We consider constrained sampling problems in paid research studies or clinical trials. When qualified volunteers are more than the budget allowed, we recommend a D-optimal sampling strategy based on the optimal design theory and develop a constrained lift-one algorithm to find the optimal allocation. Unlike the literature which mainly deals with linear models, our solution solves the constrained sampling problem under fairly general statistical models, including generalized linear models and multinomial logistic models, and with more general constraints. We justify theoretically the optimality of our sampling strategy and show by simulation studies and real-world examples the advantages over simple random sampling and proportionally stratified sampling strategies.

翻译：本文探讨付费研究或临床试验中的约束抽样问题。当合格志愿者数量超过预算允许范围时，我们基于最优设计理论提出一种D最优抽样策略，并开发约束提升算法以寻求最优分配方案。与现有文献主要处理线性模型不同，我们的解决方案能够在更广泛的统计模型（包括广义线性模型和多项逻辑模型）及更一般的约束条件下解决约束抽样问题。我们从理论上证明了该抽样策略的最优性，并通过模拟研究和实际案例展示了其相对于简单随机抽样和比例分层抽样策略的优势。