In problems with missing data, the data are often considered to be missing at random. This assumption can not be checked from the data. We need to assess the sensitivity of study conclusions to violations of non-identifiable assumptions. This thesis performs Bayesian sensitivity analysis for a missing data model with life time outcomes and covariate information. The outcome distribution is modelled through a Cox model, with a beta process prior on the cumulative hazard function. We run experiments in a simulation study to test the performance of the model in scenarios with simulated data of several sample sizes. We show the validity of the model in the context of Bayesian sensitivity analysis, and propose extensions.