Propensity score methods are increasingly being used to reduce the effect of measured confounders in observational research. In medicine, censored time-to-event data is common. Using Monte Carlo simulations, this thesis evaluates the performance of nearest neighbour matching (NNM) and inverse probability of treatment weighting (IPTW) in combination with Cox proportional hazards models for estimating marginal hazard ratios. Focus is on the performance for different sample sizes and censoring rates, aspects which have not been fully investigated in this context before. The results show that, in the absence of censoring, both methods can reduce bias substantially. IPTW consistently had better performance in terms of bias and MSE compared to NNM. For the smallest examined sample size with 60 subjects, the use of IPTW led to estimates with bias below 15 %. Since the data were generated using a conditional parametrisation, the estimation of univariate models violates the proportional hazards assumption. As a result, censoring the data led to an increase in bias.