  Application of discrete-time survival methods for continuous-time survival
prediction is considered. For this purpose, a scheme for discretization of
continuous-time data is proposed by considering the quantiles of the estimated
event-time distribution, and, for smaller data sets, it is found to be
preferable over the commonly used equidistant scheme. Furthermore, two
interpolation schemes for continuous-time survival estimates are explored, both
of which are shown to yield improved performance compared to the discrete-time
estimates. The survival methods considered are based on the likelihood for
right-censored survival data, and parameterize either the probability mass
function (PMF) or the discrete-time hazard rate, both with neural networks.
Through simulations and study of real-world data, the hazard rate
parametrization is found to perform slightly better than the parametrization of
the PMF. Inspired by these investigations, a continuous-time method is proposed
by assuming that the continuous-time hazard rate is piecewise constant. The
method, named PC-Hazard, is found to be highly competitive with the
aforementioned methods in addition to other methods for survival prediction
found in the literature.
