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Optimal and ethical designs for hypothesis testing in multi-arm exponential trials. Statistics in Medicine. 2021; 40: 2578– 2603. https://doi.org/10.1002/sim.8919, .
Multi-arm clinical trials are complex experiments which involve several objectives. The demand for unequal allocations in a multi-treatment context is growing and adaptive designs are being increasingly used in several areas of medical research. For uncensored and censored exponential responses, a constrained optimization approach is proposed in order to derive the design maximizing the power of the multivariate test of homogeneity, under a suitable ethical constraint which ensures that the allocation proportions to the treatments are ordered according to the magnitude of their effects. In the absence of censoring, the solution has a very simple closed-form that dominates the balanced allocation in terms of power and ethics. Authors’ suggestion can also accommodate delayed responses and staggered entries and can be implemented via response adaptive rules. While other targets proposed in the literature could present an unethical behavior, the suggested optimal allocation is frequently unbalanced by assigning more patients to the best treatment, both in the absence and presence of censoring. The operating characteristics of the proposal have been evaluated theoretically and by simulations, also redesigning a real lung cancer trial, showing that the constrained optimal target guarantees very good performances in terms of ethical demands, power and estimation precision. Therefore, it is a valid and useful tool in designing clinical trials, especially oncological trials and clinical experiments for grave and novel infectious diseases, where the ethical concern is of primary importance.