Improved performance on high-dimensional survival data by application of Survival-SVM

Motivation: New application areas of survival analysis as for example based on micro-array expression data call for novel tools able to handle high-dimensional data. While classical (semi-) parametric techniques as based on likelihood or partial likelihood functions are omnipresent in clinical studies, they are often inadequate for modelling in case when there are less observations than features in the data. Support vector machines (SVMS) and extensions are in general found particularly useful for such cases, both conceptually (non-parametric approach), computationally (boiling down to a convex program which can be solved efficiently), theoretically (for its intrinsic relation with learning theory) as well as empirically. This article discusses such an extension of SVMS which is tuned towards survival data. A particularly useful feature is that this method can incorporate such additional structure as additive models, positivity constraints of the parameters or regression constraints. Results: Besides discussion of the proposed methods, an empirical case study is conducted on both clinical as well as micro-array gene expression data in the context of cancer studies. Results are expressed based on the logrank statistic, concordance index and the hazard ratio. The reported performances indicate that the present method yields better models for high-dimensional data, while it gives results which are comparable to what classical techniques based on a proportional hazard model give for clinical data.