Mendelian randomization (MR) is an established approach for assessing the causal effects of heritable exposures on outcomes. Outcomes of interest often include binary clinical endpoints, but may also include censored survival times. We explore the implications of both the Cox proportional hazard model and the additive hazard model in the context of MR, with a specific emphasis on two-stage methods. We show that naive application of standard MR approaches to censored survival times may induce significant bias. Through simulations and analysis of data from the Women's Health Initiative, we provide practical advice on modeling survival outcomes in MRs.