  In causal inference, sensitivity analysis is important to assess the
robustness of study conclusions to key assumptions. We perform sensitivity
analysis of the assumption that missing outcomes are missing completely at
random. We follow a Bayesian approach, which is nonparametric for the outcome
distribution and can be combined with an informative prior on the sensitivity
parameter. We give insight in the posterior and provide theoretical guarantees
in the form of Bernstein-von Mises theorems for estimating the mean outcome. We
study different parametrisations of the model involving Dirichlet process
priors on the distribution of the outcome and on the distribution of the
outcome conditional on the subject being treated. We show that these
parametrisations incorporate a prior on the sensitivity parameter in different
ways and discuss the relative merits. We also present a simulation study,
showing the performance of the methods in finite sample scenarios.
