The goal is to reach a conclusion about the treatment value as soon as possible, to avoid subjecting patients to inferior treatments. However, repeatedly checking the results will increase the probability of Type-1 error. In such circumstances, akin to multiple testing, the alpha-value at each look must be adjusted in order to preserve the overall Type-1 Error. Alpha spending functions, (the Pocock family is one such set; the Lan-Demets spending function a more specific case) establish these adjusted alpha-values for each interim monitoring point, given the overall alpha. Typically, they establish relatively extreme thresholds for the test statistics (= low alpha) for early looks, and less extreme thresholds (higher alpha) for later looks. Thus, they constitute “stopping boundaries,” which, when crossed, indicate that statistical significance has been established. When graphed, a typical set of stopping boundaries looks like an inverted V pointing to the right. (horizontal axis represents number of events recorded, vertical axis the standardized value of the test statistic.)
See http://www.cytel.com and the product “EaSt” for good illustrations.