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Bioinformatics Advance Access originally published online on May 30, 2008
Bioinformatics 2008 24(14):1632-1638; doi:10.1093/bioinformatics/btn253
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© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Sparse kernel methods for high-dimensional survival data

Ludger Evers 1,* and Claudia-Martina Messow 2

1Department of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, United Kingdom and 2Institut für Medizinische Biometrie, Epidemiologie und Informatik, Johannes Gutenberg-Universität, 55101 Mainz, Germany

*To whom correspondence should be addressed.


  Abstract

Sparse kernel methods like support vector machines (SVM) have been applied with great success to classification and (standard) regression settings. Existing support vector classification and regression techniques however are not suitable for partly censored survival data, which are typically analysed using Cox's proportional hazards model. As the partial likelihood of the proportional hazards model only depends on the covariates through inner products, it can be ‘kernelized’. The kernelized proportional hazards model however yields a solution that is dense, i.e. the solution depends on all observations. One of the key features of an SVM is that it yields a sparse solution, depending only on a small fraction of the training data. We propose two methods. One is based on a geometric idea, where—akin to support vector classification—the margin between the failed observation and the observations currently at risk is maximised. The other approach is based on obtaining a sparse model by adding observations one after another akin to the Import Vector Machine (IVM). Data examples studied suggest that both methods can outperform competing approaches.

Availability: Software is available under the GNU Public License as an R package and can be obtained from the first author's website http://www.maths.bris.ac.uk/~maxle/software.html

Contact: l.evers{at}bris.ac.uk

Associate Editor: Limsoon Wong

Received on December 26, 2007; revised on May 8, 2008; accepted on May 29, 2008

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