  Comparing survival experiences of different groups of data is an important
issue in several applied problems. A typical example is where one wishes to
investigate treatment effects. Here we propose a new Bayesian approach based on
restricted mean survival times (RMST). A nonparametric prior is specified for
the underlying survival functions: this extends the standard univariate neutral
to the right processes to a multivariate setting and induces a prior for the
RMST's. We rely on a representation as exponential functionals of compound
subordinators to determine closed form expressions of prior and posterior mixed
moments of RMST's. These results are used to approximate functionals of the
posterior distribution of RMST's and are essential for comparing
time--to--event data arising from different samples.
