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Many clinical trials have multiple objectives and have a time-to-event outcome that may be modeled using a Weibull distribution. For two-arm trials, we obtain the optimal allocations for a few design criteria and for multi-arm trials, we provide a general approach for finding the optimal allocations. These multi-objective optimal designs meet userdefined tradeoffs among the objectives. We focus on twoobjective design problems for estimating model parameters and discriminating whether the treatments have constant hazard (exponential distribution) or non-constant hazard (general Weibull distribution). To target the desired allocations designs, we implement the doubly adaptive biased coin design (DBCD) of Hu and Zhang (2004) and evaluate its effectiveness. We compare performance of the various response-adaptive allocation strategies in an exemplary four-arm trial using a simulation study and show that our proposed response-adaptive randomization designs generally outperform a balanced design when ethics, randomization and estimation efficiency are incorporated at the onset.

Doubly adaptive biased coin designs for balancing competing objectives in time-to-event trials