Penalized Variable Selection for Multi-center Competing Risks Data

Risk Factor Identification in Heterogeneous Disease Progression with L1-Regularized Multi-state Models

Multi-state model (MSM) is a useful tool to analyze longitudinal data for modeling disease progression at multiple time points. While the regularization approaches to variable selection have been widely used, extending them to MSM remains largely unexplored. In this paper, we have developed the L1-regularized multi-state model (L1MSTATE) framework that enables parameter estimation and variable selection simultaneously. The regularized optimization problem was solved by deriving a one-step coordinate descent algorithm with great computational efficiency. The L1MSTATE approach was evaluated using extensive simulation studies, and it showed that L1MSTATE outperformed existing regularized multi-state models in terms of the accurate identification of risk factors. It also outperformed the un-regularized multi-state models (MSTATE) in terms of identifying the important risk factors in situations with small sample sizes. The power of L1MSTATE in predicting the transition probabilities comparing with MSTATE was demonstrated using the Europe Blood and Marrow Transplantation (EBMT) dataset. The L1MSTATE was implemented in the open-access R package 'L1mstate'.

Group and within-group variable selection for competing risks data

Variable selection in the presence of grouped variables is troublesome for competing risks data: while some recent methods deal with group selection only, simultaneous selection of both groups and within-group variables remains largely unexplored. In this context, we propose an adaptive group bridge method, enabling simultaneous selection both within and between groups, for competing risks data. The adaptive group bridge is applicable to independent and clustered data. It also allows the number of variables to diverge as the sample size increases. We show that our new method possesses excellent asymptotic properties, including variable selection consistency at group and within-group levels. We also show superior performance in simulated and real data sets over several competing approaches, including group bridge, adaptive group lasso, and AIC / BIC-based methods.

Variable selection with Group LASSO approach: Application to Cox regression with frailty model

In analysis of survival outcomes supplemented with both clinical information and high-dimensional gene expression data, use of the traditional Cox proportional hazards model fails to meet some emerging needs in biomedical research. First, the number of covariates is generally much larger the sample size. Secondly, predicting an outcome based on individual gene expression is inadequate because multiple biological processes and functional pathways regulate phenotypic expression. Another challenge is that the Cox model assumes that populations are homogenous, implying that all individuals have the same risk of death, which is rarely true due to unmeasured risk factors among populations. In this paper we propose group LASSO with gamma-distributed frailty for variable selection in Cox regression by extending previous scholarship to account for heterogeneity among group structures related to exposure and susceptibility. The consistency property of the proposed method is established. This method is appropriate for addressing a wide variety of research questions from genetics to air pollution. Simulated and real world data analysis shows promising performance by group LASSO compared with other methods, including group SCAD and group MCP. Future research directions include expanding the use of frailty with adaptive group LASSO and sparse group LASSO methods.