Studies in multidimensional data: Estimation of the bivariate survival curve, analysis of factorial designed microarray experiments, identification of protein complex membership

Statistical methodology for the analysis of multidimensional data of various forms is of tremendous importance in the current “information age”. This thesis studies three different forms of multidimensional data, one relating to a long-standing statistical problem, and two resulting from recent bioinformatics investigations. While the three problems under consideration are quite different, the multidimensional nature of the data is of key importance.; The first study is that of bivariate survival curve estimation, specifically related to safety and efficacy outcomes in clinical trials. We propose a non-parametric, computationally simple estimator for the bivariate survival function when one time-to-event is continuous, one is discrete, and both are subject to right-censoring. We derive a closed-form covariance estimator for the survivor function which allows for inference to be based on any of several possible statistics of interest. In addition, we derive its covariance with respect to calendar time of analysis, allowing for its use in sequential studies.; The second study focuses on the interpretation of gene expression data from factorial designed microarray experiments as they reflect genetic networks within the living, cellular environment. We discuss an analytic approach for framing biological questions in terms of statistical parameters to efficiently answer questions of interest using microarray data from factorial designed experiments. Investigators can extract pertinent and interpretable information from the data about the effects of the factors, their interactions with each other, and the statistical significance of these effects. By first examining how biological mechanisms are reflected in mRNA transcript abundance, investigators can better design microarray experiments to answer the most interesting questions.; The third study examines protein-protein interaction data and proposes a graph theoretic algorithm for protein complex membership estimation. Previous graph theoretic analyses have led to topological descriptions of the overall protein network. A more complete functional characterization of the cell demands additional methodology for the accurate, comprehensive identification of all complexes and their constituent proteins. Our algorithm accommodates both dynamic complex composition and multicomplex membership by individual proteins, two biological realities not accounted for in existing methods. The rigorous characterization of protein modules provides a platform for explicit hypothesis development regarding new protein complexes and complex interactivity.