A comparison between various conditional power (CP) criteria for early termination of a trial is performed. It is assumed the trial is carried out to decide on the hypotheses H0 that an effect size θ is not larger than θ0, and the alternative H1, with a sample size determined to yield a specified power under a certain value θ1. Early stopping for H0 or H1 may be based on CP(θ0),CP(θ1), or CP evaluated at any pre-specified value θ̃; further, one can rely on data-driven versions, such as CP(θ̂) or CP(θ̂ ± s.e.(θ̂)), θ̂ being a current estimate of θ with standard error s.e.(θ̂). The procedures considered are interpreted as sequential tests. Power functions are computed under normally distributed or binary responses; the benefits are compared using average and median sample numbers. The investigations have shown that often the choice of the argument for CP is not a too crucial point, if adapted stopping boundaries for CP are computed. However, the type I error requires particular attention, if a nuisance parameter is involved. Data-driven strategies suffer from the instability of the estimate θ̂ in early stages of the trial. For early futility stopping, adequate CP approaches with pre-specified θ̃ show properties in the range of those based on θ̂ or θ̂ + s.e.(θ̂). © 2003 Elsevier B.V. All rights reserved.
Högel, J., & Kron, M. (2004). Comparison of conditional power criteria for early termination of clinical trials. Computational Statistics and Data Analysis, 46(2), 377–395. https://doi.org/10.1016/S0167-9473(03)00172-5