Miscellanea. Properties of spending function boundaries

Abstract

Clinical trials are monitored periodically for safety and efficacy, resulting 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 α is the spending function approach. This paper proves several properties of these boundaries, including a continuity-like property for looks occurring close to each other and a monotonicity property when additional looks are taken. How past monitoring affects future boundaries is also studied.