A review of methods for futility stopping based on conditional power

Conditional power (CP) is the probability that the final study result will be statistically significant, given the data observed thus far and a specific assumption about the pattern of the data to be observed in the remainder of the study, such as assuming the original design effect, or the effect estimated from the current data, or under the null hypothesis. In many clinical trials, a CP computation at a pre-specified point in the study, such as mid-way, is used as the basis for early termination for futility when there is little evidence of a beneficial effect. Brownian motion can be used to describe the distribution of the interim Z-test value, the corresponding B-value, and the CP values under a specific assumption about the future data. A stopping boundary on the CP value specifies an equivalent boundary on the B-value from which the probability of stopping for futility can then be computed based on the planned study design (sample size and duration) and the assumed true effect size. This yields expressions for the total type I and II error probabilities. As the probability of stopping increases, the probability of a type I error alpha decreases from the nominal desired level (e.g. 0.05) while the probability of a type II error beta increases from the level specified in the study design. Thus a stopping boundary on the B-value can be determined such that the inflation in type II error probability is controlled at a desired level. An iterative procedure is also described that determines a stopping boundary on the B-value and a final test critical Z-value with specified type I and II error probabilities. The implementation in conjunction with a group sequential analysis for effectiveness is also described.