Gittins Indices and Constrained Allocation in Clinical Trials
研究了在序贯临床试验中使用Gittins指数寻找近似最优分配规则，以同时减少预期失败数和最小化最终错误概率，并通过模拟验证了小样本下的优势。
We explore the use of Gittins indices to search for near optimality in sequential clinical trials. Some adaptive allocation rules are proposed to achieve the following two objectives as far as possible: (i) to reduce the expected successes lost, (ii) to minimize the error probability at the end. Simulation results indicate the merits of the rules based on Gittins indices for small trial sizes. The rules are generalized to the case when neither of the response densities is known. Asymptotic optimality is derived for the constrained rules. A simple allocation rule is recommended for one-stage models. The simulation results indicate that it works better than both equal allocation and Bather's randomized allocation. We conclude with a discussion of possible further developments.