A common technique in survival analysis for modelling the hazard of an event as a function of explanatory variables is the Cox regression model (Cox, 1972). Previous research has demonstrated that machine learning methods outperform traditional statistical techniques when the relationship between the outcome and predictor variables is highly non-linear and/or involves many interactions. This thesis compares three neural networks designed for survival analysis to the Cox model with respect to the accuracy of prediction, how well they can distinguish between high- and low-risk observations and how sensitive the model predictions are to changes in the data on which they are trained. A simulation study and analyses of two real data sets provided the insight that selecting the optimal model for analysis of time-to-event data depends upon the particular performance evaluation metric of interest in addition to the characteristics of the data to which the models are applied.