Predicting study duration in clinical trials with a time-to-event endpoint

In event-driven clinical trials comparing the survival functions of two groups, the number of events required to achieve the desired power is usually calculated using the Freedman formula or the Schoenfeld formula. Then, the sample size and the study duration derived from the required number of events are considered; however, their combination is not uniquely determined. In practice, various combinations are examined considering the enrollment speed, study duration, and the cost of enrollment. However, effective methods for visually representing their relationships and evaluating the uncertainty in study duration are insufficient. We developed a graphical approach for examining the relationship between sample size and study duration. To evaluate the uncertainty in study duration under a given sample size, we also derived the probability density function of the study duration and a method for updating the probability density function according to the observed number of events (ie, information time). The proposed methods are expected to improve the operation and management of clinical trials with a time-to-event endpoint.