Bayesian methods for the analysis of clinical trials data have receive
d increasing attention recently as they offer an approach for dealing
with difficult problems that arise in practice. A major criticism of t
he Bayesian approach, however, has focused on the need to specify a si
ngle, often subjective, prior distribution for the parameters of inter
est. In an attempt to address this criticism, we describe methods for
assessing the robustness of the posterior distribution to the specific
ation of the prior. The robust Bayesian approach to data analysis repl
aces the prior distribution with a class of prior distributions and in
vestigates how the inferences might change as the prior varies over th
is class. The purpose of this paper is to illustrate the application o
f robust Bayesian methods to the analysis of clinical trials data. Usi
ng two examples of clinical trials taken from the literature, we illus
trate how to use these methods to help a data monitoring committee dec
ide whether or not to stop a trial early.