  We apply Gaussian process (GP) regression, which provides a powerful
non-parametric probabilistic method of relating inputs to outputs, to survival
data consisting of time-to-event and covariate measurements. In this context,
the covariates are regarded as the `inputs' and the event times are the
`outputs'. This allows for highly flexible inference of non-linear
relationships between covariates and event times. Many existing methods, such
as the ubiquitous Cox proportional hazards model, focus primarily on the hazard
rate which is typically assumed to take some parametric or semi-parametric
form. Our proposed model belongs to the class of accelerated failure time
models where we focus on directly characterising the relationship between
covariates and event times without any explicit assumptions on what form the
hazard rates take. It is straightforward to include various types and
combinations of censored and truncated observations. We apply our approach to
both simulated and experimental data. We then apply multiple output GP
regression, which can handle multiple potentially correlated outputs for each
input, to competing risks survival data where multiple event types can occur.
By tuning one of the model parameters we can control the extent to which the
multiple outputs (the time-to-event for each risk) are dependent thus allowing
the specification of correlated risks. Simulation studies suggest that in some
cases assuming dependence can lead to more accurate predictions.
