Optimal response-adaptive randomized designs for multi-armed survival trials

We considered design issues for multiple treatment arms in survival intervention trials and used optimal design theory to allocate patients adaptively in such trials. We proposed three types of optimal designs: one ensures that we have the most precise estimates of the treatment effects, another guarantees that we have the minimal sample size subject to user-specified allocation ratio assignments among treatment arms, and the third ensures that the design has minimal total hazard for the cohort. The latter two types of optimal designs are also subject to user-specified power constraints for testing contrasts among treatment effects. The operating characteristics of these optimal designs along with balanced designs are compared theoretically and by simulation, including their robustness properties with respect to model misspecifications. Our results show that the proposed optimal designs are frequently unbalanced and that they are generally more efficient and more ethical than the popular balanced designs. We also apply our response-adaptive allocation strategy to redesign a three-arm head and neck cancer trial and make comparisons.