Minimum noninferiority dose for phase I clinical trials with immunotherapy

Recent advancements in immuno-oncology have significantly improved cancer treatments. Compared with traditional clinical trials, the toxicity of these novel therapies is generally low and tolerable, shifting the focus from solely managing toxicity to improving efficacy. Furthermore, such treatments can be costly, and thus it is crucial to identify a low-dose regimen with a good therapeutic effect for broader drug accessibility. Instead of solely identifying the optimal biological dose (OBD) in a phase I/II trial, we emphasize finding a more economical but effective dose. Current methods typically aim to determine the minimum effective dose (MED) based on a predefined efficacy target, which may not reflect the best balance between efficacy and dosage. This paper introduces the minimum noninferiority dose (MND), derived from the OBD, which eliminates the need for artificially setting an efficacy target. The MND ensures the dose maintains efficacy within a reasonable range below the OBD while keeping the dosage as low as possible. Through leveraging the calibration-free odds (CFO) design to monitor toxicity, we further propose a novel Bayesian two-stage design, called CFO-MND, by incorporating a trade-off between dose and efficacy as well as adaptive randomization. Our model-free approach is versatile and applicable to a wide range of scenarios. Furthermore, we incorporate causal inference into the CFO-MND design by introducing the placebo equivalent dose. This allows for preliminary estimation of the drug's average treatment effect at the MND, which provides valuable information for subsequent trials.