality of life (HRQOL) among men diagnosed with prostate cancer. We propose to study five primary research topics: Developing efficient generalized estimating equation (GEE) procedure under non- and semi-parametric marginal regression models. Estimating a dynamic correlation between two variables, such as apoptosis (cell death) and DNA adduct damage, as a function of a continuous covariate, cell positions within a colon crypt. Developing methodologies to accommodate a new type of covariate measurement error problem caused by using predictions from a secondary mixed model as the covariate in the primary model. Accommodating analyses of incomplete data through utilizing various multiple imputation procedures including non- and semi-parametric imputations. Adopting approximate saddle point methods to statistical inferences that are suitable to analyze data from a small number of subjects/clusters/units. The major focus of the proposal is development of efficient, easily calculable methods without imposing unnecessary parametric assumptions. Special emphasis will be given to correlated observations collected from longitudinal and clustered studies.
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