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Variable selection and estimation procedures for high-dimensional survival data
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Khan, M. H. R. (2013) Variable selection and estimation procedures for high-dimensional survival data. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2687559~S1
Abstract
In survival analysis the popular models are usually well suited for data with few covariates
and many observations. In contrast for many other fields such as microarray, it is necessary
in practice to consider the opposite case where the number of covariates (number of genes)
far exceeds the number of observations. However, with such data the accelerated failure
time models (AFT) have not received much attention in variable selection literature. This
thesis attempts to meet this need, extending and applying the modern tools of variable
selection and estimation to high–dimensional censored data.
We introduce two new variable selection strategies for AFT models. The first is based
upon regularized weighted least squares that leads to four adaptive elastic net type variable
selection approaches. In particular one adaptive elastic net, one weighted elastic net and
two extensions that incorporate censoring constraints into the optimization framework of
the methods. The second variable selection strategy is based upon the synthesis of the
Buckley–James method and the Dantzig selector, that results in two modified Buckley–
James methods and one adaptive Dantzig selector. The adaptive Dantzig selector uses
both standard and novel weights giving rise to three new algorithms.
Out of the variable selection strategies we focus on two important issues. One is the
sensitivity of Stute’s weighted least squares estimator to the censored largest observations
when Efron’s tail correction approach violates one of the basic right censoring assumptions.
We propose some intuitive imputing approaches for the censored largest observations that
allow Efron’s approach to be applied without violating the censoring assumption, and furthermore,
generate estimates with reduced mean squared errors and bias. The other issue
is related to proposing some modifications to the jackknife estimate of bias for Kaplan–
Meier estimators. The proposed modifications relax the conditions needed for such bias
creation by suitably applying the above imputing methods. It also appears that without
the modifications the bias of Kaplan–Meier estimators can be badly underestimated by
the jackknifing.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Failure time data analysis, Accelerated life testing -- Statistical methods, Estimation theory, Jackknife (Statistics) | ||||
Official Date: | June 2013 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Department of Statistics | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Shaw, Ewart | ||||
Sponsors: | University of Warwick. Department of Statistics | ||||
Extent: | xv, 149 leaves : illustrations, charts. | ||||
Language: | eng |
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