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Variable selection in the general linear model for censored data

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2007, Doctor of Philosophy, Ohio State University, Statistics.
Variable selection is a popular topic in statistics today. However, for right censored data, only a few methods are available. The principle method assumes that the data comes from a Cox proportional hazards model. In 1997, Tibshirani proposed a variation of the LASSO method that minimizes the log partial likelihood subject to the sum of the absolute values of the parameters being bounded by a constant in the Cox proportional hazards model. Due to the nature of this constraint, it shrinks coefficients and produces some coefficients that are exactly zero. The resulting prediction error is smaller than that of subset selection methods. However, the proportional hazard assumption isn't always appropriate for real data. Therefore, we apply this method to the class of models (linear regression models) in which the response variable is right censored and the error is symmetric at zero, but is otherwise distribution free. The method also uses a sieve-likelihood to calculate a variation of the LASSO criterion and uses generalized cross-validation to choose the tuning parameter. Simulation shows that this method gives smaller prediction error than the method that depends on the proportional hazard assumption in some scenarios, especially for larger sample sizes. The performance of the proposed method is also examined via a data set from a study of the ganglioside content of primary brain tumors and a data set from a study of bone marrow transplants in Chronic Myelogenous Leukemia patients.
Dennis Pearl (Advisor)

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Citations

  • Yu, L. (2007). Variable selection in the general linear model for censored data [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1173279515

    APA Style (7th edition)

  • Yu, Lili. Variable selection in the general linear model for censored data. 2007. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1173279515.

    MLA Style (8th edition)

  • Yu, Lili. "Variable selection in the general linear model for censored data." Doctoral dissertation, Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=osu1173279515

    Chicago Manual of Style (17th edition)