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.

Some statistical considerations in the clinical development of cancer immunotherapies

“…38,[40][41][42] The Nelson-Aalen estimator is a nonparametric estimator of the cumulative hazard rate function, given byH(t) = ∑…”

“…In such cases, one limitation of a time‐specific endpoint is that it does not capture the entire event‐free curve and only evaluates the probability of event occurrence at one landmark time, of which the selection sometimes may be arbitrary. Under the PH assumption, the hypothesis test based on a time‐specific probability has lower statistical power and requires a larger sample size compared to the log‐rank test because the latter evaluates all the data up to the time when the maximum number of events is achieved. Since efficacy studies often include interim analysis for early stopping, one major limitation of the time‐specific probability endpoint is that patients need to be followed for a fixed period (up to the landmark time) for endpoint availability, which is a significant operational challenge in multicenter multiregional clinical trials.…”

“…To address the statistical and operational challenge of the need for conducting interim analysis, statistical designs using the Nelson‐Aalen estimator of the time‐to‐event distribution have been proposed . The Nelson‐Aalen estimator is a nonparametric estimator of the cumulative hazard rate function, given by , with d i the number of events at t i and n i the number of patients at risk at t i .…”

“…Huang et al proposed a class of optimal designs for time‐specific probability endpoint. The design can be set up in both the single‐arm and 2‐arm randomized settings that allow 1 or 2 interim analyses.…”

Two‐stage phase II survival trial design

“…To test survival probability at a fixed landmark time point, Case and Morgan and Huang et al developed optimal two‐stage designs. Huang and Thomas extended their methodology to include three‐stage designs. In addition, Lin et al and Wu and Xiong proposed multiple‐stage designs.…”