We consider a design problem for a clinical trial with multiple treatment arms and time-to-event primary outcomes that are modeled using the Weibull family of distributions. The D-optimal design for the most precise estimation of model parameters is derived, along with compound optimal allocation designs that provide targeted efficiencies for various estimation problems and ethical considerations. The proposed optimal allocation designs are studied theoretically and are implemented using response-adaptive randomization for a clinical trial with censored Weibull outcomes. We compare the merits of our multiple-objective response-adaptive designs with traditional randomization designs and show that our designs are more flexible, realistic, generally more ethical, and frequently provide higher efficiencies for estimating different sets of parameters.
Keywords: Censoring; D-optimal design; Ethical concern; Response-adaptive randomization; Weibull distribution.