Including long- and short-term data in blinded sample size recalculation for binary endpoints

In order to calculate the sample size for a clinical trial with a binary outcome needed to achieve a certain power at a given significance level, one needs to specify the clinically relevant effect as well as the event rate pooled over the treatment groups. However, before conducting the trial the event rates are unknown and the pooled event rate needs to be estimated. A misspecification of this parameter might lead to a study that is either under- or overpowered. In the internal pilot study design the pooled event rate is reestimated during the trial. For this reestimation the current methods only use data of those patients that have concluded the whole study. Instead, a method is proposed that also takes into account data at an earlier point of the trial, a point which, within the internal pilot study, has been passed by a greater number of patients than the trial's endpoint. Characteristics of the proposed estimator and the related recalculated sample size are investigated. Analytical computations of the actual type I-error rate are given for small sizes of the internal pilot study. These calculations are completed by simulation studies for larger sample sizes of the internal pilot study. The results show that the inflation of the type I-error rate is often negligible and generally not higher than observed for the fixed sample size design and for the classical recalculation procedure. However, as compared to the conventional approach the proposed procedure may show a considerably lower variability of the resulting sample size and thus an improved ability to achieve the target power.