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. We theoretically justify the optimality of our sampling strategy and show by simulations and a real data example its advantage over simple random sampling and proportionally stratified sampling.

翻译：在有偿研究或临床试验中,我们考虑有限的抽样问题。 当合格志愿者超出预算允许的范围时,我们建议基于最佳设计理论的D-最佳抽样战略,并开发一个有限的升降单算法以找到最佳分配。 我们在理论上证明我们的抽样战略的最佳性,并通过模拟和真实数据来展示其优于简单随机抽样和比例分层抽样的优势。