In a rare life-threatening disease setting the number of patients in the trial is a high proportion of all patients with the condition (if not all of them). Further, this number is usually not enough to guarantee the required statistical power to detect a treatment effect of a meaningful size. In such a context, the idea of prioritizing patient benefit over hypothesis testing as the goal of the trial can lead to a trial design that produces useful information to guide treatment, even if it does not do so with the standard levels of statistical confidence. The idealized model to consider such an optimal design of a clinical trial is known as a classic multi-armed bandit problem with a finite patient horizon and a patient benefit objective function. Such a design maximizes patient benefit by balancing the learning and earning goals as data accumulates and given the patient horizon. On the other hand, optimally solving such a model has a very high computational cost (many times prohibitive) and more importantly, a cumbersome implementation, even for populations as small as a hundred patients. Several computationally feasible heuristic rules to address this problem have been proposed over the last 40 years in the literature. In this paper, we study a novel heuristic approach to solve it based on the reformulation of the problem as a Restless bandit problem and the derivation of its corresponding Whittle Index (WI) rule. Such rule was recently proposed in the context of a clinical trial in Villar, Bowden, and Wason [16]. We perform extensive computational studies to compare through both exact value calculations and simulated values the performance of this rule, other index rules and simpler heuristics previously proposed in the literature. Our results suggest that for the two and three-armed case and a patient horizon less or equal than a hundred patients, all index rules are a priori practically identical in terms of the expected proportion of success attained when all arms start with a uniform prior. However, we find that a posteriori, for specific values of the parameters of interest, the index policies outperform the simpler rules in every instance and specially so in the case of many arms and a larger, though still relatively small, total number of patients with the diseases. The very good performance of bandit rules in terms of patient benefit (i.e., expected number of successes and mean number of patients allocated to the best arm, if it exists) makes them very appealing in context of the challenge posed by drug development and treatment for rare life-threatening diseases.

中文翻译：

---

在罕见的危及生命的疾病的临床试验中评估的强盗策略

在一种罕见的危及生命的疾病环境中，试验中的患者人数占所有患有该疾病的患者（如果不是全部）的比例很高。此外，这个数字通常不足以保证检测有意义大小的治疗效果所需的统计功效。在这种情况下，将患者受益优先于假设检验作为试验目标的想法可以导致试验设计产生有用的信息来指导治疗，即使它没有在标准的统计置信水平下这样做。考虑临床试验的这种优化设计的理想模型被称为经典的具有有限患者视野和患者受益目标函数的多臂老虎机问题。这种设计通过在数据积累和患者视野范围内平衡学习和收入目标来最大化患者利益。另一方面，优化求解这样的模型具有非常高的计算成本（很多时候令人望而却步），更重要的是，即使对于小至一百名患者的人群，实施起来也很麻烦。在过去的 40 年中，文献中提出了几种计算上可行的启发式规则来解决这个问题。在本文中，我们研究了一种新颖的启发式方法来解决它，该方法基于将问题重新表述为不安强盗问题及其相应的 Whittle Index (WI) 规则的推导。最近在 Villar 的临床试验中提出了这样的规则，鲍登和沃森 [16]。我们进行了广泛的计算研究，以通过精确值计算和模拟值来比较该规则、其他索引规则和文献中先前提出的更简单启发式的性能。我们的结果表明，对于两臂和三臂病例以及患者视野小于或等于 100 名患者，所有指标规则都是先验当所有武器都以统一的先验开始时，就预期的成功比例而言，实际上是相同的。然而，我们发现后验的，对于感兴趣的参数的特定值，索引策略在每个实例中都优于更简单的规则，特别是在许多臂和较大但仍然相对较小的疾病患者总数的情况下。强盗规则在患者利益方面的出色表现（即，预期的成功次数和分配到最佳治疗组的平均患者人数，如果存在的话）使得它们在药物开发和治疗所带来的挑战的背景下非常有吸引力罕见的危及生命的疾病。