Alternatives to the standard Fleming, Harrington, and O’Brien futility boundary

Abstract

Background Phase III clinical trials comparing a standard treatment to a new therapy are often monitored for futility, that is, convincing evidence that the outcome of the new treatment is not as good as that specified by the alternative hypothesis. Fleming, Harrington, and O’Brien (FHOB) proposed a popular futility monitoring method, based upon repeated testing of the alternative hypothesis at some fixed p-value (often set at p = 0.005). Purpose To demonstrate several interesting properties of the boundary, and to suggest alternative boundaries on the null hypothesis normalized test statistic, which cross zero at 50% of the expected total information. Methods The FHOB boundary is redefined as a boundary on the null hypothesis normalized test statistic and re-parameterized. Results FHOB-type boundaries are shown to be a function only of the significance level and power of the primary test of hypothesis, and the p-value used for repeated testing of the alternative hypothesis. The boundary can be ‘centered’ (in the sense of crossing zero) at some fixed percentage of the expected total information and the rate at which the boundary increases is related to the significance level and power of the primary test of hypothesis. Limitations Other futility monitoring boundaries exist and have differing operating characteristics. Conclusions The standard FHOB boundary, based upon repeated testing of the alternative hypothesis at p = 0.005 may be considered unnecessarily conservative in some settings and a monitoring boundary is proposed that is more likely to lead to a recommendation of futility when the null hypothesis is true.