Blinded sample size re-estimation accounting for uncertainty in mid-trial estimation

Abstract: For randomized controlled trials to be conclusive, it is important to set the target sample size accurately at the design stage. Comparing two normal populations, the sample size calculation requires specification of the variance other than the treatment effect and misspecification can lead to underpowered studies. Blinded sample size re-estimation is an approach to minimize the risk of inconclusive studies. Existing methods proposed to use the total (one-sample) variance that is estimable from blinded data without knowledge of the treatment allocation. We demonstrate that, since the expectation of this estimator is greater than or equal to the true variance, the one-sample variance approach can be regarded as providing an upper bound of the variance in blind reviews. This worst-case evaluation can likely reduce a risk of underpowered studies. However, blinded reviews of small sample size may still lead to underpowered studies. We propose a refined method accounting for estimation error in blind reviews using an upper confidence limit of the variance. A similar idea had been proposed in the setting of external pilot studies. Furthermore, we developed a method to select an appropriate confidence level so that the re-estimated sample size attains the target power. Numerical studies showed that our method works well and outperforms existing methods. The proposed procedure is motivated and illustrated by recent randomized clinical trials.