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

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.