Artif Intell Med - Support vector methods for survival analysis: a comparison between ranking and regression approaches.


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JECTIVE: To compare and evaluate ranking, regression and combined machine learning approaches for the analysis of survival data.METHODS: The literature describes two approaches based on support vector machines to deal with censored observations. In the first approach the key idea is to rephrase the task as a ranking problem via the concordance index, a problem which can be solved efficiently in a context of structural risk minimization and convex optimization techniques. In a second approach, one uses a regression approach, dealing with censoring by means of inequality constraints. The goal of this paper is then twofold: (i) introducing a new model combining the ranking and regression strategy, which retains the link with existing survival models such as the proportional hazards model via transformation models; and (ii) comparison of the three techniques on 6 clinical and 3 high-dimensional datasets and discussing the relevance of these techniques over classical approaches fur survival data.RESULTS: We compare svm-based survival models based on ranking constraints, based on regression constraints and models based on both ranking and regression constraints. The performance of the models is compared by means of three different measures: (i) the concordance index, measuring the model's discriminating ability; (ii) the logrank test statistic, indicating whether patients with a prognostic index lower than the median prognostic index have a significant different survival than patients with a prognostic index higher than the median; and (iii) the hazard ratio after normalization to restrict the prognostic index between 0 and 1. Our results indicate a significantly better performance for models including regression constraints above models only based on ranking constraints.CONCLUSIONS: This work gives empirical evidence that svm-based models using regression constraints perform significantly better than svm-based models based on ranking constraints. Our experiments show a comparable performance for methods including only regression or both regression and ranking constraints on clinical data. On high dimensional data, the former model performs better. However, this approach does not have a theoretical link with standard statistical models for survival data. This link can be made by means of transformation models when ranking constraints are included.

Resumo Limpo

jectiv compar evalu rank regress combin machin learn approach analysi surviv datamethod literatur describ two approach base support vector machin deal censor observ first approach key idea rephras task rank problem via concord index problem can solv effici context structur risk minim convex optim techniqu second approach one use regress approach deal censor mean inequ constraint goal paper twofold introduc new model combin rank regress strategi retain link exist surviv model proport hazard model via transform model ii comparison three techniqu clinic highdimension dataset discuss relev techniqu classic approach fur surviv dataresult compar svmbase surviv model base rank constraint base regress constraint model base rank regress constraint perform model compar mean three differ measur concord index measur model discrimin abil ii logrank test statist indic whether patient prognost index lower median prognost index signific differ surviv patient prognost index higher median iii hazard ratio normal restrict prognost index result indic signific better perform model includ regress constraint model base rank constraintsconclus work give empir evid svmbase model use regress constraint perform signific better svmbase model base rank constraint experi show compar perform method includ regress regress rank constraint clinic data high dimension data former model perform better howev approach theoret link standard statist model surviv data link can made mean transform model rank constraint includ

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