Collaborative Research: Analysis of longitudinal multiscale data in immunological bioinformatics --- Feature selection, graphical models, and structure identification

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This project aims to develop a system of statistical analysis tools to tackle several important challenges in analysis of complex bioinformatics data, which involves a variety of response variables and tens of thousands independent variables. The interest often lies in identifying the key independent variables associated with the response variables, and understanding such associations as well as the interactions among the independent variables.The extreme magnitude and complexity of bioinformatics data have posed serious challenges for data analysis. To overcome these challenges, we propose (i) to systematically and properly integrate multi-scale data before we can apply our novel modeling and analysis methods since the data we explore are collected by numerous independent studies at phenotypic, cellular, protein, and genetic levels with information from very different time and dimension scales; (ii) to develop feature screening criteria for a mixed type of longitudinal data using the combination of correlation tests in bivariate longitudinal regression models and the Benjamini-Hochberg-Yekutieli procedure, (iii) to develop graphical models that allow the variables being a mix of continuous and discrete longitudinal variables, with the nodes representing variables and each edge indicating the dependence of the two relevant variables conditional on the other variables; and (iv) to investigate the functioning form of each predictor by resorting to the data themselves under the framework of a mixed effects regression model with a continuous or discrete response and a high dimensional vector of predictors, with the resulting procedure allowing a user to simultaneously determine the form of each predictor effect to be zero, linear or nonlinear.