1. Develop and study Bayesian methods of inference for DNA microarray data. We will: Develop Bayesian parametric models for examining differential gene expression between two or more groups of subjects, examine log-normal models and Bayesian hierarchical analysis of variance models for characterizing the relationships between tissue types and genes, investigate Bayesian gene selection algorithms for identifying genes that are differentially expressed between the tissue types, examine novel prior distributions that allow the mean gene expression levels to be correlated a priori, and study the inclusion of subject specific covariates. Theoretical properties of the proposed methods will be examined, robustness properties will be investigated and their performance evaluated, ii) Develop and study formal Bayesian methodologies for controlling the False Discovery Rate (FDR) in the analysis of DNA microarray data. We will propose a Bayesian criterion to controlling the FDR, investigate its theoretical properties, and compare its performance to non-Bayesian approaches. ? 2. Develop and study Bayesian methods for joint models for longitudinal and survival data. i) We investigate several novel models, including univariate and multivariate longitudinal data models that often arise in cancer vaccine and AIDS clinical trials, investigate a novel methodology for linking the trajectory function in the longitudinal component to the survival component of the model and characterize its properties, study semiparametric specifications for the trajectory function in the longitudinal component by taking a Dirichlet process prior for the random effects instead of the usual normal distribution, examine model development, prior elicitation, computations, carry out comparisons with the fully parametric model, and study a Bayesian model selection tool called the multivariate L measure. We will also investigate the use of other model selection criteria for these types of models, including the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and the Deviance Information Criterion (DIC). ii) We will develop Bayesian semiparametric measurement error survival models for examining relationships between a time-to-event, such as survival time, and gene expression level. Prior distributions and gene selection algorithms for determining which genes are most highly associated with survival time will be studied, and computational algorithms will be investigated and implemented. ? 3. Develop and study Bayesian methods for cancer prevention studies with applications to DNA microarray data. We propose a new Bayesian survival model for cancer prevention studies. We will examine the relationship of our model with existing lagged-regression models. These models will be further studied in the context of DNA microarray data analysis. In particular these models will be used for examining the relationship between gene expression level and a lagged time-to-event in the cancer prevention context. ? ?
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