Statistical methods of multivariate analysis for large and complex data

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The complexity of biological data has driven tremendous developments of statistical methods. The long-term goal of this research program is to develop new multivariate statistical methods for analyzing high dimensional biological data. The more immediate goal is to develop three methods for detecting groups of related variables that involved with disease pathogenesis. My first short-term objective is to identify the groups of variables that mediate the relationship between a risk factor and an outcome using penalized estimation approach. It is motivated by the identification of mediators for the association between BMI and breast cancer from hundreds of measured metabolites. I plan to utilize a sparse latent factor model for the multivariate metabolites, and the dependency among them will be described by a sparse factor loading matrix. Then each factor will link to only a small subset of variables so this will enhance the interpretability of the biological structure. To recover the factors that mediate the relationship among BMI and breast cancer, I plan to implement additional penalties on the regression coefficient vectors for the effect of BMI on mediating factors and for the effect of mediating factors on breast cancer. The key methodological development is to address the high dimensional problems in mediation analysis. My second short-term objective is to find the group of variables associated a latent factor underlying a mixture of continuous and polytomous multivariate outcomes. It is motivated by the study of the genetic variants associated with psychiatric disorders. Because of the complexity of psychiatric disorders, the categorical psychiatric diagnoses have been believed to be imprecise to characterize the nature of the disorder. Endophenotypes, which are measurable quantitative traits hypothesized to the underlying disease syndromes, have been considered as an alternative to the categorical disease phenotypes. My recent work utilized a penalized structural equation modelling to detect the genetic variants associated with the underlying disease syndromes for multiple quantitative endophenotypes. I plan to extend the method for a mixture of continuous and polytomous phenotypes to enhance its applicability in psychiatric genetic studies. My third short-term objective is to build a test statistic to identify a group of variables associated with a subset of outcomes, where the specific subset is unknown. It is motivated by a genetic application to detect the existence of a subset of multiple diseases associated with a group of genetic variants. After establishing those methods, I will build R packages to share with the scientific community. With the development of biotechnology, more statistical problems will emerge and this research program will grow concurrently beyond this five-year proposal.