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：我们考虑有偿研究或临床试验中的约束抽样问题。当合格的志愿者人数超过预算允许时，我们基于最优设计理论推荐一种D-最优抽样策略，并开发了约束的升一算法来寻找最优分配。与主要处理线性模型的现有文献不同，我们的解决方案在相当一般的统计模型下解决了约束抽样问题，包括广义线性模型和多项逻辑斯蒂模型，并适用更一般的约束条件。我们从理论上证明了抽样策略的最优性，并通过模拟研究和实际案例展示了其相比于简单随机抽样和比例分层抽样策略的优势。