  Survival analysis is a fundamental tool in medical research to identify
predictors of adverse events and develop systems for clinical decision support.
In order to leverage large amounts of patient data, efficient optimisation
routines are paramount. We propose an efficient training algorithm for the
kernel survival support vector machine (SSVM). We directly optimise the primal
objective function and employ truncated Newton optimisation and order statistic
trees to significantly lower computational costs compared to previous training
algorithms, which require $O(n^4)$ space and $O(p n^6)$ time for datasets with
$n$ samples and $p$ features. Our results demonstrate that our proposed
optimisation scheme allows analysing data of a much larger scale with no loss
in prediction performance. Experiments on synthetic and 5 real-world datasets
show that our technique outperforms existing kernel SSVM formulations if the
amount of right censoring is high ($\geq85\%$), and performs comparably
otherwise.
