Nonparametric Survival Analysis under Shape Restrictions
type: CreativeWork
description: The main problem studied in this thesis is to analyse and model time-to- event data, particularly when the survival times of subjects under study are not exactly observed. One of the primary tasks in the analysis of survival data is to study the distribution of the event times of interest. In order to avoid strict assumptions associated with a parametric model, we resort to nonparametric methods for estimating a function. Although other nonparametric approaches, such as Kaplan-Meier, kernel-based, and roughness penalty methods, are popular tools for solving function estimation problems, they suffer from some non-trivial issues like the loss of some important information about the true underlying function, difficulties with bandwidth or tuning parameter selection. In contrast, one can avoid these issues at the cost of enforcing some qualitative shape constraints on the function to be estimated. We con ne our survival analysis studies to estimating a hazard function since it may make a lot of practical sense to impose certain shape constraints on it. Specifically, we study the problem of nonparametric estimation of a hazard function subject to convex shape restrictions, which naturally entails monotonicity constraints. In this thesis, three main objectives are addressed. Firstly, the problem of nonparametric maximum-likelihood estimation of a hazard function under convex shape restrictions is investigated. We introduce a new nonparametric approach to estimating a convex hazard function in the case of exact observations, the case of interval-censored observations, and the mixed case of exact and interval-censored observations. A new idea to handle the problem of choosing the minimum of a convex hazard function estimate is proposed. Based on this, a new fast algorithm for nonparametric hazard function estimation under convexity shape constraints is developed. Theoretical justification for the convergence of the new algorithm is provided. Secondly, nonparametric estimati…
abstract: The main problem studied in this thesis is to analyse and model time-to- event data, particularly when the survival times of subjects under study are not exactly observed. One of the primary tasks in the analysis of survival data is to study the distribution of the event times of interest. In order to avoid strict assumptions associated with a parametric model, we resort to nonparametric methods for estimating a function. Although other nonparametric approaches, such as Kaplan-Meier, kernel-based, and roughness penalty methods, are popular tools for solving function estimation problems, they suffer from some non-trivial issues like the loss of some important information about the true underlying function, difficulties with bandwidth or tuning parameter selection. In contrast, one can avoid these issues at the cost of enforcing some qualitative shape constraints on the function to be estimated. We con ne our survival analysis studies to estimating a hazard function since it may make a lot of practical sense to impose certain shape constraints on it. Specifically, we study the problem of nonparametric estimation of a hazard function subject to convex shape restrictions, which naturally entails monotonicity constraints. In this thesis, three main objectives are addressed. Firstly, the problem of nonparametric maximum-likelihood estimation of a hazard function under convex shape restrictions is investigated. We introduce a new nonparametric approach to estimating a convex hazard function in the case of exact observations, the case of interval-censored observations, and the mixed case of exact and interval-censored observations. A new idea to handle the problem of choosing the minimum of a convex hazard function estimate is proposed. Based on this, a new fast algorithm for nonparametric hazard function estimation under convexity shape constraints is developed. Theoretical justification for the convergence of the new algorithm is provided. Secondly, nonparametric estimati…
author: Fani, Shabnam
license: https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
date published: 2014
date modified: 2026-07-24T01:06:10Z
provider: University of Auckland
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: ResearchSpace@Auckland

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property ID: Handle
value: https://hdl.handle.net/2292/24255