Design considerations in clinical trials with cure rate survival data: A case study in oncology

Group sequential design with maximin efficiency robust test for immunotherapy with generalized delayed treatment effect

The delayed treatment effect is a common feature of immunotherapy, characterized by a gradual onset of action ranging from no effect to full effect. In this study, we propose a generalized delayed treatment effect function to depict the delayed effective process precisely and flexibly. To reduce potential power loss caused by the delayed treatment effect in a group sequential trial, we employ the maximin efficiency robust test, which enhances power robustness across a range of possible delays. We present novel approaches based on the Markov chain method for determining group sequential boundaries, calculating the power function, and estimating the maximum sample size through iterative regressions between the square root of the maximum sample size and the normal quantile of power. Extensive simulation studies validate the effectiveness of our approaches, particularly in balanced trials, demonstrating the validity of group sequential boundaries and the accuracy of maximum sample size estimations. Additionally, we utilize a real trial as an example to compare our considered trial with group sequential trials using the log-rank and generalized piecewise weighted log-rank tests. The results show significantly reduced maximum sample sizes, highlighting the economic advantage of our approach.

M&M: A maximum duration design with the Maxcombo test for a group sequential trial of an immunotherapy with a random delayed treatment effect

A random delayed treatment effect is expected in a confirmatory clinical trial for an immunotherapy due to the individual heterogeneity of physiological conditions. For this reason, the delay time will be assumed to follow a continuous distribution that is difficult to estimate accurately based on the early-phase data, which hinders the specification of the most powerful weighted log-rank test. Therefore, we propose a simulation-based maximum duration design with a robustly powerful Maxcombo test for a group sequential trial for the immunotherapy with the random delayed treatment effect. The design obtains the group sequential boundaries by a simulation procedure and determines the required maximum sample size using a one-dimensional search in which another simulation procedure is used to calculate empirical power. The simulation researches proved the accuracy of the group sequential boundaries and their robustness against the misspecified maximum sample sizes for large samples and revealed their moderate sensitivity against the misspecified survival distributions under the null hypothesis of no difference. The studies investigated whether the type I error rate would inflate under the "inferior" null hypothesis and evaluated the robustness against different distributions of the delay time in terms of the empirical power among the Maxcombo tests and component weighted log-rank tests.

Cancer immunotherapy trial design with long-term survivors

Cancer immunotherapy often reflects the improvement in both short-term risk reduction and long-term survival. In this scenario, a mixture cure model can be used for the trial design. However, the hazard functions based on the mixture cure model between two groups will ultimately crossover. Thus, the conventional assumption of proportional hazards may be violated and study design using standard log-rank test (LRT) could lose power if the main interest is to detect the improvement of long-term survival. In this paper, we propose a change sign weighted LRT for the trial design. We derived a sample size formula for the weighted LRT, which can be used for designing cancer immunotherapy trials to detect both short-term risk reduction and long-term survival. Simulation studies are conducted to compare the efficiency between the standard LRT and the change sign weighted LRT.