This paper describes how a multistage analysis strategy for a clinical trial can assess a sequence of hypotheses that pertain to successively more stringent criteria for excess risk exclusion or superiority for a primary endpoint with a low event rate. The criteria for assessment can correspond to excess risk of an adverse event or to a guideline for sufficient efficacy as in the case of vaccine trials. The proposed strategy is implemented through a set of interim analyses, and success for one or more of the less stringent criteria at an interim analysis can be the basis for a regulatory submission, whereas the clinical trial continues to accumulate information to address the more stringent, but not futile, criteria. Simulations show that the proposed strategy is satisfactory for control of type I error, sufficient power, and potential success at interim analyses when the true relative risk is more favorable than assumed for the planned sample size. Copyright © 2013 John Wiley & Sons, Ltd.