Please use this identifier to cite or link to this item: http://hdl.handle.net/11023/3546
Title: Group Selection in Semiparametric and Nonparametric Accelerated Failure Time Models
Author: Huang, Longlong
Advisor: Lu, Xuewen
Kopciuk, Karen
Keywords: Statistics
Abstract: In survival analysis, a number of regression models can be used to estimate the effects of covariates on the censored survival outcome. When covariates can be naturally grouped, group selection is important in these models. Motivated by the group bridge approach for variable selection in a multiple linear regression model, we consider group selection in a semiparametric accelerated failure time (AFT) model using Stute's weighted least squares and a group bridge penalty. This method is able to simultaneously carry out feature selection at both the group and within-group individual variable levels and enjoys the powerful oracle group selection property. Although the group bridge penalized approach can effectively remove unimportant groups, it cannot effectively remove unimportant variables within the important groups. To overcome this limitation, the adaptive group bridge method is proposed. We show that the adaptive group bridge method obtains the oracle property. Simulation studies indicate that the group bridge and adaptive group bridge approaches for the AFT model can correctly identify important groups and variables even with high censoring rates. A real data analysis is provided to illustrate the application of the proposed methods. We further study a nonparametric accelerated failure time additive regression (NP-AFT-AR) model whose covariates have nonparametric effects on the survival time. The proposed model is more flexible than the linear model and can be fitted to high-dimensional censored data when some components are unknown non-linear functions. B-splines are used to approximate the nonparametric components. A group bridge penalized variable selection approach based on the inverse probability-of-censoring weighted least squares is developed to select nonparametric components. The proposed approach is able to distinguish the nonzero components from the zero components and estimate the nonzero components simultaneously. Computational algorithms and theoretical properties of the proposed method are established. Simulation studies indicate that the proposed method has satisfactory performance even with relatively high censoring rates. Two real data analyses are used to illustrate the application of the proposed method to survival data analysis.
URI: http://hdl.handle.net/11023/3546
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