Estimation and Group Selection in Partially Linear Survival Models

Afzal, Arfan

Estimation and Group Selection in Partially Linear Survival Models

dc.contributor.advisor	Lu, Xuewen
dc.contributor.author	Afzal, Arfan
dc.contributor.committeemember	Ambagaspitiya, Rohana
dc.contributor.committeemember	Shen, Hua
dc.contributor.committeemember	Deardon, Rob
dc.contributor.committeemember	Zhao, Yichun
dc.date	2018-06
dc.date.accessioned	2018-01-24T21:49:30Z
dc.date.available	2018-01-24T21:49:30Z
dc.date.issued	2018-01-17
dc.description.abstract	In survival analysis, different regression models are available to estimate the effects of covariates on the censored survival outcome. The proportional hazards (PH) model has been the most popular model among them because of its simplicity and desirable theoretical properties. However, the PH model assumes that the hazard ratio is constant over observed time. When this assumption is not met or we are interested in the risk difference, the additive hazards (AH) model is a useful alternative. On the other hand, assuming linear structure of covariate effects on survival in these models may be too strict. As a remedy to that, partially linear survival models are getting increasingly popular as it combines the flexibility of nonparametric modeling with the parsimony and easy interpretability of parametric modeling. Nonetheless, building these models becomes a challenging problem when predictors or covariates are high-dimensional and grouped. Consequently, it becomes crucial to select important groups and important individual variables within groups by the so called bi-level variable selection method to reduce the dimension of the data and build a sensible and useful semiparametric model for applications as the methods for individual variable selection in such cases may perform inefficiently by ignoring the information present in the grouping structure. To fill gaps in estimation and group selection in partially linear survival models with high-dimensional data, in this thesis, we propose new methods for estimation and group selection in two partially linear survival models, namely, the partially linear AH model and the partially linear PH model. In the first part of this thesis, we consider estimation in a partially linear AH model with left-truncated and right-censored data when the dimension of covariates is fixed and the risk function has a partially linear structure. We construct a pseudo-score function to estimate the coefficients of the linear covariates and the B-spline basis functions. The proposed estimators are asymptotically normal under the assumption that the true nonlinear functions are B-spline functions whose knot locations and the number of knots are held fixed. In the second and third parts, we study group variable selection in the partially linear AH model and the partially linear PH model with right censored data. In such regression models with a grouping structure among the explanatory variables, variable selection at the group and within group individual variable level is important to improve model accuracy and interpretability. Motivated by the hierarchical grouped variable selection in the linear PH model and the linear AH model, we propose a hierarchical bi-level variable selection approach for high-dimensional covariates in the linear part of the partially linear AH model and the partially linear PH model, respectively. The proposed methods are capable of conducting simultaneous group selection and individual variable selection within groups in the presence of nonparametric risk functions of low-dimensional covariates. For group selection in the partially linear AH model, the rates of convergence and selection consistency of the proposed estimators are established using martingale and empirical process theory; after reducing the dimension of the covariates, we suggest the use of the method in the first part for inference in the partially linear AH model. For group selection in the partially linear PH model, similar theoretical results of the proposed estimators are obtained, and the oracle properties such as asymptotic normality of the estimators are discussed. Finally, computational algorithms and programs are developed for utilizing the proposed methods. Simulation studies indicate good finite sample performance of the methods. For each model, real data examples are provided to illustrate the application of the methods.	en_US
dc.identifier.citation	Afzal, A. (2018). Estimation and Group Selection in Partially Linear Survival Models (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.	en_US
dc.identifier.doi	http://dx.doi.org/10.11575/PRISM/5392
dc.identifier.uri	http://hdl.handle.net/1880/106311
dc.language.iso	en	en_US
dc.publisher.faculty	Science	en_US
dc.publisher.institution	University of Calgary	en
dc.rights	University 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.	en_US
dc.subject.classification	Statistics	en_US
dc.title	Estimation and Group Selection in Partially Linear Survival Models	en_US
dc.type	doctoral thesis	en_US
thesis.degree.discipline	Mathematics & Statistics	en_US
thesis.degree.grantor	University of Calgary	en_US
thesis.degree.name	Doctor of Philosophy (PhD)	en_US
ucalgary.item.requestcopy	true
ucalgary.thesis.checklist	I confirm that I have submitted all of the required forms to Faculty of Graduate Studies.	en_US