最优队列阶梯设计

中文摘要 AI 辅助

阶梯聚类随机试验将结果收集限制在每个聚类从对照转向干预的有限时间窗口内。这可以减少重复测量的负担，但聚类和参与者在不同治疗序列中的分配需要仔细考虑。我们为具有连续结局的封闭队列阶梯试验开发了一个最优设计框架，允许不同序列的聚类规模不同。在线性混合模型下，我们通过序列特定的信息贡献来表达处理效应精度，并建立了聚类分配比例中方差准则的凸性。一个等价定理刻画了最优分配，反转对称性为几种三序列和四序列设计提供了解析解。我们还考虑了在固定参与者总数下序列分配和聚类规模的联合优化。数值研究表明，不等聚类规模的价值取决于观察窗口和相关性结构：收益通常适中，但在特定设置下可能相当可观。与完整阶梯楔形设计的比较展示了重复测量和额外聚类之间的权衡，阶梯设计在相当精度下在某些设置中实现了更低的成本。以心理社会癌症护理和试验招募为动机的示例区分了假设性设计调整与原始研究。结果支持在重复测量是主要约束时，联合选择序列分配、聚类规模和观察窗口。

英文摘要

Staircase cluster randomized trials restrict outcome collection to a limited window around each cluster's transition from control to intervention. This can reduce the burden of repeated measurement, but the allocation of clusters and participants across treatment sequences requires careful consideration. We develop an optimal design framework for closed-cohort staircase trials with continuous outcomes, allowing cluster sizes to differ across sequences. Under a linear mixed model, we express treatment-effect precision through sequence-specific information contributions and establish convexity of the variance criterion in the cluster allocation proportions. An equivalence theorem characterizes optimal allocations, and reversal symmetry yields analytical solutions for several three- and four-sequence designs. We also consider joint optimization of sequence allocation and cluster sizes under a fixed participant total. Numerical investigations show that the value of unequal cluster sizes depends on the observation window and correlation structure: gains are often modest but can be substantial in selected settings. Comparisons with complete stepped-wedge designs demonstrate a trade-off between repeated measurements and additional clusters, with staircase designs achieving lower costs in some settings at comparable precision. Illustrations motivated by psychosocial cancer care and trial recruitment distinguish hypothetical design adaptations from the original studies. The results support choosing sequence allocation, cluster sizes, and observation windows jointly when repeated measurement is a major constraint.

发表机构

• Indian Institute of Technology Kanpur（坎普尔印度理工学院）

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