Constrained D-optimal Design for Paid Research Study

TL;DR

This paper introduces a constrained D-optimal sampling method for paid research studies that optimizes participant selection under complex models and constraints, improving over traditional sampling strategies.

Contribution

It develops a generalized constrained lift-one algorithm for D-optimal design applicable to various statistical models beyond linear, with theoretical justification and practical validation.

Findings

The proposed method outperforms simple random sampling.

Simulation studies demonstrate improved efficiency.

Real-world examples confirm practical advantages.

Abstract

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.