Cancer immunotherapy trial design with random delayed treatment effect and cure rate

Immunotherapies are increasingly used for treating patients with advanced-stage cancers. However, cancer immunotherapy trials often present delayed treatment effects and long-term survivors which result nonproportional hazard models and challenge the immunotherapy trial designs. In this article, we proposed a general random delayed cure rate model for designing cancer immunotherapy trials. A sample size formula is derived for a weighted log-rank test. The accuracy of sample size estimation is assessed and compared with the existing methods via simulation studies. The sensitivities for misspecifying the random delay time are also studied through simulations.