Browsing by Author "Huang, Longlong"

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    Group Selection in Semiparametric and Nonparametric Accelerated Failure Time Models
    (2017) Huang, Longlong; Lu, Xuewen; Kopciuk, Karen; Deardon, Rob; Sajobi, Tolulope; Yan, Ying; Hu, Joan
    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.
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    Jackknife empirical likelihood for smoothed weighted rank regression with censored data
    (2012-07-24) Huang, Longlong; Lu, Xuewen; Kopciuk, Karen
    Rank regression is a highly-efficient and robust approach to estimate regression coefficients and to make inference in the presence of outlying survival times. Heller (2007) developed a smoothed weighted rank regression function, which is used to estimate the regression parameter vector in an accelerated failure time model with right censored data. This function can be expressed as a U-statistic. However, since inference is based on a normal approximation approach, it could perform poorly when sample sizes are small and censoring rates are high. To increase inference accuracy and robustness, we propose a jackknife empirical likelihood method for the U-statistic obtained from the estimating function of Heller. The jackknife empirical likelihood ratio is shown to be a standard Chi-squared statistic. Simulations were conducted to compare the proposed method with the normal approximation method. As expected, the new method gives better coverage probability for small samples with high censoring rates. The Stanford Heart Transplant Data, Veterans Administration Lung Cancer Data and Multiple Myeloma Data sets are used to illustrate the proposed method.