Experiments such as clinical trials should be carried out with specifi
c objectives. For example, in a trial designed to prevent disease, spe
cific considerations should be made concerning the impact of the trial
on the health of the target population, including the participants in
the trial. These objectives should be assessed continually in light o
f data accumulating from the trial. Accumulating evidence should be ju
dged in the context of changing circumstances external to the trial, a
nd the trial's design possibly modified. An important type of modifica
tion is stopping the trial. This is a sequential decision problem that
can be addressed using a Bayesian approach and the methods of dynamic
programming. As an example we consider a vaccine trial for the preven
tion of haemophilus influenzae type b. The objective we consider is mi
nimizing the number of cases of this disease in a Native American popu
lation over a specified horizon. We assess the prior probability distr
ibution of vaccine efficacy. We also assess the probability of regulat
ory approval for widespread use of the vaccine, depending on the data
presented to the regulatory officials. In deciding whether to continue
the trial we weigh the impact of the possible future results by their
(predictive) probabilities. We address the sensitivity of the optimal
stopping policy to the prior probability distribution, to the assesse
d probability of regulatory approval, and to the horizon.