  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.
