| dc.description.abstract | With the advancing of data collection technologies, high-dimensional and large-scale data sets become available in many areas of science, specifically in biomedicine. One of important questions when mining such “big” data is to identify critical factors that may be predictive of the outcomes of interest, for example for disease diagnosis and prognosis. In this thesis, we introduce several models with solution algorithms that exploit sparse dependency structures to discover the variables playing important roles in survival and longitudinal data.
First, we focus on penalized Cox’s models to deal with the high-dimensional survival data with
group predictors. Most of the existing penalized methods for Cox’s model are the group lasso methods that show deficiencies, including the over-shrinkage problem. In addition, the contemporary algorithms either exhibit the loss of efficiency or require the group-wise orthonormality assumption. In Chapter 3, we investigate and comprehensively evaluate three group penalized methods for Cox’s models: the group lasso and two nonconvex penalization methods—group SCAD and group MCP—that have several advantages over the group lasso. We develop the fast and stable algorithms and a new R package grpCox to fit these models without the initial orthonormalization step. These methods perform group selection in both non-overlapping and overlapping cases.
Second, we study the multi-state models to analyze longitudinal data, in which the change of status over time is of interest. Due to the lack of an efficient and practical variable selection tool to practitioners, we develop the L1-regularized multi-state model framework for simultaneous parameter estimation and variable selection in Chapter 4. We use a local quadratic approximation of the log-partial likelihood and devise the one-step coordinate descent algorithm to solve the corresponding optimization problem, which can offer significant improvement on the computational efficiency. The proposed method is implemented in our R package L1mstate.
Finally, we investigate multivariate joint models to study the relationship between multiple time-varying measurements and the survival outcome, considering the potential correlation between these time-varying measurements. We address the problems of identifying the time-varying measurements that have strong associations with the time-to-event outcome, and simultaneously selecting predictive baseline covariates for both the longitudinal measurements and survival outcome of interest, which has no available tools so far to the best of our knowledge. In Chapter 5, we develop a variable selection framework for the multivariate joint models. Specifically, we propose novel penalized joint models for different association structures between the longitudinal and the survival submodels using different types of sparsity-inducing penalties. To tackle high-dimensional challenge that arises in the case of multiple longitudinal measurements, many covariates, and random effects, we develop an estimation procedure based on Laplace approximation of the joint likelihood. | |
