Properties of spending function boundaries

Clinical trials are monitored periodically for safety and efficacy, resulti ng in several 'looks' at interim data. If no account is taken of this, the type I error rate may be substantially higher than planned. One of the most popular methods of generating interim boundaries that result in an overall type I error rate of a is the spending function approach. This paper prove s several properties of these boundaries, including a continuity-like prope rty for looks occurring close to each other and a monotonicity property whe n additional looks are taken. How past monitoring affects future boundaries is also studied.