Statistical Methods for Integrative Analysis of Multiple Types of Data

Recent technological advances have made it possible to collect multiple types of genomic data on the same set of subjects. It is of great interest to integrate multiple genomic data types to address various imperative biological problems, such as to understand the mechanisms of complex diseases, to predict disease outcomes, and to classify patients into risk groups. Multi-platform genomic data present unprecedented opportunities to address the above issues but also pose significant statistical and computation challenges that cannot be adequately tackled using existing methods. In the first part of the dissertation, we develop a structural equation modeling (SEM) framework to jointly model the relationships among various types of genomic variables and phenotypes. We extend the current SEM framework to include semiparametric transformation models for potentially right-censored time to event. We develop an efficient nonparametric maximum likelihood estimation approach to estimate the model parameters. In the second part of the dissertation, we develop a robust score test based on imputed data for testing the association between a phenotype and a partially missing genomic variable. We impute the missing values based on a semiparametric model for the genomic variable against other genomic and non-genomic variables. The proposed test preserves the type I error even when the imputation model is misspecified. We develop a spline-based method to estimate the semiparametric imputation model. In the third part of the dissertation, we develop a method based on statistical boosting and penalized estimation for the prediction of a potentially right-censored time to event using multiple types of high-dimensional genomic variables. The proposed method properly accounts for the differences in size and predictive power across data types. We propose an efficient and stable computation method that is based on existing algorithms for penalized estimation. In all three parts of the dissertation, we evaluate the proposed methods using extensive simulation studies and demonstrate their advantages over existing methods. We provide applications for each proposed method to a large-scale multi-platform genomic study, The Cancer Genome Atlas.Doctor of Philosoph