Wu, JingjingLu, XuewenZhong, Wenyan2019-01-312019-01-312019-01-25Zhong, W. (2019). Bi-level Variable Selection in Semiparametric Transformation Models for Right Censored Data and Cure Rate Data (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.http://hdl.handle.net/1880/109877In this dissertation, I investigated the bi-level variable selection in the semi-parametric transformation models with right-censored data and the semi-parametric mixture cure models with right censored and cure rate data, respectively. The transformation models under the consideration include the proportional hazards model and the proportional odds model as special cases. In the framework of regularized regression, we proposed a computationally efficient estimation method that selects significant groups and variables simultaneously. Three penalty functions, i.e., Group bridge, adaptive group bridge and composite group bridge penalties which can integrate grouping structure of covariates, were adopted for bi-level variable selection purpose. In Chapter 2, the objective function, which consists of the negative weighted partial log-likelihood function plus one of the three penalties, has a parametric form and is convex with respect to the parameters. This leads to an easy implementation of the optimization algorithm for which convergence is guaranteed numerically. We showed that all the three proposed penalized estimators achieve the group selection consistency, and moreover, the adaptive group bridge estimator and the composite group bridge estimator enjoy the oracle properties, i.e., both estimators possess the group and individual selection consistency simultaneously and are asymptotically normal as if the true unimportant covariates were known. In Chapter 3, we further extended the bi-level variable selection procedure to the semi-parametric mixture cure models. The semi-parametric mixture cure models are formulated by a logistic regression for modelling the cure fraction and a class of semi-parametric transformation models for modelling the survival function of remaining uncured individuals. Incorporating a cure fraction, the proposed model is more flexible than the standard survival models, and the proposed approach is capable to distinguish important covariates and groups from unimportant ones and estimate covariates’ effects simultaneously in both the incidence and the latency parts. We proposed a new iterative E-M algorithm to handle two latent variables. We illustrated the finite sample performance of the proposed methods via simulations and two real data examples. Simulation studies indicated that the proposed methods perform well even with relatively high dimension of covariates.enUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.bi-level variable selectionsemiparametric transformation modelmixture cure rate modelgroup bridgeEducation--Mathematicsdoctoral thesishttp://dx.doi.org/10.11575/PRISM/36134