Project Summary The broad, long-term objectives of this research are the development of novel and high-impact statistical methods for medical studies of chronic diseases, with a focus on trans-omics precision medicine research. The specific aims of this competing renewal application include: (1) derivation of efficient and robust statistics for integrative association analysis of multiple omics platforms (DNA sequences, RNA expressions, methylation profiles, protein expressions, metabolomics profiles, etc.) with arbitrary patterns of missing data and with detection limits for quantitative measurements; (2) exploration of statistical learning approaches for handling multiple types of high- dimensional omics variables with structural associations and with substantial missing data; and (3) construction of a multivariate regression model of the effects of somatic mutations on gene expressions in cancer tumors for discovery of subject-specific driver mutations, leveraging gene interaction network information and accounting for inter-tumor heterogeneity in mutational effects. All these aims have been motivated by the investigators' applied research experience in trans-omics studies of cancer and cardiovascular diseases. The proposed solutions are based on likelihood and other sound statistical principles. The theoretical properties of the new statistical methods will be rigorously investigated through innovative use of advanced mathematical arguments. Computationally efficient and numerically stable algorithms will be developed to implement the inference procedures. The new methods will be evaluated extensively with simulation studies that mimic real data and applied to several ongoing trans-omics precision medicine projects, most of which are carried out at the University of North Carolina at Chapel Hill. Their scientific merit and computational feasibility are demonstrated by preliminary simulation results and real examples. Efficient, reliable, and user-friendly open-source software with detailed documentation will be produced and disseminated to the broad scientific community. The proposed work will advance the field of statistical genomics and facilitate trans-omics precision medicine studies of chronic diseases.