Abstract
Machine learning approaches have been recently attempted to tackle the prediction tasks in survival analysis. However, most existing methods aim to learn the prognostic function directly via linear regression or ranking models, unable to exploit the underlying density family, notably the famous CoxPH model. In this paper we propose a novel estimator for the CoxPH model based on the margin maximization principle, which was proven to achieve superb generalization performance in standard classification problems in machine learning. The censored data are effectively handled by incorporating cost-sensitive margin violation loss. We demonstrate the improved prediction performance on several survival datasets.
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Notes
Technically it is called right-censored. There are other types of censoring: the left-censored means the observed time is no earlier than the event time, and the in-between-censored indicates that we only have an interval observation within which the true event time lies. As these types of censoring are relatively rare, we deal with only right-censored cases in this paper.
Technically, one should replace it with: \(\frac {P(t\leq T\leq t+dt|T\leq t,\mathbf {x})}{dt}\) for dt → 0.
The prognostic index of the subject with the covariates x can be chosen as −b⊤x (i.e., higher for longer survival) or any monotone non-decreasing link applied to it.
Here, the bias term is ignored presuming that the features are centralized (i.e., having zero mean).
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This study was supported by the Research Program funded by the SeoulTech (Seoul National University of Science & Technology).
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Kim, M. Large-margin learning of Cox proportional hazard models for survival analysis. Appl Intell 49, 1675–1687 (2019). https://doi.org/10.1007/s10489-018-1363-3
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DOI: https://doi.org/10.1007/s10489-018-1363-3