Quantifying the bias in the estimated treatment effect in randomized trials having interim analyses and a rule for early stopping for futility.

In this paper, we consider the potential bias in the estimated treatment effect obtained from clinical trials, the protocols of which include the possibility of interim analyses and an early termination of the study for reasons of futility. In particular, by considering the conditional power at an interim analysis, we derive analytic expressions for various parameters of interest: (i) the underestimation or overestimation of the treatment effect in studies that stop for futility; (ii) the impact of the interim analyses on the estimation of treatment effect in studies that are completed, i.e. that do not stop for futility; (iii) the overall estimation bias in the estimated treatment effect in a single study with such a stopping rule; and (iv) the probability of stopping at an interim analysis. We evaluate these general expressions numerically for typical trial scenarios. Results show that the parameters of interest depend on a number of factors, including the true underlying treatment effect, the difference that the trial is designed to detect, the study power, the number of planned interim analyses and what assumption is made about future data to be observed after an interim analysis. Because the probability of stopping early is small for many practical situations, the overall bias is often small, but a more serious issue is the potential for substantial underestimation of the treatment effect in studies that actually stop for futility. We also consider these ideas using data from an illustrative trial that did stop for futility at an interim analysis.