Optimal Designs With Interim Analyses for Randomized Studies With Long-Term Time-Specific Endpoints

Abstract

With the advent of novel cancer therapies targeting molecular pathways or the immune system, time-to-event variables evaluated at longer times (e.g., 6 or 12 months) are increasingly used as the primary endpoint in randomized Phase II trials. Two-stage “Simon” designs have often been used in single-group phase II oncology trials to reduce the expected sample size under the null hypothesis. We develop optimal two-stage and three-stage randomized two-group designs with analogous optimality criteria. Accurate implementation of the Simon design can be difficult, and the difficulty increases with a longer-term endpoint, because it requires complete information from each accrued patient. Earlier work of Case and Morgan generalized the Simon design so it can be implemented without an accrual pause. We derive optimal designs that allow a brief preplanned pause (⩾ 0) in accrual before interim analyses to more efficiently use data from the accrued patients, and to allow focused data collection before the interim analyses. We provide software (R package OptInterim) that creates the optimal designs and also simulates their properties to check asymptotic approximations and the robustness of the designs to differing conditions. Various design options are illustrated using an example based on a recent colorectal cancer drug trial.

Key Words:

• Long-term time-specific endpoint
• Oncology
• Time-to-event